Elise Peter

Serge Fausto

Thomas

Laurent

Martí, Jérémie, Rémy Luciano

Armel, Bérangère, Bappa, Jayasi, Brindusa Anthony

Luis

Pablo Lara

Patricio Solange

Jonathan Lenglet

Sylvain

Keywords: . . . . . . . . . Material flow analysis, supply chain, downscaling, data reconciliation, cereals, France. Chapter Filières, analyse de flux de matières, empreintes environnementales, aide à la décision, analyse multicritère Environmental Supply chains, material flow analysis, environmental footprints, decision-aiding, multicriteria analysis

A special thanks to my sport coaches :) and ¡Gracias a todos los Argentinos que compartieron mate conmigo! Thanks to the Aussois research group on territorial ecology and especially to Anne-Lorène, Daniela, Petros and Manuel from the energy team! Thank you to

"The hell of the living is not something that will be: if there is one, it is what is already here, the hell where we live every day, that we form by being together. There are two ways to escape suffering it. The first is easy for many: accept the hell and become such a part of it that you can no longer see it. The second is risky and demands constant vigilance and learning: seek and be able to recognize who and what, in the midst of the hell, are not hell, then make them endure, give them space."

Italo Calvino, The invisible cities, 1972.

Résumé

Les conséquences de nos modes de production et de consommation sur l'environnement mondial sont reconnues et analysées depuis plusieurs décennies : changement climatique, effondrement de la biodiversité, tensions sur de nombreuses ressources stratégiques etc. Notre travail s'inscrit dans un courant de pensée visant à développer d'autres indicateurs de richesse. Dans une perspective de durabilité forte, nous nous concentrons sur une comptabilité biophysique (non monétaire), apte à pointer les externalités environnementales. Si une part importante des recherches dans ce domaine a été dédiée aux échelons nationaux, nous nous intéressons ici aux échelles locales, et en particulier aux régions françaises. Après avoir étudié les caractéristiques d'outils existants utilisés dans les domaines de l'économie écologique et de l'écologie industrielle, comme l'Empreinte Ecologique, l'Analyse de Flux de Matières (AFM), l'Analyse de Cycle de Vie ou l'Analyse Entrée-Sortie, nous nous focalisons sur les filières de production que nous analysons à partir des quantités de matières qu?elles mobilisent au cours des étapes de production, transformation, transport et consommation. La méthode développée, AFM Filière, permet de produire des schémas de flux cohérents au niveau national, dans chaque région, et quand les données le permettent, à des niveaux infra-régionaux. Ceux-ci sont basés sur un processus systématique de réconciliation des données disponibles. Nous évaluons la précision de ces données d'entrée, ce qui permet de fournir des intervalles de confiance sur les résultats, pouvant à leur tour pointer vers des manques de connaissance. En particulier, nous fournissons une évaluation détaillée de la précision de l'enquête permanente sur le transport routier de marchandises (TRM), une pièce maîtresse de l'AFM Filière. Nous montrons au passage que réaliser le bilan matières sur une période de plusieurs années permet non seulement de s'affranchir du problème des stocks, mais aussi de réduire significativement l'incertitude sur les échanges entre régions. Nous adaptons par la suite la méthode des chaînes de Markov absorbantes pour tracer les flux jusqu'à leur destination finale et allouer les pressions sur l'environnement produites tout au long de la filière. Les flux de matières peuvent également être couplés à des modèles économiques afin de prévoir leur évolution en réponse à certaines politiques. En collaboration avec le Laboratoire d'Economie Forestière (LEF), nous fournissons ainsi la première tentative de représentation des flux sur la filière forêt-bois française, et analysons l'impact de différentes politiques de réduction des exports de bois brut sur l'économie et sur les flux physiques. Enfin, nous montrons comment il serait possible d'articuler ces analyses de filières avec les méthodes d'analyse qualitative, en particulier celles déployées dans le domaine de l'écologie territoriale, pour analyser les jeux d'acteurs dans la filière. Nous situons notre travail dans le cadre normatif de la démocratie délibérative. A ce titre, nous réfléchissons aux apports de la comptabilité biophysique aux processus de décisions publiques incluant diverses parties prenantes. Nous dressons un panorama des étapes clé d'un processus d'aide à la décision, des méthodes multicritères mais également des différentes formes que peut prendre la participation des citoyens. Nous proposons finalement une méthode d'aide à la délibération conçue pour des contextes de décision caractérisés par de fortes incertitudes et des conflits de valeurs. Celle-ci est fondée sur l'élicitation de la satisfaction et du regret éprouvé par chaque partie prenante face à un futur donné. Enfin, en partant des principales critiques adressées à la quantification, nous proposons en conclusion une réflexion sur les conditions qui permettraient de mettre la comptabilité biophysique au service de l'émancipation démocratique.

I Analyzing regional supply chains through their material flows

2 A brief introduction to supply chain analysis 2.1 A wide range of approaches: from strategic management to industrial ecology .

List of abbreviations

• ADEME: agence de l'environnement et de la maîtrise de l'énergie (French environment and energy management agency),

• AMC: absorbing Markov chains,

• CGDD: commissariat général au développement durable (French commission for sustainable development),

• EF: Ecological Footprint,

• EW-MFA: economy-wide material flow analysis,

• Exp: scenario with taxes on exports (chap. 7),

• fw: fuel wood (chap. 7),

• HRW: hard round wood (chap. 7),

• hsw: hard sawn wood (chap. 7),

• INSEE: institut national de la statistique et des études économiques (French national statistics and economic surveys institute),

• IO: input-output,

• IOA: input-output analysis,

• IW: industrial wood,

• LCA: life cycle assessment,

• MC: Markov chains,

• MCA: multicriteria analysis,

• MCDA: multicriteria decision-aiding,

• MFA: material flow analysis,

• NVC: nonviolent communication,

• pw: plywood (chap. 7),

• SC-MFA: supply chain material flow analysis,

• SFA: substance flow analysis,

• SitraM: système d'information sur le transport de marchandises (French information system on freight),

• SOeS: service de l'observation et de la statistique (French observation and statistics service),

Introduction

Chapter 1

Introduction

Territories, supply chains, environment, biophysical accounting, deliberation, decision-aiding... these are the key words that will accompany us throughout this thesis. Territory is a polysemous word; we use it to refer to a delimited geographical area, generally a subnational administrative unit, and to the people who live in it and transform it. With the recognition of global environmental issues, countries... and territories, asserted their will to transition towards more sustainable societies. When facing a problem, one of the things that comes in mind is to attempt to understand the underlying mechanisms it stems from (i.e. the causes and not the symptoms) in order to efficiently act upon them. It this view, there is a need for improving the understanding and evaluation of environmental impacts of human activities at all scales. Impacts (for example, biodiversity losses) are however particularly hard to forecast as they depend on a multiplicity of local factors. Environmental pressures (for instance carbon emissions) are easier to measure and can act as reasonable proxies for impacts (if we decrease pressures we will decrease impacts). These pressures need to be measured in physical units, which is what we call biophysical accounting1 . More broadly, as we will see, biophysical accounting is defined in opposition to monetary accounting in recognition of the fact the latter alone is not suited to monitor, nor foster, environmental sustainability. Going further on the analysis, most environmental pressures occur through production activities aiming at providing goods and services to consumers. These activities are organized into networks of processes called supply chains, which are simultaneously parts of local economies, connections between territories and links between producers and consumers. Supply chains therefore seem to be interesting subjects of study to understand the underlying mechanisms of environmental pressures... This way of structuring problems and improving knowledge may efficiently contribute to decision-aiding.

Then, once one has reached enough knowledge on a problem, one can evaluate options if not in full, at least in brighter light. Sustainability issues being characterized by inter-connections between the environmental and socio-economic spheres, these options usually imply trade-offs which need to be arbitrated... if possible in a legitimate way. This legitimacy in turn arguably stems from deliberation, that is, the process of weighing alternatives, putting the emphasis on logic and reason, usually followed by a decision by vote or consensus. This is, in a few words, the path that we propose to investigate. Throughout this manuscript, we will do our best not only to present the practical questions addressed in the thesis, but also to situate them in the wider normative conception of our research. The title of the thesis is attempting to reflect this dichotomy. While the first part, Environmental assessment of territories through supply chain analysis, summarizes the methodological option technically developed, in short, a focus on regional supply chains and their links with local and global environmental pressures, the latter, Biophysical accounting for deliberative decision-aiding, rather informs on the reasons that guided this technical effort, again, in short, our wish to focus on physical indicators and to see how they can be integrated in public deliberation processes to advance towards more sustainable policies. It is noteworthy that similar technical developments could have been pursued with other motivations, for instance, to take a fashionable concept, in the perspective of green growth. Conversely, a number of other research leads could have been consistent with our goals, and we will present some of them in this introduction. Finally, the idea of a clear hierarchy, with a normative question guiding technical developments, is not a correct description of the actual research process. Indeed, we experienced in our own way that each technical development is partly self-propelled, and that research questions can evolve over time... In this introduction, we first propose a short overview of global environmental stakes, then present the paradigms to which we relate and show why biophysical accounting matters in this context. After studying existing environmental assessment tools, we draw the contours of our work. Finally, in a perspective of collective action, we reflect on the links between scientific knowledge and decision-making on sustainability issues and frame our research lead in this area.

An unsustainable path

To a large extend, unsustainability is easier to apprehend and less polysemous than sustainability. Arguably, it is easier to recognize an unsustainable trend than to describe what a sustainable society would be like, or yet again, it is easy for most people to agree on what is not sustainable while the contours of a sustainable society can be controversial. We wish to dedicate our first lines to the description of such unsustainable trends. Various broad scale analyses of such trends are available in the literature (e.g., [START_REF] Brown | World on the edge: how to prevent environmental and economic collapse[END_REF], therefore we will only provide a few illustrative examples and focus on environmental stakes.

1.1.1 From 1970's theories of environmental collapse...

In 1972, researchers from the MIT system dynamics group published The Limits to Growth [START_REF] Meadows | The limits to Growth[END_REF] where they attempted to model the consequences of rapid demographic and economic growth in a finite world. The world is modeled through five main variables: population, industrial output, food production, natural resources and pollution. Several tens of equations link those variables together; for instance pollution growth has a negative effect on life expectancy and therefore on population size, which in turn works in the direction of reducing pollution. Contrasted scenarios were tested and lead to the same long-term conclusion of collapse in the course of the 21 st century: figure 1.1 for instance represents the model output for the reference scenario.

Figure 1.1: Scenario 1 of The Limits to Growth. "The world society proceeds in a traditional manner without any major deviation from the policies pursued during most of the twentieth century. Population and production increase until growth is halted by increasingly inaccessible nonrenewable resources. Ever more investment is required to maintain resource flows. Finally, lack of investment funds in the other sectors of the economy leads to declining output of both industrial goods and services. As they fall, food and health services are reduced, decreasing life expectancy and raising average death rates." [START_REF] Meadows | Limits to growth: the 30-year update[END_REF] The conditions of such collapse are eventually analyzed: overshoot of carrying capacity, delay in reaction, erosion of the environmental capacity during the overshoot phase, and finally, rapid variation (exponential growth). Interestingly, this understanding, acquired through computer simulations, is well in line with Jared Diamond's description of the collapse of the Mayan, Greenland Vikings, or Sumerian civilizations, in the field of anthropology and evolutionary biology [START_REF] Diamond | Collapse: How societies choose to fail or succeed[END_REF].

... To today's environmental concerns

Scientists have forged a term, the Anthropocene, to designate a new geological era, where man has become the greatest force modifying the biosphere, the atmosphere, the hydrosphere and the geosphere [START_REF] Lorius | Voyage dans l'Anthropocène, cette nouvelle ère dont nous sommes les héros[END_REF]. In a 2009 article, Johan Rockström and colleagues attempt to identify and quantify planetary boundaries that must not be transgressed if one wants to prevent "unacceptable environmental change" [START_REF] Rockström | A safe operating space for humanity[END_REF]. Their results point to the fact that three boundaries have already been overstepped: biodiversity loss, climate change and interference with the nitrogen cycle. Noteworthy, neither current status nor sustainable thresholds are yet quantified for two out of nine boundaries (chemical pollution and atmospheric aerosol loading). The authors further underline that even if the notion of safe distance between current status and thresholds relies on social values, such as the degree of aversion to risk, many other boundaries (e.g. ocean acidification, global freshwater use, land use Chapter 1. Introduction from these ecosystems on the economy. Finally, it is guided by a philosophical viewpoint, non determinism and non-nihilism, that is, "it really is possible for things to be other than they are, and we really can distinguish better from worse states of the world " [START_REF] Daly | Ecological economics: principles and applications[END_REF].

We situate our work in the normative presuppositions of ecological economics and strong sustainability. In this view, monetary accounting appears insufficient to conduct proper analysis, although it is by far the most developed. We thus choose to concentrate our effort on biophysical accounting, that is accounting in physical, non-monetary, units. The 1980's gave birth to a new research field precisely aiming at the study of material and energy flows through industrial systems, industrial ecology [START_REF] Billen | L'écosystème Belgique: essai d'écologie industrielle[END_REF][START_REF] Frosch | Strategies for manufacturing[END_REF]. As one can guess from the name, the underlying belief behind it is that concepts and methods developed in ecology can be transposed to study industrial societies and bring about new knowledge that would be useful for policy-making. Metaphors of the economy as an ecosystem are often used: resources are drawn by extraction activities and are successively used by transformation industries, similar to trophic chains, before being distributed, consumed and ending-up as wastes that are recycled, or rejected in the environment. The term metabolism is also often used to refer to the functioning of the system, based on material and energy flows. The objective of closing the loops, that is, achieving less material and energy inputs, less wastes and pollution outputs and more efficiency and recycling, is at the core of industrial ecology's identity [START_REF] Allenby | Achieving sustainable development through industrial ecology[END_REF]. Additionally, in France, the last few years have seen the emergence of territorial ecology, a field aiming at downscaling the conceptual frameworks of sustainability (Buclet et al., 2015). Territories are not only defined by their administrative limits, but also by their ecological, economic, social and identity coherence. In this sense, they are part of regional, national and global trajectories but retain singular dynamics that are worth studying. Territorial ecology uses both quantitative and qualitative analyses, and tries to connect them: once material and energy flows have been assessed, it is important to understand who are the actors behind these flows, how they are organized, what are their relationships of power, competition or cooperation and how they participate in the identity of the territory by valuing its material and immaterial resources. Buclet et al. (2015) indeed underline the risk for industrial ecologists to narrow their vision to engineering-optimization strategies and aim at a broader view, that would leave more room for social sciences and heterodox economics.

Finally, we relate our focus on biophysical accounting to reflections on other indicators of wealth, that is, alternatives to the growth domestic product (GDP). Mathis Wackernagel, cofounder of the Ecological Footprint, proposes his own definition of sustainability: "living well within the means of one planet". This very short sentence clearly illustrates that a minimal set of two headlines indicators is needed for measuring progress in a society: one related to current well-being, and the other to sustainability. The Commission on the Measurement of Economic Performance and Social Progress also formulated this wish: "The assessment of sustainability is complementary to the question of current well-being or economic performance, and must be examined separately. [...] To take an analogy, when driving a car, a meter that added up in one single number the current speed of the vehicle and the remaining level of gasoline would not be of any help to the driver. Both pieces of information are critical and need to be displayed in distinct, clearly visible areas of the dashboard " [START_REF] Stiglitz | Commission sur la mesure de la performance économique et du progrès social[END_REF]. If GDP itself has no pretension to measure either of those two dimensions, its common use as a target for economic policy4 suggests that it is in practice routinely used as a proxy for well-being: if we have growth then we will be fine. The important amount of literature dedicated to the limits of, and misconceptions about GDP have so far had little impact on policy-makers. Interestingly, this illustrates the fact that for the human mindset, knowing that a statement is incorrect is not a sufficient incentive to stop using it... We will come back in conclusion to the question of statistics and alternatives to GDP, based in particular on the works of members of the Forum for other indicators of wealth (FAIR). Now that we established that biophysical accounting was essential for measuring sustainability, but also for helping societies advance towards reduced environmental footprints, we will ask ourselves the following question: How can we complement existing environmental assessment tools, specifically at subnational scales? to which we devote the next section. The focus on local scales, consistent with the idea of territorial ecology, is additionally motivated by the fact that local territories, and regions in particular, are delegated increasing jurisdiction and seem less seem to benefit from unexploited opportunities to implement a transition to sustainability.

Existing environmental assessment tools: which tool for which question?

Evaluating the material basis of a territory is a way to identify relevant direct and indirect levers of action to improve the situation. Two angles can be mobilized in this perspective:

• The distinction between internal and external sustainability, described by [START_REF] Boutaud | Le développement durable : penser le changement ou changer le pansement ?[END_REF], is based on the localization of environmental impacts. For instance, air pollution due to road traffic is rather an issue of internal sustainability while greenhouse gazes (GHG) emissions are an external, i.e. worldwide, issue. This distinction is relevant in the sense that a territory could be tempted to favor its internal sustainability (its local environment and livings conditions) at the expense of its external sustainability (the weight it places on the world).

• Producer and consumer responsibilities are complementary points of view to examine the two forms of environmental pressures: those physically occurring inside the administrative boundaries of a territory and those occurring worldwide in order to satisfy the consumption of this territory. The two perspectives, illustrated in figure 1.4 are useful to inform decision-makers. Taking the example of climate negotiations, China is for instance the first carbon emitter but a large part of its emissions can be associated with manufacturing of products for western consumers (Réseau-Action-Climat, 2013).

Highlighting the structure of the local economy and its inter-dependence with foreign economies has therefore the following purposes:

• Revealing critical links for both the economy itself and the environment, ignored.

Mass conservation: Material Flow Analysis (MFA) MFA is based on the physical principle of mass conservation (Eurostat, 2001): for any given territory or industrial process (car production for instance), the difference between what goes in and what comes out of the system is equal to stock variation in this system during the period of study. This methodological constraint makes MFA easy to integrate into an accounting framework and also ensures, at least theoretically, not to forget anything in the balance sheet. In counterpart, MFA does not always cover all aspects of a territorial assessment. While Substance Flow Analyses (SFA), for instance applied to metals, traces a chemical component inside a system, economy-wide MFA (EW-MFA), results in aggregates that are not associated to processes existing in the territory. Moreover EW-MFA is not well-suited to inform on consumer responsibility: pressure occurring outside of the system, refered to as indirect flows or hidden flows, cannot be taken into account without calling for other tools, and are in fact often ignored in local scales studies. [START_REF] Kovanda | Analysis of regional material flows: The case of the Czech republic[END_REF] also criticize the use of the DMC (Domestic Material Consumption) indicator, thats adds up quantities of different nature (raw materials and finished products). At regional and local scales, results moreover depend for a large part on the hypotheses used to remedy data shortage, and can only be assessed on a case-by-case basis. Nevertheless, MFA appears as a (paramount) preliminary to other methods.

Products from cradle to grave: Life-Cycle-Assessment (LCA) LCA is the most "disaggregated" method since it was originally conceived for studying products, considered as functional units. Inversely to SFA, it starts from the product (or service) to get to the materials and pressures involved in each step of its manufacturing. Therefore, one has to chose where to truncate the study so that it be both relevant and feasible. For example, while SFA can help tracing the circulation of copper in the French economy [START_REF] Bonnin | Development of a dynamic material flow analysis model for French copper cycle[END_REF], the LCA of a electric appliance will capture only a part of this circulation in its inventory (the copper physically present in the device as well as an estimate of the copper needed to produce the device), among other substances. The main appeal of this method lies in the fact that it allows to highlight impact transfers between stages of the life-cycle. It also allows to estimate a large panel of pressures and potential impacts, both local (air polluation, water pollution, waste production, and other nuisances) and global (contribution to climate change, contribution to ocean acidification, depletion of scarce resources). This helps showing which compromises must be found.

Inter-dependence of economic sectors: Input-Output Analysis (IOA) Introduced by Wassily Leontief in the 30s, IOA is first an economic method measuring both direct and indirect flows between all economic sectors and all factors of production: work, capital, resources and pollutions. Leontief himself considered using Input-Output Tables (IOT) beyond pure economic matters [START_REF] Leontief | Environmental Repercussions and the Economic Structure: An Input-Output Approach[END_REF]. The success of this extremely enriching approach and the adoption of IOT in the System of National Accounts (SNA) of most countries, which occurred in exchange of sensible simplifications [START_REF] Duchin | Input-output economics and material flows[END_REF] 5 , helped spreading environmental applications. The last twenty years have thus seen a work of reappropriation of this formalism for environmental issues, as part of the development of industrial ecology [START_REF] Duchin | Input-output economics and material flows[END_REF], the most common application being the allocation of pressures between consuming sectors and final demand based on traded values. The introduction of physical IOT (PIOT) is an example of attempt to better capture the physical reality of economy. Their use is however subject to interpretation, as debated between [START_REF] Hubacek | Applying physical input-output analysis to estimate land appropriation (ecological footprints) of international trade activities[END_REF] [START_REF] Suh | A note on the calculus for physical input-output analysis and its application to land appropriation of international trade activities[END_REF], [START_REF] Giljum | Beyond the simple material balance: a reply to Sangwon Suh's note on pjysical input-output analysis[END_REF] and [START_REF] Weisz | Physical and monetary input-output analysis: what makes the difference?[END_REF]. Additionally, those PIOT are very difficult to build given the lack of data and important simplifications have to be conducted, including materials aggregation, making a deep analysis of results harder. Finally, although monetary IOT are in many cases only available at the national scale, it is possible to regionalize them provided that local economic data are available and with the help of a number of ad hoc hypotheses [START_REF] Cordier | Ecosystème estuarien et système économique régional : faisabilité d'une intégration par modélisation Input-Output. Application au cas de l'habitat halieutique dans l'estuaire de la Seine[END_REF].

Toward an integration of methods

Progress can be obtained when these methods are combined. This combination can take different forms: complementarity, hybridization or complete integration. Understanding the explicit and implicit hypotheses of each method is a necessary preliminary to their integration. For example, LCA results (or at least partial LCA results) can be used to complement material flow data in order to assess environmental pressures "embodied" in imported and exported products. This is for instance used to estimate hidden flows in MFA or also in the standard computation of EF (both for extraction factors and carbon emission factors).

Example of hybridization is given by coupling attempts between LCA and IOA [START_REF] Treolar | Extracting embodied energy paths from input-output tables: towards an input-output based hybrid energy analysis method[END_REF]. One of the deficiencies of LCA is the truncation issue, that can lead to results ignoring up to 50% of impacts [START_REF] Lenzen | Truncation error in embodied energy analyses of basic iron and steel products[END_REF]. Indeed, process analysis is precise for direct impacts but not feasible for the totality of indirect impacts, especially for high order ones6 , which forces practitioners to fix a threshold a priori based on expert knowledge. On the contrary, IOA has the property to be very comprehensive and to take all pressures into account, at the expense of a detailed picture, due the need for aggregation of some economic sectors. In practice, the pressure attributed to a product are in fact the same for alls product belonging to the same category. The hybridization between IOA and LCA involves accounting for direct impacts and the first order indirect impacts thanks to the precise LCA results, and completing them with IOA results on indirect impact linked to the same category of products. This is a good example of how the joint use of two methods enables to make the best of the comprehensiveness of a top-down approach and the precision of a bottom-up approach.

The phase of full integration is reached when the coupling of two tools gives birth to a new method. In their work, [START_REF] Nakamura | The waste input-output approach to material flow analysis[END_REF] have extended IOA to take wastes into account and make a connection with MFA through the implementation of a mass conservation constraint. This implies a clear definition of the concepts of resource, material, product, byproduct and waste in order to prevent double-counting. This extension allows to determine the different resources physically embodied in any complex end-product, although the authors studied the automotive industry in particular [START_REF] Nakamura | Upiom: a new tool of mfa and its application to the flows of iron and steel associated with car production[END_REF]. their Waste Input-Output (WIO) model also assesses environmental pressures of a product during its production, use and end-of-life phases, offering an new alternative to LCA. Another approach, based on PIOT, was proposed in the European project FORWAST [START_REF] Schmidt | Forwast 6.4 -documentation of the final model used for the scenario analysis[END_REF]. Another example of strong integration between MFA and IOA is the adaptation of Absorbing Markov Chains (AMC), recently used to study the worldwide cycles of metals (copper, nickel, iron) [START_REF] Eckelman | Markov chain modeling of the global technological lifetime of copper[END_REF]. The question is then to understand the fate of a substance in the global economy once it has been extracted: where does it go? how is it used? how long does it stay in society? How many times is it used? How much energy is invested in it during its lifespan? More generally, [START_REF] Duchin | Embodied resource flows in a global economy[END_REF] insist on its assets to trace factors of production as well as polluting emissions in the economy and to identify critical dependence links towards a particular resource.

We finally want to stress the recent development of territorial LCA, pursued by Eleonore Loiseau in her PhD thesis, which we find quite close to our concerns [START_REF] Loiseau | Methodogical proposals for performing an environmental assessment of territories based on the Life Cycle Assessment (LCA) framework[END_REF]. It is an attempt to adapt the LCA framework to territorial analysis and address both production and consumption viewpoints, making use of a bottom-up approach (i.e. use of local data) when possible, which is the case for most production activities, and a top-down approach (i.e. use of a proxy) in others cases, especially for household consumption of goods and services. In the latter case Environmentally-Extended IOA (EE-IOA) is used.

A focus on supply chains and biomass

Considering the above state of the art as well as our personal areas of interest, we believe a focus on supply chains can usefully supplement existing research efforts. A supply chain is by definition a group of sectors organized to produce, transform and distribute specific goods to consumers. It is therefore an obvious object of study when it comes to analyzing the links between production and consumption. In practice, there is an opportunity to develop tools that would more systematically take advantage of existing information, either drawn from national databases or local sources. Moreover, to our knowledge, there has been so far few attempts in France to assess uncertainties of material flow studies [START_REF] Bonnin | Development of a dynamic material flow analysis model for French copper cycle[END_REF][START_REF] Dubois | A fuzzy constraint-based approach to data reconciliation in material flow analysis[END_REF], and thus to determine, given available data sources, the degree of precision worth pursuing with this methodology. Finally, it is clear that the relevant scale of study is defined by the problem and that there are in fact most of the time several relevant scales nested in one another [START_REF] Debuisson | Les modes d'interaction pour une dynamique territoriale soutenable : un apport à l'écologie territoriale[END_REF]. Although imperfect because constrained by administrative boundaries, we think a multi-scale approach providing results at the national, regional, departmental levels is likely to cover at least part of these concerns. We will thus aim at such a multi-scale view in a supply chain MFA (SC-MFA) model.

We will then show how environmental pressures can be associated to material flows but will not go as far as assessing their impacts on local and global ecosystems which would be a study in itself. Moreover, we believe knowledge on environmental pressures is already a good basis for enlightening sustainability policies. Beyond this main focus on environmental stakes, we are aware of the interest of decision-makers on issues of local employment and creation of wealth, especially in a time of economic crisis. Territorial supply chains, although they only partially cover these aspects (a territory is more than a juxtaposition of supply chains), can bring about relevant perspectives on them. Thus, we wish to explore the feasibility, limitations and potentialities of coupling SC-MFA with existing models in environmental sciences and social sciences. We couldn't do so if we aimed at studying every supply chain of a territory, or even all the main ones. We therefore prioritize methodological developments over applications and only analyze two supply chains in this thesis: the French cereal supply chain and the French forest-wood supply chain. Beyond our own interest in biomass and renewable resources, all the more so in the context of energy transition, this choice is motivated by the fact that the agri-food and forest-wood sectors are rooted in territories and based on local resources. More details are of course provided in the dedicated chapters.

In short, the work developed in Parts I and II of this thesis is complementary to that of territorial LCA in the sense that:

• We do not provide a holistic environmental assessment of a territory,

• Rather, we analyze a limited number of supply chains in a spatialized and multi-scale way (national, regional and sometimes local level),

• By doing so we not only tackle the production and consumption viewpoints but also provide the link between them, through transformation industries and transport.

In this section, we provided an overview of some existing tools for environmental assessment of territories and more specifically analyzed to what extend they could pinpoint externalities. We showed supply chains were a relevant subject of study for linking production to consumption and for analyzing the material basis and the creation of wealth of territorial economies. Our efforts will therefore be directed to developing a multi-scale supply chain material flow analysis (SC-MFA) model, and in a second step to extending it to environmental and socio-economic aspects. Aware of the fact that scientific information does not easily translates into policy-making, which is perhaps all the more true when science does not speak the monetary language, we consider the question: How can we help to bridge the gap between knowledge and decision-making? which we will now attempt to frame.

Knowledge and action

"To know in order to predict, predict to enable action." 7 Auguste Comte "Waiting to know enough in order to act in full light is to be condemned to inaction." 8 Jean Rostand "Knowledge kills action, for in order to act we require the veil of illusion." Friedrich Nietzsche Scientists played a key role in describing and raising awareness on environmental issues, such as biodiversity loss and climate change. Yet, triggering actions to solve these problems has proven to be a far more difficult enterprise. Our research being decision-oriented, linking knowledge and action is of particular interest to us which is why we propose here a short overview of studies on this question.

The rational-legal model that implicitly accompanied modern societies since the industrial revolution is based on the articulation between the man of science and the man of action [START_REF] Weber | Le Savant et la Politique[END_REF]. When confronted to a problem, the scientist provides a rational explanation of how the world works and the decision-maker uses this objective knowledge to implement the correct policy, in line with the above quotation from Auguste Comte. In this model, experts are defined as men of science that intervene in a decision process, but still carry purely objective knowledge. The introduction of environmental issues however changes this deterministic representation of science: because of an infinite number of interactions, the system under study now escapes analytical modeling. The system is no longer complicated, it is complex; it can no longer be decomposed into small subsystems each of which would be easy to model. Uncertainty then becomes inseparable from scientific knowledge. This reversal of perspective, still not fully digested by public opinions, can lead to a feeling of powerlessness and to the rejection of science as a whole, whereas science can still provide key information for decision-making. For instance, in an update of The Limits to Growth, [START_REF] Meadows | Limits to growth: the 30-year update[END_REF] state: "We are not predicting that a particular future will take place. We are simply presenting a range of alternative scenarios: literally, 10 different pictures of how the twenty-first century may evolve. We do this to encourage your learning, reflection, and personal choice. We do not believe that available data and theories will ever permit accurate predictions of what will happen to the world over the coming century. But we do believe that current knowledge permits us to rule out a range of futures as unrealistic". [START_REF] Funtowicz | Science for the post-normal age[END_REF] argue that in this new era, science should be based on assumptions of unpredictability and incomplete control. They define post-normal science in comparison with traditionnal problem-solving strategies (core science, applied science and professionnal consultancy) using two attributes: post-normal science is appropriate when both system uncertainties and decision stakes are high. Acknowledging that the "old dichotomy between facts and values" is transcended, and that there is a "plurality of legitimate perspectives", they argue for an extension of peer communities to all stakeholders influenced by a decision.

In the same spirit, Van [START_REF] Van Kerkhoff | Linking knowledge and action for sustainable development[END_REF] undertake a literature review of the links between research-based knowledge and action for sustainable development. Among conventional views, they identify the "trickle down" model, which holds that "good research will be taken up by practitioners without additional effort" and is illustrated by the Montreal Protocol which effectively tackled the problem of ozone depletion, and the "'transfer and translate" model, which is still linear, "founded on a one-way transfer of science to users", but additionally requires a translation, an adoption and a diffusion process among relevant users' communities. For the authors, the latter model is for instance well-adapted to explain the massive adoption of intensive practices in agriculture. Its appeal is that "it does not require a great deal of change on the part of the research community, does not conflict with academic goals or incentives, or challenge the view that technical solutions will provide the answers to sustainable development". Kerkhoff and Lebel then examine the critiques of these conventional representations. The main criticism of the linear model is probably the fact that science is socially and institutionally embedded. For instance, social and political processes can stimulate or deter research in some areas. Additionally, researchers may be tied to political and economic interests. Research therefore appears "less autonomous, less certain, and more controversial ". Although they acknowledge that "actions toward sustainability are ultimately the result of social and political decisions", the authors identify participation, integration, negotiation and learning processes as possible responses to the critiques of conventional models as described in figure 1.6. in setting research agendas, encouraged by research funding requirements. Under negotiation models, researchers seek out influential individuals or lobby groups to redefine or introduce new sustainability problems and work with them to further that agenda in political circles. Finally, in learning models, researchers invite practitioners to work with them throughout a research-action cycle, often managed by highly-trained facilitators, with responsibility for linking research-based knowledge and action formally shared.

From the practitioner's point of view, there is an equally increasing consideration given to research-based knowledge. Consulting academic sources is an option for those practitioners who have sufficient academic background to use them. Specific products created by the research community targeted at practitioners can reach a wider audience if practitioners seek them out (recall the 4% of medical practitioners who had consulted the evidence-based syntheses). Knowledge brokers can be useful intermediaries in helping practitioners identify and access research. Next, practitioners may consult or hire researchers to provide Annu. Rev. Environ. Resourc. 2006.31:445-477 The key issues of uncertainty and pluralism of perspectives are also examined in the work of [START_REF] Pielke | The honest broker: making sense of science in policy and politics[END_REF]. To the question of whether or not science can compel action, the author answers "Yes, but only in particular circumstances characterized by shared values and low uncertainties about the relationship of alternative courses of action and those valued outcomes". On the contrary, he notes it is common that :

• Competing interests try to limit the scope of possible choices,

• Conflict exists about the desirability of different outcomes,

• Uncertainty exists on the relationship between actions and outcomes and there is little hope to reduce this uncertainty.

Paradoxically, Pielke shows that uncertainty can both play in favor or against democratic decision-making. On the one hand, it can be "a resource for various interests in the process of bargaining", typically some interest groups can call for inaction until better knowledge is available. On the other, uncertainty may in some cases be considered as a realization of John Rawls' veil of ignorance [START_REF] Rawls | A theory of justice[END_REF] and help reaching a reasonable compromise: "there may be greater room for political compromise when winners and losers are unknown or at risk ".

We can derive a first conclusion from these analyses: regarding sustainability issues, a decision process limited to experts and decision-makers will unlikely be effective. As we will see in part III, participation has long been recognized as a central piece of sustainability policies, sometimes to the point of arousing hostility [START_REF] Cooke | Participation: The New Tyranny[END_REF]. At the same time, integrating stakeholders in the decision process of course complicates it. For instance, how much power should be transfered to them? On this matter, [START_REF] Rousseau | La décision participative : une démarche pour gérer efficacement les conflits environnementaux -document de travail 96-24[END_REF] distinguish between consultation, negociation and concertation (also refered as participative decision): in the case of consultation, stakeholders have no saying in the decision and can only express their opinion on a project; negociation implies a necessity of co-decision due to the interdependence of actors looking for acceptable agreements; participative decision is located somewhere in between, that is stakeholders can influence the decision but do not generally have the final say. In this case, they will likely support the decision if they originally agreed on the decision-making process. Interestingly, [START_REF] Manin | L'idée de démocratie délibérative dans la science politique contemporaine. introduction, généalogie et éléments critiques[END_REF] argues there is no direct filiation between this form of procedural legitimacy, implemented by institutions to limit conflicts, and theoretical developments on deliberative democracy, which also holds that legitimacy stems from a procedure, in this case, from an argumentative deliberation process among equal citizens. Bases of the social choice theory and its relationship with deliberative democracy will be further presented in Part III.

Another highlighted difficulty is that consequences of policies can be difficult to predict. Again, a possible response to this issue is the involvement of a large-enough panel of stakeholders in a transparent decision process. Mistakes can be made, but it is easier to reconsider a choice when one can transparently trace back the decision process to see how it was previously justified, and specifically what values sustained it. Additionally, uncertainties may be large but one can attempt to quantify them. This effort should be pursued so that decision-makers can take into account the degree of confidence of information.

Finally, socio-ecologic systems, which are the subject of sustainability science, are not only difficult to predict but also difficult to describe because they are multi-dimensional. Classically, a first distinction can be made between the anthroposphere (man) and the environment. Clearly each of these two aspects are themselves multi-dimensional and the question arises of where to set the balance between the comprehensiveness of the description and the efficiency, or even the feasibility of the decision process: some dimensions need to be left out or aggregated while maintaining a reasonable distortion of reality. Dashboards of economic, social and environmental indicators have flourished, both in the corporate sector, following the corporate social responsibility initiative, and in the public sector, with official national sustainability indicators. The fact that actions rarely have positive impacts on all dimensions adds complexity to the decision process. How can one arbitrate between these different dimensions? In the field of corporate management, Michael Jensen argues that scorecards are flawed because ultimately, one can only maximize one criterion [START_REF] Jensen | Value maximization, stakeholder theory, and the corporate objective function[END_REF]. We will study to what extend multicriteria analysis can address to this argument in the context of public decision-making (Part III).

This section helped us to narrow our initial objective of bridging the gap between research results and decision-making. After defining basic concepts of decision-aiding, we will try 1.4. Structure of the thesis to study deliberation procedures between multiple stakeholders that encompass principles from multicriteria analysis and can handle uncertainty.

Structure of the thesis

Figure 1.7 explains the structure of the thesis in the form of a flowchart. In Part I and Part II, we will address the first research question presented in this introduction: we will present our developments on supply chain material flow analyis (SC-MFA) and its potential extensions to environmental and socio-economic aspects. More specifically, Chapter 2 will introduce different approaches of supply chain analysis and clarify the scope of our research, Chapter 3 (article) presents the SC-MFA model in the case of the French cereal supply chain, Chapter 4 (article) provides the uncertainty assessment of the French domestic road freight survey, a crucial part of the SC-MFA model. Chapter 5 studies formal links between different methods aiming at tracing flows upstream or downstream, Chapter 6 (article) implements it in the continuation of the study on cereals to analyze environmental pressures embodied in the supply chain. Chapter 7 (article) investigates the possibility of coupling SC-MFA with economic modeling in the case of the French forest-wood supply chain and Chapter 8 shows the links between SC-MFA and a few social sciences' approaches on the issue of actor analysis and local creation of wealth. Part III is dedicated to the second research question: helping bridging the gap between knowledge and policy-making. Chapter 9 introduces the principles of multi-criteria decision aiding, participation and deliberation, and Chapter 10 presents a deliberation-aiding procedure and discusses its possible implementation in the case of the Afterres 2050 sustainable agriculture scenarios. Finally, we summarize in the conclusion the contributions, limits and perspectives of our work, and ask ourselves, given the potential pitfalls of quantification, what guidelines could be useful in order to count wisely. Coupling material flows with economic modeling: a case study on the French forest-wood supply chain (Chapter 7). Territorial supply chains from a social sciences' perspective (Chapter 8).

Guidelines for biophysical accounting, and democratic challenges.

Decisions are hard to make because of uncertainties, because they often affect many stakeholders that can have conflicting interests, and because they rarely have a positive impact on all criteria: we choose to study public deliberation procedures that would be suited to handle these three issues (Part III).

Chapter 2

A brief introduction to supply chain analysis

In the introductory chapter, we only presented methods related to biophysical accounting and environmental footprints. Here, we rather propose an overview of approaches used to analyze supply chains, which as we will see, originate from many different disciplines.

2.1 A wide range of approaches: from strategic management to industrial ecology

The term value chain was popularized by Michael Porter in the 1980's in the field of strategic management [START_REF] Porter | Competitive advantage of nations: creating and sustaining superior performance[END_REF]. It focuses on the firm level and consists in decomposing the firm's activities into successive tasks required to bring their product or service from its original design to its delivery to consumers. These tasks not only include "primary" activities (operations, logistics, marketing, after-sale services), but also all "support" activities such as human resources management and quality control. The idea is to study each link in order to understand which ones positively contribute to the competitive advantage of the company and which ones would be best provided by others. In other words, the goal is to identify activities that add the most value to the final product in order to reduce costs and increase differentiation. This concept has been extended to industry value chain, which situates the firm as part of a whole supply chain as figure 2.1 shows.

have concerned ex French colonies, with a particular focus on exports of agricultural commodities (e.g. cotton, rubber, coffee) to France. It is now promoted by the Food and Agriculture Organization (FAO) as a way of "assessing how public policies, investments and institutions affect local production systems" [START_REF] Tallec | Commodity chain analysis: constructing the commodity chain functional analysis and flow charts[END_REF] and according to [START_REF] Raikes | Global commodity chain analysis and the French filière approach: comparison and critique[END_REF], the method was used to justify interventionist measures against liberalization policies carried out by the World Bank. [START_REF] Tallec | Commodity chain analysis: constructing the commodity chain functional analysis and flow charts[END_REF] define the term commodity chain as: "the name given to the succession of operations and of agents which, starting upstream with a raw material, eventually emerge downstream, after several stages of transformation and increases in value, with one or more final products at consumer level. A chain is thus a series of operations (transformations) of agents and of markets, which lead to physical flows and their counterparts in monetary value".

The first implementation step is to identify relevant activities as well as boundaries of the study: one usually follows a primary product downstream, that is through its successive transformations, until final consumer or export. One can also start from a final commodity and identify providers at each stage of production, however "the general rule is that only agents who deal directly with the commodity [...] should be included in the chain", which excludes for instance providers of fertilizers, pesticides and machinery. Then, one identifies agents behind the activities and group them in homogeneous technical and socio-economic functions. Last, a flowchart is drawn as illustrated in figure 2.2 and one attempts to quantify both physical and monetary flows and to analyze them.

Finally, coming back to the field of industrial ecology, a biophysical approach on supply chains was proposed in the 1983 study entitled "L'écosystème Belgique -Essai d'écologie industrielle"3 [START_REF] Billen | L'écosystème Belgique: essai d'écologie industrielle[END_REF]. In this work, the authors focus on the Belgian economy by decomposing it into supply chains, as shown in figure 2.3. They analyze material flows and stocks of some of these supply chains in detail, using Sankey diagrams representations (an example of the iron supply chain is given in figure 2.4). In addition, in the second part of the essay, environmental pressures linked to the Belgian economy are quantified (waste generation, energy flows and emission of pollutants) and associated to specific supply chains when possible. Beyond the scientific endeavor, the authors express the wish to use this more global perspective on the economy, pinpointing environmental externalities, to rethink what is and what is not profitable, and to open a debate on the productive system's reorientation.

Scope of our work

Our work can be directly affiliated to this last approach of territories and supply chains. It also bears some similarities with the Approche filière, however differences need to be pointed out. Firstly, we do not wish to restrict our analysis to agricultural supply chains. Secondly, the method used allows us to study flows between industrial sectors but not through collection or distribution networks. Thirdly we do not distinguish large from small agents nor production practices, for instance we don't distinguish organic from conventional supply chains. These limits will be further discussed in Chapter 8. Furthermore, we adopt the following strategic bias: we want to explore the possibility of relying only on existing datasets and not on a bottom-up, survey-based, data collection process. This of course sets the finer scale we can study, systematic information only being available down to a certain level. We will see that, while we can have reasonable confidence in results at the regional level, it is not always the case at the department level, and going deeper cannot be done without coarse simplifications. Our main purpose is to produce SC-MFAs at the level of France and of all French regions in an efficient, semi-automatic way, with the assumption that they could then provide a basis for deeper territorial analyses.

In a longer-term perspective, it can be pointed out that:

• Only two chains were studied in this thesis, but the goal would be to analyze all the main chains (much like what was done in [START_REF] Billen | L'écosystème Belgique: essai d'écologie industrielle[END_REF], but at regional scales),

• In practice though, supply chain analyses have intrinsic limits (because of data availability, and because human activities cannot be fully studied though supply chains),

• Strategies to develop more comprehensive environmental assessments of territories are discussed in the conclusion.

Introduction

Material flow analysis (MFA) is a systematic assessment of the flows and stocks of materials within a system defined in space and time [START_REF] Brunner | Practical Handbook of Material Flow Analysis[END_REF]. Depending on the pursued objective (e.g. detoxification, dematerialization etc.), this framework has been [START_REF] Bringezu | Material flow analysis[END_REF]. In this paper, we are interested in mapping the flows of specific resources throughout the economy, both from a spatial and a processing point of views; i.e., we aim to trace the associated flows from the extraction of raw materials to the processing, trade and consumption of the derived products based on the resource under consideration. These studies are known as MFA on the level of goods, as defined by [START_REF] Baccini | Metabolism of the Anthroposphere -Analysis, Evaluation, Design 2e[END_REF] 1 . In their original work, [START_REF] Billen | L'écosystème Belgique: essai d'écologie industrielle[END_REF] conducted such MFA on 6 supply chains at the scale of Belgium (iron, glass, plastic, lead, wood and paper, and food products). Since then, MFA has been mostly applied to metals 2 [START_REF] Ciacci | Historical evolution of anthropogenic aluminum stocks and flows in Italy[END_REF][START_REF] Eckelman | Markov chain modeling of the global technological lifetime of copper[END_REF][START_REF] Liu | Mapping the global journey of anthropogenic aluminum: A trade-linked multilevel material flow analysis[END_REF][START_REF] Dahlström | Combining economic and environmental dimensions: Value chain analysis of UK iron and steel flows[END_REF][START_REF] Bonnin | Development of a dynamic material flow analysis model for French copper cycle[END_REF] to cite only a few. Some studies were also undertaken on construction materials [START_REF] Smith | Resource flow analysis: measuring sustainability in construction[END_REF] and wood [START_REF] Hashimoto | Data book: material and carbon flow of harvested wood in Japan[END_REF][START_REF] Binder | Transition towards improved regional wood flows by integrating material flux analysis and agent analysis: the case of Appenzell Ausserrhoden, Switzerland[END_REF][START_REF] Cheng | Spatial and temporal flows of China's forest resources: Development of a framework for evaluating resource efficiency[END_REF][START_REF] Liu | Forest sustainability in China and implications for a telecoupled world[END_REF]. Regarding food products, few studies actually quantified flows between the production, transformation and consumption stages [START_REF] Wirsenius | The biomass metabolism of the food system: A model-based survey of the global and regional turnover of food biomass[END_REF]Blezat-Consulting, 2010), rather focusing on the supply of a product unit [START_REF] Narayanaswamy | Resource flow and product chain analysis as practical tools to promote cleaner production initiatives[END_REF][START_REF] Mintcheva | Indicators for environmental policy integration in the food supply chain (the case of the tomato ketchup supply chain and the integrated product policy)[END_REF][START_REF] Virtanen | Carbon footprint of food -approaches from national input-output statistics and a LCA of a food portion[END_REF], on nitrogen flows [START_REF] Billen | The food-print of paris: long-term reconstruction of the nitrogen flows imported into the city from its rural hinterland[END_REF], or on land embodied in trade [START_REF] Hubacek | Applying physical input-output analysis to estimate land appropriation (ecological footprints) of international trade activities[END_REF]. [START_REF] Binder | Implementing the results of material flow analysis[END_REF] raised the important issue of the practical usefulness of large-scale MFA studies for policy-making. Three main obstacles were identified in comparison with MFA at the scale of an industrial unit: "(i) the numbers of stakeholders involved increases [...] and it becomes unclear who is responsible for taking action; (ii) the uncertainty of the data increases; and (iii) the goals [...] are not always clearly defined". In order to bridge the gap between research findings and policy-making, many authors have rightly argued that MFA should be coupled with social, economic or/and environmental models [START_REF] Binder | From material flow analysis to material flow management Part I: social sciences modeling approaches coupled to mfa[END_REF]. This kind of coupling was for instance successfully implemented by [START_REF] Rochat | Combining material flow analysis, life cycle assessment, and multiattribute utility theory[END_REF] who combined MFA, Life Cycle Assessment (LCA) and multi-scenarios, multi-criteria, multi-stakeholders analysis to address the issue of PET plastic management in Columbia. One could also refer to the study carried out by [START_REF] Bouman | Material flows and economic models: an analytical comparison of SFA, LCA and partial equilibrium models[END_REF] who used SFA, LCA and partial equilibrium models to evaluate industrial systems and compare pollution management scenarios. Coupling MFA with a social model aims at better understanding the behaviors of stakeholders and the interactions between them in order to study how to improve resource management. For instance, [START_REF] Binder | Transition towards improved regional wood flows by integrating material flux analysis and agent analysis: the case of Appenzell Ausserrhoden, Switzerland[END_REF] used a multi-agent model to study the management of regional wood flows in Switzerland. As mentioned by [START_REF] Kytzia | Economically extended-MFA: a material flow approach for a better understanding of food production chain[END_REF], the coupling of MFA with an economic model can be performed to study economic consequences of environmental policy, or on the contrary, to study the effectiveness of economic tools to tackle environmental issues. Finally, the coupling with an environmental model, for example with LCA, makes it possible to build environmental accounts (such as footprints) from the producer's and from the consumer's perspective. As underlined by many authors (Peters and Hertwich, 2006b;[START_REF] Skelton | Mapping flows of embodied emissions in the global production system[END_REF], these points of view are both complementary and paramount for policy-making. The producer's point of view informs on environmental pressures that occur on a territory: a variety of measures (incentives, regulations, information...) can be taken to address these pressures. The consumer's point of view informs on the responsibility of the consumer for environmental burdens occurring locally or far away (end products purchased by final consumers trigger global supply chains and thus it can be argued that consumers bear the subsequent environmental pressures).

The present paper is the first step of a project aiming at analyzing local supply chains from an economic, social and environmental perspective for decision-aiding. In particular we aim at analyzing environmental pressures along supply chains, i.e. from the producer's to the consumer's viewpoint. The paper has two main objectives. The first one is to assess the feasibility of downscaling a national MFA to simultaneously obtain MFAs on every subterritory the country is composed of (e.g. every regions). This makes the study more time-efficient while also ensuring the comparability of the data and the consistency of aggregated results (the regional data will sum up to the national data). This also helps to get a better grasp on inter-regional trade, which is rarely known with precision. These results can then serve as a basis for discussion and refinements with local stakeholders. The second goal is to undertake a multi-scale MFA. We strongly believe that multi-scale analysis is a powerful decision-help tool given social-environmental issues are unlikely to be resolved at any single administrative level. Indeed, each level has specific jurisdictions and discusses with specific actors. We further discuss the potential of multi-scale analysis at the end of the results section. Such a perspective has already been adopted in France in the case of Paris and its region where economy-wide MFAs were produced on three different geographical scales (from the city to the région level; [START_REF] Barles | Urban metabolism of paris and its region[END_REF]). Here, we undertake studies at the national, regional, departemental and SCoT3 scales.

In order to illustrate the interest of the tool we have developed, we have chosen to apply it to a basic class of commodities, i.e., cereals. This choice is motivated by the following considerations:

• At the world's scale, but more generally at any scale, the supply of cereals and cereals products is strategic given their direct and indirect (through meat consumption) role in human diets and their increasing use for other purposes (e.g. bioethanol),

• Cereals are, in terms of weight of production, the most important agricultural good in France; the supply chain is represented all over the territory and, at the same time, a strong heterogeneity can be observed between regions,

• The supply chain is well structured making it easier to model and collect the necessary data.

• Finally, it is possible to account for most end-products derived from cereals with a limited set of descriptive product categories, bread being the most obvious one in the case of France.

The paper is organized as followed: the first section depicts the methodological framework and the sources and hypotheses used in the modeling phase, we present and discuss the results in the second section before concluding on the perspectives for further research in the field of MFA. chain in France

Materials and methods

Methodological framework

In order to semi-automatically produce MFAs at subnational scales, we start by building a consistent MFA at the country level. For this purpose, we use on the one hand a supply and use tables (SUTs) framework as a way to present and organize the data, and on the other hand a constraint optimization algorithm aiming at reconciling inconsistent data. We underline here that while we use a typical Input-Output framework, we don't go into any IOA (e.g. computation of the Leontief matrix)4 .

It is worth noting our resource-specific MFA based on SUTs is close to the concept of Material System Analysis (MSA) introduced by [START_REF] Moll | Iron and steel, a materials system analysis -pilot study examining the material flows related to the production and consumption of steel in the European Union[END_REF] on the case of European iron and steel flows, and taken up by OECD (2008b). However, while MSA is considering all material inputs and outputs along the supply chain (i.e. life-cycle-wide), we only focus at this step on one good: cereals5 .

Supply and use tables

Handling a large quantity of data is a major difficulty in MFA and calls for a proper way of organizing the information. SUTs appear to be the most convenient framework to achieve this goal. They comprise a Supply As shown above, the supply table comprises the supply matrix V and the imports vector I whereas the use table comprises the use matrix U , the exports vector E and the (final) consumption vector C. For instance U ij refers to the quantity of product i that is used by sector j and C i refers to the quantity of product i that is consumed by end-users on the territory. The constraints linking these elements are discussed in section 3.2.1.3.

Using SUTs implies to make a list of the goods deriving from the primary resource under study, i.e. the primary material itself, semi-products, by-products and end-products. Finding the appropriate level of details for both products and industries is an iterative process between looking for sources of information and trying to fill the tables. With a small number of highly aggregated product categories, the study isn't likely to provide useful information and with a very detailed list of products and industries, filling the data, especially at local scales, won't be feasible. A good knowledge of existing classifications in the national statistical system, for instance economic sectors, products or traded commodities classifications, is also required because correspondences between them will be needed. We used the most precise level of classification of economic sectors available in France for most of the sectors in the study: the NAF 2008 classification (732 sub-classes). For some important products such as bioethanol, this classification was however not precise enough. In those cases, we created our own sectors, knowing information on factories location was available from the cereals' supply chain federation. This initial step of supply-chain structure analysis is the most time-consuming and cannot be automatized. In fact, it consists in building a model of the supply chain: a too coarse model will not make sense while a too detailed one will be intractable. The final version of our study includes 19 products and 18 sectors (displayed in figure A.1 in Supplementary Material section A).

Boundaries of the study, units and allocation choices

We used a typology proposed by [START_REF] Nakamura | Waste Input-Output Analysis: Concepts and Application to Industrial Ecology[END_REF] to define the scope of the study. Inputs from sector a to sector b can take three different forms: primary material inputs, that will be physically incorporated in the production of sector b (e.g. wheat for flour production), material ancillary inputs, that are necessary for production of sector b but not part of it (e.g. machines), and finally flows of services. For this MFA on cereals we track the flows from product to product until cereal grains are no more physically present in the output of the process. Thus, we go for instance from wheat to flour and to bread and biscuits while we stop the study at animal feed without analyzing the embodied cereals in the meat finally consumed (which would be virtual allocation and not a physical flow of cereals).

Like other MFA studies on the level of goods, we converted all flows to a common unit6 . Here, flows are expressed in cereals grains equivalent (c.g.e.). The c.g.e. weight equals the real weight when the product under consideration is entirely made out of cereals (e.g. flour), otherwise (e.g. bread, beer...), it represents the weight of the cereal content of the product.

To sum things up, our SUTs framework distinguishes itself from SUTs traditionally used in national accounts by the finer-grained description of the products and industries categories, by the fact that it focuses on a single supply chain and by the choice of the unit.

Data reconciliation

The principle of mass conservation provides a few constraints on the SUTs. When the data comes from distinct sources, these constraints are of course very unlikely to be fulfilled. Making the original data fit the constraints is commonly referred to as the data reconciliation process. The constraints are discussed below.

We first apply the law of mass conservation on each product: the amount of product that was used during the considered time period by transforming industries, exports and final consump-Chapter 3. Downscaling material flow analysis: the case of the cereal supply chain in France tion, had to be supplied by local industries or by imports (constraint 1). The corresponding equation is:

X j Vij + Îi = X j Ûij + Êi + Ĉi i = 1..n (3.1)
We use hats above letters to refer to the data resulting from the reconciliation process (original data are represented without a hat). In the general case, equation D.1 should contain additional terms to account for initial and final stocks (or alternatively one term of stock variation). We however go around this issue as explained in section 3.2.2.5. Moreover, losses are treated as a sector (without outputs) in matrices U and V .

We apply a similar principle of conservation to every transforming industrial sector (constraint 2): the sum of a sector's inputs is equal to the sum of its outputs:

X i Vij = X i Ûij j = 1.
.m and j is a transforming sector (3.2)

A sector producing raw materials is not concerned by this constraint because it only has outputs.

We moreover implement a few process constraints to verify classical technical conversion factors between products (constraint 3). These equations link one or more inputs of a transforming sector with one or more of its outputs. For instance the yield of conversion of wheat grains into flour translates into the following constraint for the milling sector : S flour,mills = 0.77 ⇤ U wheat,mills . We present those equations in table A.1 in section A of Supplementary Material. Finally, we want all terms to remain positive (constraint 4) and most of the terms to remain null (constraint 5) because of the supply chain modeling choices (for instance the primary production sector cannot produce transformed products).

Our goal is to minimize the discrepancy between original data and estimated/final data while respecting the constraints. This problem can be expressed in many ways depending on the expression of the distance between original and final data. We choose here one of the simplest, a weighted least square problem under constraints:

min ✓ X i X j ( Vij V ij ) 2 2 V ij + X i X j ( Ûij U ij ) 2 2 Uij + X i ( Îi I i ) 2 2 Ii + X i ( Êi E i ) 2 2 Ei + X i ( Ĉi C i ) 2 2 Ci ◆
subject to the set of constraints 1 to 5 (3.3)

In equation 3.3, refers to the assumed standard deviation of the data. They make it possible to treat data sources differently depending on the assumed (or possibly measured, or constrained) uncertainties on the data. The chosen weights are discussed later in the paper.

Downscaling technique

From an administrative point of view, metropolitan France is currently divided in 22 administrative régions. Each région is further subdivided into départements (96 in total), the next and last administrative authority being towns and cities (about 36000 in total). The lack of data at local scale is problematic. The smaller the scale, the less the availability of the data. For

Materials and methods

57

this reason, one can try to estimate the missing data using other existing variables along with data available at a larger scale, by defining appropriate proxies.

The general proxy expression of the estimation of local data would be:

Y n+1 = f (Y n , X n+1 1 , .. , X n+1 k ) (3.4)
Here the exponents refer to the geographical level of the data (for instance, if n represents the country level, n + 1 represents the regional level). f is the model linking the quantity of interest at level n, Y n (known), and k explanatory variables available at level n + 1, X n+1 j , to the quantity of interest at level n + 1 that we are looking for: Y n+1 .

The possibilities of testing complex proxy models are of course very limited by the scarcity of the information. Researchers who faced the lack of data in their local MFA studies actually used a single proxy (or explanatory variable) to estimate missing data [START_REF] Barles | Urban metabolism of paris and its region[END_REF][START_REF] Kovanda | Analysis of regional material flows: The case of the Czech republic[END_REF][START_REF] Niza | Urban metabolism[END_REF]. This is usually based on reasonable hypotheses such as "consumption is almost proportional to the population". We applied the same approach here and conducted linear regression tests whenever the sample existed and was of sufficient size7 . We studied the possibility of having a multiple explanatory variables model but concluded it wasn't robust enough given the limited size of the geographic sample [START_REF] Smaranda | Data mining for material flow analysis: application in the territorial breakdown of French regions[END_REF]. Moreover, we found that the R 2 index, which represents the proportion of the variability of the sample that has been explained by the model, was high enough in the case of a simple one-explanatory-variable-linear model to consider it satisfactory. Results are presented in Table 3.2.2. For instance, if we want to estimate the regional use of wheat by the milling industry in region i, U ri wheat,mills , with the number of employees working in this sector E mills , equation 3.4 becomes: U ri wheat,mills = U fr wheat,mills ⇤ E ri mills / E fr mills (3.5)

Once enough direct data or proxies have been gathered, it is possible to fill the SUTs. New columns are added to consider inter-regional trade of good. By construction, the imports of product i to region a from region b, Ir a,b i , are equal to the exports of product i from region b to region a, Er b,a i , so we only use the Ir variable (matrix) in the program. We then apply the same data reconciliation process as the one described above. An additional constraint however needs to be implemented: one wants to ensure the coherence of the results regarding aggregation and disaggregation. The regional data must sum up to the national total. With the same notations as above for the exponents, the general expression of the aggregation constraint (constraint 6) is:

X i Xn+1, i = Xn where X represent matrix V , Û , Î, Ê or Ĉ (3.6)
In equation 3.6, I and E refer to international imports and exports only: there is no aggregation constraint on inter-regional trade.

There exists no trade database at subnational scales that perfectly matches our products classification. Therefore, a few traded categories are more aggregated than our own categories. For instance the wheat category in the transport database includes both our common wheat and durum wheat categories. Table A.9 in section B of Supplementary Material shows the full correspondence and section B depicts the changes that had to be made to take this limitation into account. chain in France Finally, no trade data is available below the level of the département. Therefore, at this scale, we only compute production and consumption (intermediate and final) flows, using the usual proxis and then apply the resource equals use constraint on each product to determine the amount of net imports (or net exports). Thus, we no longer use any optimization or data reconciliation process below the scale of the département.

Data sources and hypotheses

Figure A.1 in Supplementary Material section A shows the classifications used in this study for product and sector categories together with the chosen model of the supply chain: it indicates for instance that the starch industry uses common wheat and maïze and supplies starch and residues. In order to fill the SUTs, the information we are looking for fall into different categories: primary production, intermediate consumption, stocks, trade, livestock consumption and final consumption. As mentioned in the previous section, we use direct data when it exists and proxy data otherwise. Each type of information is discussed below in relationship to table 3.2.2 that summarizes the sources and table 3.2.2 that presents the chosen proxies. The question of data uncertainties is discussed in the last paragraph of the section. the explanatory and response variables). One usually assumes the null hypothesis is false when the p-value is below 0.05. Here, we can validate the explanatory models for cereals, flour and livestock feed production whereas the samples are too small to validate the starch and malt production models. Insee's CLAP database is used to get the number of employees; number and location of factories come from the yearly report of the Passion Céréales association (inter-profession). Hypotheses were not tested when no data was found at the regional scale.

a

In other european countries where such census is not available, results from the Capri-Dynaspat model [START_REF] Leip | Linking an economic model for European agriculture with a mechanistic model to estimate nitrogen and carbon losses from arable soils in europe[END_REF]) could be used. chain in France

Primary production

Detailed data on cereals production is published in the annual agricultural statitics available down to the level of the département. We therefore used a land-use proxy (see table 3.2.2) to estimate the production of cereals at the scale of a group a cities.

Intermediate consumption

The annual report of the French inter-profession of cereals (Passion-Céréales, 2013) provides information on the quantities used and produced by different industries in the supply chain.

Based on this data, we established conversion factors between products (table A.1 in Supplementary Material section A), that are used to constrain the problem (see section 3.2.1.3). When the data couldn't be found in specific regional reports, which is the general case, we estimated the subnational intermediate consumptions using the downscaling technique presented in the previous section and the proxies in table 3.2.2.

Losses and by-products

In the current version of the supply chain model, losses are only considered at the farm and during grain storage, because these losses are the most significant and are estimated by the ministry of agriculture. We additionally take into account by-products (residues from transformation industries). In a sustainability perspective, the material efficiency of the supply chain can be estimated (it could be defined as a ratio of 1 losses/inputs), as well as the fate of by-products in order to make sure they are recovered.

Livestock feed

Regional consumption of cereals for livestock feed are not directly known, mainly because the cereals are distributed in various forms: mostly self-consumption at the farm and consumption of industrial compound products, and marginally grains bought by the farmer. We therefore designed a model to estimate these consumptions. Figure 3 .4, A.5 and A.6 in Supplementary Material section A show the original feed intakes per type of animal or product. Care was taken in order to avoid double-counting: either the lifecycle or the annual approach was used for each product. For instance, we use the lifecycle approach for pigs (meaning we multiply the number of pigs slaughtered during one year by the cereals intake of one pig during its lifespan) and the annual approach for nursing cows (meaning we multiply the livestock at the end of the year by the per capita annual feed intake). Once local cereal feed consumption is estimated, we split it between compound feed and raw feed thanks to information and hypotheses on the animal feed industry (tables 3.2.2 and 3.2.2).

Figure 3.1: Principles of the livestock feed model. Input data is shown in grey.

Stocks

Information about stock is partial, notably because of confidentiality issues. Averaging the figures over several years solves this issue since the variations of stock tend to compensate one year after another. For instance, table A.2 in Supplementary Material section A shows that stock variation explains up to 12% of the national apparent consumption in 2003 whereas this number falls to -0.6% over the period average. In this work we therefore study the period 2001-2009.

Trade

As shown in table 3.2.2, for the national MFA, we use the imports and exports data of the ministry of agriculture, providing information with detailed product categories directly in weight of grain equivalent. For MFAs at subnational scales, we use the SitraM database, maintained by the French ministry of ecology. We underline 3 main difficulties with this data :

1. We had to design a correspondence table between the transport statistics classification and our own product classification : table A.9 in Supplementary Material section A.

2. Assumptions had to be made regarding the national trade by railway since the classification is not as detailed as for the other modes of transport: we assume that cereals represent 75% of the "Agricultural products and living animals" category. This is the proportion found for international export by railroad in 2005. chain in France 3. Theoretically, there is a compatibility issue between data from the customs (international trade) which provides the first origin and final destination of a product and the national data which provides the last loading or unloading of the merchandise. This issue can lead to double counting for regional imports and/or for exports8 . We partially solved the problem by redistributing the international trade by sea using the market shares of French harbors for cereals exports. This means in particular that sea exports of regions without any harbors were entirely reallocated to regions with harbors. We were not able to do the same for road, river or railway transport. Still, this operation is significant since more than half the French exports of cereals are made by sea: on average, between 2001 and 2009, France exported about 14 Mt of cereals by sea, 6 Mt by road, 5 Mt by river, and 1,5 Mt by railroad. Table A.7 in Supplementary Material section A shows the impact of this operation on the total international exports of every regions.

Final consumption

Final consumption of cereal products occurs in two forms: food products (bread, biscuits, pasta...) and industrial products (bioethanol and many products derived from starch). In France, local consumption patterns are not precisely documented, at least not precisely enough to be used in this study. For most of the products, we considered the per capita consumption to be equal all over France. Regarding bread, we used a study depicting the diversity of food consumption patterns in France in the mid 1990's that presents statistical information on the gap between regional and average consumption of bread per household [START_REF] Babayou | Les disparités régionales de la consommation alimentaire des ménages français[END_REF]. This consumption estimation is not built as an apparent consumption (resulting from the difference between production, stock variation and trade) but on direct households surveys. Table A.8 (supplementary material) presents the adopted regional adjustment factors for per capita bread consumption, reconstructed from this report. For subregional scales, no data was found in the report. Following the conclusions of [START_REF] Babayou | Les disparités régionales de la consommation alimentaire des ménages français[END_REF], that the urban vs. rural and north vs. south typology was the most suited to explain the variability in the bread consumption patterns (rather than regional cultural differences for instance), we estimated the gap between local and average consumptions based on this typology. Table 3.5 shows the corresponding adjustment factors.

Urban Rural North

-10% +21%

South -7% +25%

Table 3.5: Per capita bread consumption variability among different categories of towns in the mid 1990's in France.The table makes the distinction between cites in the north and in the south of France and between urban and rural cities (cities with less than 2000 inhabitants are considered rural). According to [START_REF] Babayou | Les disparités régionales de la consommation alimentaire des ménages français[END_REF], this typology is the most suited to explain the differences between bread consumption patterns in France.

According to the national MFA, bread accounts for about 40% of the consumption of cereals for food purposes, and for one third of the total consumption of cereals. This adjustment on local bread consumption is therefore significant.

Data uncertainty

Uncertainties on input data [START_REF] Laner | Systematic evaluation of uncertainty in material flow analysis[END_REF] review existing literature regarding uncertainty handling in MFA and provide recommendations relatively to the goals of each study. Our case study typically falls in the category of descriptive MFA as they describe it and we use an approach similar to the one implemented in software STAN [START_REF] Cencic | Material flow analysis with software STAN[END_REF]: input data are expressed by a mean and a standard deviation reflecting the level of confidence in the data. As we mentioned in section 3.2.1.3, the weighted least squares optimization leads to higher alteration (difference between output and input data) of variables with higher uncertainties. Since none of the sources used provides detailed information on data uncertainty, this step is based on assumptions and on educated guesses. Following [START_REF] Danius | Data uncertainties in material flow analysis[END_REF], we treat data differently depending on its origin. Below, we list the different origins from the ones we trust the most to the ones we trust the less:

1. official statistics at local, regional or national scale, based on cross-checking of surveys (some of which are exhaustive) : e.g. agricultural production, employment... The last one typically applies to road freight statistics which are based on a survey9 . The estimation of total road freight in the country (all goods combined) is quite accurate (less than 1% of error according to the calculation of the statistical office (SOeS, 2012)), however the extrapolation on subpopulations, meaning on specific goods in specific regions, can be deteriorated a lot because of the small size of the sample. Collaboration with the statistical office is in progress in order to estimate the intervals of confidence on these subpopulations. Generally we consider that small flows have a larger relative error than large ones for data extracted from the same source, but we prevent null flows from having a vanishing standard deviation (this would be unrealistic).

Although the attribution of uncertainty weights is based on objective elements such as the source of the data, this part of the process is not the most robust and the model would benefit from a sensitivity analysis that would show the impact of a change for each input variable. This was however too demanding to accomplish in this paper (this would require to rewrite our Matlab code in a more efficient language such as C for the simulations for the computational time to remain within reasonable bounds).

Uncertainties on output data Using common terminology in statistics, we can describe our problem as follow: if we call a supply-use table with uncertainties on each parameter a supply-use table distribution (STUD), chain in France then our goal is to obtain a posterior STUD from our prior STUD. Given the number of constraints we know our result is of much lower dimension than the number of variables and a direct sampling of the posterior STUD is then possible by Monte-Carlo simulations. The intervals of confidence of output variables are thus inferred from theses simulations. Numerous input datasets are randomly generated knowing the standard deviation of input data, and assuming a Gaussian distribution (although this is not a requirement). After a while, typically in our case, a few tens of simulations, the process reaches convergence. The confidence intervals represented on the diagrams correspond to two standard deviations (95% of possible values if the actual distributions are indeed gaussian). We analyze the results in section 3.3.

Software integration

We wrote a program to properly integrate our databases, the original SUTs, the optimization and Monte-Carlo processes, and the visualization of results. As table 3.2.3 illustrates, it made it possible to implement a model with a large quantity of variables, simultaneously computing all sub-entities of a given territory. Figure 3.2 presents the software background on the study in relation to figure 3.3 which shows the manual and automatic steps conducted to produce regional results.

Results and discussion

We use Sankey diagrams to display our results 10 . They have long been used in flow studies and are very efficient in wrapping a large quantity of information [START_REF] Schmidt | The sankey diagram in energy and material flow management[END_REF]. We use the Chapter 3. Downscaling material flow analysis: the case of the cereal supply chain in France following convention: flows circulating inside the territory are represented by horizontal lines while flows entering or leaving it are represented by vertical lines. Although the core of the paper only shows results under this form, all input and ouput datasets are available by request to the authors.

Results for France and French regions

We split the national results into two diagrams in order to make them more readable. Figure 3.4 shows the production, imports and exports of cereals as well as the flows related to livestock consumption (raw or compound feed). With a yearly average of 34 Mt of grains produced, common wheat is the most commonly grown cereal in France (53% of the total cereal production) before corn (23%) and barley (16% .5 shows the domestic use of each cereal along with imports and exports of transformed products, until final human consumption on the territory. Starch and wheat mill industries clearly stand out as the two main supply chains with respectively 6.2 Mt and 4.4 Mt of grain (wheat and corn) processed. They also produce most of the by-products (3.3 Mt or 81% of the residues). Then comes the malting industry with about 1.6 Mt of barley processed. Other supply chains (bioethanol, pasta and couscous, rice, canned corn, cornmeal) are less significant although together, they add up to 2 Mt 12 . On the imports side, the main flows correspond to flour, starch and glucose, pasta and rice, adding up to 1.1 Mt or 85% of the total imports of transformed products. On the exports side, the main flows correspond to starch and glucose, malt and flour adding up to 2.9 Mt or 78% of the total exports of transformed products. On the consumption side, the main flow corresponds to bread (with 2.6 Mt or 34%), starch and glucose (with 1.8 Mt or 23%), and biscuits (with 1.2 Mt or 16%). Pasta, beer, rice, bioethanol, flour, canned corn add up to 2.2 Mt. 83% of cereals are consumed through food and drink products and 17% through other industrial products 13 . All these figures provide convenient points of comparison for sub-national geographic levels.

One thousand Monte-Carlo simulations were conducted for the national model. The convergence is very quick: on average, the average standard deviation reaches 95% of its final value after less than 100 simulations. According to the Monte-Carlo process, the range of coefficients of variation goes from 1% to 20%, small flows having a larger relative interval of confidence (i.e. a bigger relative uncertainty) in the general case. The output uncertainty has been reduced compared to the input uncertainty through the enforcement of the constraints, for instance wheat production uncertainty (expressed as the coefficient of variation) goes from 2% in the input to 1% in the output. Finally, we checked that each output value belong to the 95% confidence interval of the input.

Figures A.2, A.3, A.4, A.5 and A.6 in supplementary materials show MFAs of five regions (among the 22 computed) each of which present a specific profile (producing region, livestock region, region with a large transformation activity, exporting region...). Considering the whole dataset, figure 3.6 show the most important flows accross regions. Three types of flows stand out: most of them are linked to international exports, some other to livestock activities in Bretagne and the rest to transformation activities in Nord-Pas-de-Calais. These flows result from the model, they are not the mere visualization of the trade database. Firstly, the model output flows distinguish between products that are otherwise grouped in the trade classification: for instance common and durum wheat as well as residues and livestock feed are initially grouped. Secondly, given their high uncertainty compared to other flows (e.g. production), output inter-regional trade flows sometimes differ significantly from input values: for instance the original database does not mention any export above 500 kt from the Centre region while the map shows 4 flows leaving this region. chain in France Table 3.7: Surface and population of the four territories under study.

Multi-scale analysis

We show diagrams in an aggregated form in order to make the comparison between geographical scales clearer 14 . As indicated in section 3.2.1.4, results at the level of the SCoT (that is, below the level of the département) are not obtained through the usual optimization process and only show net trade. Results for the Isère département are skipped, because they were close to what is observed at the SCoT level, but are available upon request.

12 Bioethanol production increased a lot from the end of the 2000-2010 decade: in 2013, about 2.2 Mt of cereals were used for this purpose, compared to the 0.5 Mt that appear in our results for the 2001-2009 yearly average.

13 Following Passion-Céréales (2013), we consider that half of the starch production serves non-food purposes. 14 The graphical scale (i.e. width of line per kt) is different in diagrams 3.8, 3.9 and 3.10 in order to improve the readability of the figures.

The comparison of figures 3.8 and 3.9 shows that the supply chain's structure at the level of France and Rhône-Alpes are very different15 . Indeed, unlike France:

• With a yearly average of 1.1 Mt of grains produced, corn is the most commonly grown cereal in Rhône-Alpes (51% of the total cereal production) before common wheat (29%),

• The region is not caracterized by a significant net export capacity, human and livestock consumption almost adding up to local production, however, inter-regional trade has a important role in the working of the supply chain. In particular, the region is a net exporter of corn, inter-regional exports being the biggest outlet of the corn supply (with 55%), whereas it is a net importer of common wheat (38% of the supply comes from outside the territory),

• Many industries, such as the starch industry, are not represented in the region, which leads to significant imports of transformed products (in fact, regional industries almost exclusively process common and durum wheat).

One thousand Monte-Carlo simulations were run at the regional level 16 . Each flow from one region to another has been computed by the model. We however only show aggregated results because they come with a smaller uncertainty range. As we can see on figure 3.9, uncertainty ranges of trade flows (even aggregated) are usually quite large. For instance the 95% confidence interval of imports of cereals indicates that the flow can reasonably take values from 305 kt to 1101 kt, the most likely being 703 kt. Of course this reflects the choices made for the uncertainty of input data, where region-to-region flows were given a high uncertainty for the reasons discussed in section 3.2.2.8.

If we now turn to the comparison of the Rhône-Alpes and of the SCoT of Grenoble's supply chains, we can see that they share many characteristics. One of the possible explanation is that the territory of the SCoT is a small image of the region itself, since it comprises both mountain and plain areas. Two differences are however worth pointing out: the relative net exports capacity of the SCoT is larger than the region's, and contrarily to what happens in Rhône-Alpes, in the SCoT, human consumption is larger than livestock consumption. Corn is the most commonly grown cereal in the SCoT whereas wheat is the only cereal processed for human consumption purposes. This implies that the territory depends on imports for the supply of many transformed products. This is not necessarily problematic in itself (the smaller the area the less likely it is to be self-sufficient), but we point out that the multi-scale analysis provides information, e.g., on the range of scale this situation can be found.

Potential interest for practical policy-making

The national MFA as well as the study of interregional flows points to the fact that the cereals supply chain is export-oriented. The fact most exported goods are raw materials can raise the question of lost added value and employment on the national territory. Furthermore, being able to compare regions is important for national objectives. For instance, it makes it possible to assess the pros and cons of regional specialization strategies on the three fronts of sustainability (economic, social and environmental). chain in France From another angle, the type of tool described here is potentially helpful for a better integration of the different levels of decisions through the ability to analyze more and more detailed geographical scales. In the case of France, various administrative levels have leverage on some parts of the supply chain, and each one on a different aspect. For instance, local (group of cities) levels can foster or discourage the development of certain type of activities, either through subsidies, public orders (e.g. organic food in schools) or by administrative authorizations. The regional level is often in charge of coordinating local initiatives while the global strategy and objectives are established at the national level. A multi-scale tool can help in identifying more efficiently the most appropriate type and level of decisions for a given objective.

Generally speaking, through the analysis of the most important supply chains present at the various geographic scales (a substantial endeavor in itself) one opens up the possibility of addressing a number of social and environmental issues and of identifying potential lock-ins and/or leverages for a sustainability transition; we briefly mention a few key questions here. What are the critical supply chains in terms of employment for a given territory? What are their weaknesses and opportunities relatively to the territory's resources (in a wide meaning of the word)? What type of environmental impacts are associated to them, and where do they occur (is the territory externalizing major impacts)? Regarding the case of cereals, energy use / emission of greenhouse gases, use of water and use of pesticides are of particular interest. A production map coupled with ecosystem services analyzes 17 will show what are the critical areas/productions, while the supply chain point of view will show how impacts can be shared between producers and consumers. A supply chain perspective may also help decision-makers anticipate climate change impacts (e.g., how a change in cereal production type and pattern affects employment and/or consumption on the territory?) Conversely, how can consumer-driven sustainability demands (local production, for example, or reduction of demand for meat-based products) affect existing supply chains and promote new ones, both in terms of employment and (local and distant) environmental impacts? Addressing a number of these questions will of course require a scenario approach, or at least an analysis of contrasted options.

Conclusion

Regarding our first objective, that is assessing the feasibility of constructing non-survey MFA at local scales, we argue that the proposed methodology is an efficient investment: efforts are needed to design the initial model (in relation to the downscaling objective) but results are then available almost directly for any territory covered by the data. Moreover, the data reconciliation process provides consistent and comparable results among territories. The method could be adapted in other countries, at least in European countries, providing data sources are adapted. Secondly, we tested our multi-scale model and analyzed its results in the case of the cereals supply chain of four nested territories: France, the Rhône-Alpes région, the Isère département and the SCoT of Grenoble. This example shows that it is possible to identify the key differences in local supply chains and to understand how they are currently articulated. It would be interesting to compare these downscaling results with local surveys: this could inspire future research especially in regions providing detailed supply/use or input-output tables, which is not currently the case in France.

Uncertainties are unavoidable in this kind of studies and it is important to assess them [START_REF] Rechberger | Uncertainty in material flow analysis[END_REF]. We tried to do so, although acknowledging that the evaluation itself is still imperfect. In order to improve it, at least three elements would be useful: an iteration with local stakeholders and experts during the design of the model and the choice of data inputs, a better knowledge on the interval of confidence of statistical data used as input (work is for instance under way regarding road freight statistics), and finally, a sensitivity analysis to understand the weight of each input variable in the results of the model. As underlined in the introduction, we consider MFA as a first step towards a broader analysis of economic, social and environmental aspects of local supply chains. Additional work has to be conducted to reach this goal. For instance, regarding environmental aspects, studying the coupling between material flows and the associated major environmental footprints (energy use, greenhouse gases emissions, water use, use and emission of pollutants...) provides relevant leads for our future investigations of this topic. MFA helps to bridge the geographical gap between producers and consumers and can provide good insights on their shared responsibility. [START_REF] Calame | Essai sur l'oeconomie[END_REF] argue that subnational territories and supply chains are the two key players for organizing a sustainable society in the 21 st century thus replacing the the couple state -company, which played a pivotal role in the 20 th century, but which they find ill-suited to face the new challenges of sustainability). In their opinion, they could organize both territorial coherence (from city to regional scale) and production chains. There are several underlying ideas to these statements. Firstly, by insisting on supply chains rather than on the companies, one brings the collaborative aspect of exchanges to the forefront to balance the competitive aspects of free markets. Secondly, the focus on territories is driven by the necessity of building on local strengths to balance local weaknesses in the undertaking of a sustainability transition. Finally, local/regional levels are more reactive, and closer to actual social needs and environmental threats, although of course a multiplicity of approaches targeted at the whole spectrum of decision scales is needed to address sustainability issues.

The present MFA study is one of the tools that can be used to foster such a view, as it has the potential to meet decision-makers concerns by providing key information on local supply chains viewed from the economic (creation of wealth), social (local employment) and environmental (flows of environmental pressures from producers to consumers) perspectives. In a time when the fragility of the complex globalized system makes it mandatory for all to strengthen their capacity of absorbing exogenous shocks, the development of such tools at the service of subnational institutions is a necessity.

Introduction

Material flow analysis (MFA) is a systematic assessment tool used to assess the flows and stocks of a system during a period of time. Either focusing on specific substances or on the whole economy, it has been widely applied to countries and more recently to subnational scales [START_REF] Binder | Transition towards improved regional wood flows by integrating material flux analysis and agent analysis: the case of Appenzell Ausserrhoden, Switzerland[END_REF][START_REF] Kovanda | Analysis of regional material flows: The case of the Czech republic[END_REF][START_REF] Niza | Urban metabolism[END_REF]. Regarding these studies, [START_REF] Rechberger | Uncertainty in material flow analysis[END_REF] raise two key questions: "What level of precision do we achieve, and what level of precision do we require?" These questions can be related to the remarks of [START_REF] Binder | Implementing the results of material flow analysis[END_REF] regarding the lack of implementation of MFA in policy making: indeed, if the precision of results is not properly analyzed, the reliability of the studies may be questioned. On the material flow studies contrary, analyzing uncertainties helps preventing premature conclusions and points to the main lacks of information. For instance, it would not make sense to try to explain a 10% difference on the per-capita consumption of two regions if it can be explained by an overlapping of confidence intervals. [START_REF] Laner | Systematic evaluation of uncertainty in material flow analysis[END_REF] review the existing MFA literature and propose a classification of uncertainty management methods into three types of approaches: qualitative and semi-quantitative approaches (e.g., [START_REF] Graedel | Multilevel cycle of anthropogenic copper[END_REF]), approaches based on data quality classification (e.g., [START_REF] Weidema | Data quality management for life cycle inventories: an example of using data quality indicators[END_REF][START_REF] Hedbrant | Data vagueness and uncertainties in urban heavy-metal data collection[END_REF][START_REF] Danius | Data uncertainties in material flow analysis[END_REF] and statistical approaches (e.g., [START_REF] Cencic | Material flow analysis with software STAN[END_REF][START_REF] Dubois | A fuzzy constraint-based approach to data reconciliation in material flow analysis[END_REF]. They insist on the distinction between "random" uncertainty (that cannot be reduced) and "epistemic" uncertainty (that is due to a lack of knowledge). [START_REF] Patricio | Uncertainty in material flow analysis indicators at different spatial levels[END_REF] provide uncertainty quantifications of Economy-Wide Material Flow Analysis (EW-MFA) for different spatial levels in Sweden: national, regional and urban levels1 . Uncertainties of input data are estimated based on available statistical information, expert judgment and empirical estimates to account for imputation errors, for instance when a proxy is used. Domestic transport is identified as a major source of uncertainty when tackling regional and urban levels. Generally speaking, they underline that the lack of direct information implies larger uncertainties as the spatial resolution increases. They also insist on the fact that evaluating uncertainties is more common in Substance Flow Analysis (SFA) studies than in EW-MFA where they are generally treated qualitatively.

In France, the statistical service of the ministry of ecology (SOeS) compiles information from various sources to provide centralized data updated every year on both international and domestic freight (SitraM database). As about 85% of merchandises transported between French regions travel by road, a specific survey, called the TRM2 survey, is dedicated to domestic road freight. It consists of a poll on French trucks (more details are provided in the methods section). Uncertainties being inherent to polls, the SOeS assesses every year the precision of the survey for the total aggregated result, that is, whatever the good transported and whatever the regions of loading and unloading. For instance, the 2010 quality assessment indicates a precision of about 1.5% on a total of about 2 Gt, which can be interpreted as: there is a 95% chance for the real value to belong to an interval between 1970 Mt and 2030 Mt. Until now, however, uncertainties have never been estimated for disaggregated flows whereas these information are becoming more and more used. For instance, among the 22 French regions3 , 4 have already undertaken an EW-MFA and several other are launching studies. Typically, domestic freight data can be obtained by NST 2007 positions (382 categories) up to the NUTS 3 levels (96 French départements) for loading and unloading. Extrapolations for each flow are provided along with the number of observations they are based on (see the glossary next section for a proper definition). The SOeS warns that results based on less than 10 observations shouldn't be used because they are probably not significant. This article is aiming at a more precise assessment of the uncertainties. Especially, we try to:

• Check whether or not our results lead to a similar threshold of 10 observations,

• Quantify uncertainties above this threshold.

We believe this information can directly benefit ongoing and future MFA studies in France, and also foster research on similar topics in other countries, especially in Europe. Indeed, following the Council Regulation No 1172/98 on statistics on the carriage of goods by road, EU countries as well as candidate countries must carry surveys on road freight similar to the TRM survey. If uncertainty calculation seems to be a common practice in some countries (as Sweden and Germany as we show in the case studies), it may not be the case everywhere and it is especially unlikely for uncertainties to be available for any possible aggregation level of the flows. Moreover, to our knowledge, the question of uncertainty reduction through a multi-year average MFA has not been fully explored yet, while in some cases providing more accurate results for a 3-year average (for instance) may be more relevant than providing less precise annual results.

The article is structured into three sections. Data sources and methods are depicted in a first section. A second section is dedicated to theoretical results, and provides formulae to compute uncertainties for a single year and for a multi-year average. Because the precision required of course depends on the problem, case studies ranging from EW-MFA to MFA focusing on specific products are presented in a third section. This last section also includes a basic comparison of the French, Swedish and German surveys. Finally, a summary of the main findings and perspectives for future research are proposed in the conclusion.

Materials and methods

Glossary

For the sake of clarity, we provide definitions of the following terms that are used throughout the article:

• Population. All vehicles-weeks in France (typically 52 times the number of vehicles). The population total size is N (a quantity that varies from year to year), and elements of this population are denoted i (1  i  N ). Vehicles-weeks are elements obtained by considering that each vehicle provides an independent elementary unit each week of the year. An element is therefore one vehicle surveyed for a single week.

• Subpopulation. Vehicles-weeks that meet specific criteria for at least one of their travels: specific loading area, specific unloading area and specific type of merchandise transported. We are interested in well-defined subpopulations, identified by a given origin (o), destination (d) and category of goods (c) transported. These subpopulations are symbolically represented by an index c i , taking two values: c i = 1 if i belongs to the desired c =(o, d, c) subpopulation, and c i = 0 otherwise. • Sample. Vehicles-weeks surveyed. A sample is noted s and is a collection of elements of the population, usually of predetermined size S. The number of times a given element i is represented in a sample is noted S i . For a sampling method without replacement (as is the case for the TRM survey), S i = 0 or 1. • Subsample. Subpopulation restricted to a sample; subsample sizes are denoted n. Note that the selection of a subsample is a post-selection procedure once the sample is drawn, and not a subsequent resampling of the sample. This definition does not conform with the conventional use of the word.

• Number of observations. Number of elementary operations of loading/unloading meeting specific criteria (specific loading/unloading/good); a single vehicle-week can report several observations of the same good between the same loading and unloading places.

• Characteristic quantity. Any quantity of interest on the total population, for example the total quantity transported per year (tonnes) corresponding to specific criteria (loadingunloading-good). Quantities of interest are denoted y in a generic way. The mot important quantity one tries to estimate through survey sampling is the total of a quantity of interest on the whole population

T = N X i=1 y 0 i ., (4.1)
where y 0 i = N w y i and N w = 52 is the number of weeks of the annual survey. The number of weeks scaling is due to the fact that elements are vehicles-weeks and not vehiclesyear (see the Supplementary material first section for more details). In the probabilistic description adopted here, y i are parameters, not random variables. For a subpopulation, the associated total is

T c = X i2c y 0 i = N X i=1 c i y 0 i . (4.2)
• Inclusion probability. The inclusion probability ⇡ i relates to element i and defines its probability of being present in the sample. By construction the probability of absence is

⇡ i = 1 ⇡ i .
Unequal probability sampling methods are characterized by the fact the ⇡ i is not constant (not independent of i); it is the form of sampling adopted in the TRM survey.

• Coefficient of variation. Also known as relative standard deviation, it is a measure of dispersion equal to the ratio of the standard deviation sigma ( ) to the mean mu (µ).

• Uncertainty. In this article, only uncertainties due to the sampling methodology are taken into account4 . They are provided in the form of 95% confidence intervals, that is nearly twice (1.96) the coefficient of variation, given an hypothesis of Gaussian distribution. We therefore use the notation µ +/-2 /µ (expressed in %). Uncertainties above 100% mean the extrapolation (µ) is not significant and shouldn't be used.

• Extrapolation. procedure allowing us to estimate the quantities of interest in the whole population from a sample.

Description of the methodology of the TRM survey

The TRM survey focuses on motor vehicles registered in France, less than 15 years old, belonging to one of the two following categories: lorries of loading capacity (LC) higher than 3.5 tonnes and road tractors of maximum permissible laden weight (MPLW) above 5 tonnes.

The design experiment is constructed with an unequal probability sampling method, taking advantage of known contextual information about the vehicles. The unequal drawing probabilities are defined based on three factors: the age of the vehicle, the loading capactity of the vehicle and the activity of the owner. The goal is to draw more "young" vehicles and vehicles which have a high loading capacity because they have a higher contribution in the total tonnes and tonnes-kilometeres transported. Half of the sample is renewed every year in order to make the year-to-year evolution more reliable.

Once the answers are collected, sampling weights are corrected for non-response and improved by a calibration procedure (CALMAR method), aiming at reconciling data estimated from the survey with otherwise known totals, for instance the number of trucks registered in each region, the number of trucks of each type etc. More information about this procedure can be found in [START_REF] Cgdd-Soes | Fiche qualité de l'enquête transport routier de marchandises[END_REF].

The owners (or users) of the vehicles drawn for the survey are asked about the use of the vehicle during one week (the answer is mandatory). The unit of the survey is therefore the vehicle-week.

In 2010, the survey had the following characteristics (CGDD-SOeS, 2011):

• population size: 527,403

• sample size: 77,921

• number of usable forms: 49,933

• sampling rate: (sample size / population size) ⇥ 1/52 weeks = 0.28%

Formulae for totals and associated uncertainty estimation

We only collect here the relevant expressions for total estimators and their variance. Some details about these expressions and their justification is provided in the first section of this paper's Supplementary material.

The extrapolation of the annual characteristic totals is performed with the help of the Horvitz-Thomson (HT) estimator:

b T = X i2s y 0 i ⇡ i , (4.3)
The HT estimator variance can itself be estimated by

b V s ( b T ) = X i2s (1 ⇡ i ) ✓ y 0 i ⇡ i P k2s (1 ⇡ k )y 0 k /⇡ k P k2s (1 ⇡ k ) ◆ 2 . (4.4)
For a subpopulation c, the HT estimator can be expressed as

b T c = X i2s y 0 i c i ⇡ i , (4.5)
with the associated variance estimator

b V s ( T c ) = X i2s (1 ⇡ i ) ✓ y 0 i . s i ⇡ i P k2s (1 ⇡ k )y 0 k s k /⇡ k P k2s (1 ⇡ k ) ◆ 2 (4.6) material flow studies
The 95% confidence limit is readily obtained from the variance of the estimator under a Gaussian distribution assumption 5 b e 95% = 2

q b V s ( b T ) b T . (4.7)

Data processing

The study is based on data from the French road freight surveys from 2002 to 2010; the data have been made anonymous for confidentiality purposes. For each truck of the samples, the following three types of information are given:

• targeted information: location of loading, location of unloading, category of good transported, reported tonnes, reported tonnes-kilometers,

• sampling information: statistical weight of each truck,

• contextual information (used for the sampling): age of the vehicle, type of vehicle, activity of the transporter, region of registration.

From this disaggregated information, we recreated all existing combinations of aggregation levels, distinguishing between:

• 3 levels of loading: 1 country (nuts 1), 22 régions (nuts 2), 96 départements (nuts 3),

• 3 levels of unloading (same),

• An illustration of such combinations is provided in the accompanying Supplementary Material file. We computed confidence intervals for each extrapolation (about 900,000 extrapolations in total for the period 2002-2010) with a C++ program implementing Eq. (4.7).

Theoretical results

Estimating uncertainties based on subsample sizes

We built a file based on the surveys from 2002 to 2010 containing the following fields for each extrapolation:

• n: size of the subsample used for the extrapolation (see subsample in the glossary),

• e: 95% error (see uncertainty in the glossary), computed from Eq. (4.7).

5

The service producing the survey also uses a 95% confidence interval to compute the uncertainty on the total (all flows aggregated).

Theoretical results

87

Extrapolations were first sorted out in 15 classes depending on the size of the subsample they are based on. 5%, 50% and 95% quantiles of uncertainties were then computed for each class6 .

Power law fits to the data are proposed in figure 4.1. Applying these models, table 4.1 provides the values for lower, median and upper uncertainty estimations for different values of subsample sizes. The R 2 of the median model, that is the proportion of variability it explains, is equal to 0.87, which is satisfactory. We conducted similar studies for two other predictor variables, that are available in the supplementary material. First, we took the number of observations (see glossary) as predictor variable, since it is currently the default variable provided by the French statistical office. The derived model has an R 2 of 0.77, which is still acceptable but indicates that the size of the subsample is a better predictor and should be preferred when available. Finally, we tested the hypothesis "the higher the quantity transported the smaller the uncertainty", using the number of tonnes transported as the explicative variable. This last model is the least efficient, with an R 2 of only 0.637 . Table 4.1: Lower, median an upper uncertainties estimations for given subsample sizes (rows).

We see that below a size of 15 vehicles-week, there is risk for the statistic not to be significant (above 100% of uncertainties), although it can be significant in some cases. Above 150 vehiclesweek, there is a 95% chance that the uncertainty is lower than 50%, the median estimation being 30%. Lower dots correspond to 5% percentiles, middle dots to medians and upper dots to 95% percentiles. Explicative models were calibrated in order to properly fit the dots. The piecewise models e (%) = a/n b are drawn in blue lines and the parameters are provided in the two tables.

The R 2 of the median model is 0.87. It is interesting to notice that for the three models, the slope increases when the size of the subsample reaches a threshold: upper bounds are the first to decrease, followed by median (for nearly 2000 individuals) and lower bounds.

Estimating the reduction of uncertainty when averaging over several years

Let T i be the estimation of tonnes transported for a given subsample (given loading and unloading locations, and transported product) during the year ↵. The average over several years n y is:

T = 1 n y X ↵ T ↵ . (4.8)
Assuming T ↵ are independent variables, we would have:

V (T ) = X ↵ V ✓ T ↵ n y ◆ = 1 n y P ↵ V (T ↵ ) n y = 1 n y V (T ), (4.9)
where V (T ) is the mean of the V (T ↵ ) over n y years. Then:

(T ) = ✓ V (T ) n y ◆1/2 , (4.10)
and the associated error (twice the coefficient of variation):

e = 2 (T ) T = 2 T ✓ V (T ) n y ◆1/2 . (4.11)
In reality one cannot assume that the annual totals T ↵ are independent variables because every year, half of the sample is reconducted. To recover statistical independence, we chose to build alternative independent samples by removing redundant vehicles-weeks. If we call p the size of a full sample for one year and consider that this size is stable over the n y years considered, we see that the full sample over n y years will have a size of n y p while any independent sample over n y years will have a size of p + (n y 1)p/2 (see the table 3 of the Supplementary Material file and its accompanying comment).

This argument suggests to substitute [p + (n y 1)p/2]/p to n y in the last expression of Eq. (4.11), leading to the following predictor for the error e:

e = 2 p 1 + (n y 1)/2 pP ↵ V (T ↵ )/n y P ↵ T ↵ /n y . (4.12)
This relation is plotted on figure 7 of the Supplementary Material for an average over 3 years, where the uncertainty e is represented as a function of

x = 2 q V (T )/T with V (T ) = P ↵ V (T ↵ )/n y and T = P ↵ T ↵ /n y .
The linear behavior holds with good accuracy, with the correct slope predicted by Eq. (4.12). To obtain this plot, we sorted out observations depending on the value of the predictor and in each class and computed the median of the uncertainties obtained by applying Eq. (4.6) to the independent sample.

The results displayed in table 4.2 allow us to validate this model over all the possible number of years one could use for this averaging procedure. To construct this table, we have constructed the samples as explained above for each averaging option, and compared a fitted slope with the predicted one; the difference between the two is clearly negligible for all practical purposes. Theoretically, the uncertainty of the average could still be lowered because the part of the sample removed is not 100% correlated with the part kept. However, it is not possible to know the level of correlation between these sample parts, so that we advise to break the sample over several years as explained in this section and use Eq. (4.12) as a basic predictor. material flow studies Note that the value 1 slope can be interpreted as the reduction of uncertainty obtained thanks to the averaging operation (e.g. for a 3 year-average, we can expect a reduction of uncertainty of about 30%).

Case studies

4.4.1 Implications for regional EW-MFA: the case of the Bourgogne region

The methodology for Economy-Wide Material Flow Analysis was standardised by Eurostat ( 2001). Its objective is to quantify the physical inputs into an economic system, material accumulation in this system and outputs to other economies or back to nature, as illustrated by table 4.3. This table shows the material balance of the Bourgogne region as computed by Alterre-Bourgogne (2013).

We only consider the uncertainties of road freight statistics and we use Gauss's law of propagation to capture their impact on EW-MFA results. Of course this requires the use of a correspondence table between freight and EW-MFA classifications: we use the table provided by the French official guide for regional EW-MFA (CGDD, 2014).

Regional (Eurostat nuts 2 level) results are presented in table 4.3. We can see that at this level road freight uncertainties are very low for total imports and exports (about 5%) and low to moderate when we start disaggregating by product categories (between 5% and 21%). Also note that with 95% intervals of confidence of respectively 2.5% and 6% DMI (Domestic Material Input) and DMC (Domestic Material Consumption) indices seem robust to road freight uncertainties, although DMC is more subject to variations. This conclusion is confirmed by the results for the four départements of Bourgogne (nuts 3 levels) displayed in table 4.4: while DMI uncertainties vary between 5% and 8%, DMC uncertainties vary between 12% and 21%. At this geographical level, DMCs should therefore be compared with great care and intervals of confidence should be given. This higher sensitivity of the DMC index to input data uncertainties was already underlined in [START_REF] Patricio | Uncertainty in material flow analysis indicators at different spatial levels[END_REF].

The disaggregation effect: a focus on agro-products and wheat

In this section, we show the results for two categories of products: all products from agriculture, forestry and fishery on the one hand and wheat on the other hand (in the NST 2007 classification these correspond respectively to the codes 01 and 0111). In addition, we distinguish between three levels of spatial disaggregation: total domestic road freight, total road imports and total road exports of each French region and inter-regional road freight. The results presented in figure 4.2 clearly show that geographical and product disaggregation rapidly lead to loss of precision given the decrease in the size of the subsample. The most disaggregated results (interregional trade of wheat) show that there is a very large variability of uncertainties depending on the flows (here, depending on loading and unloading regions), ranging from 31% to 183%.

This clearly shows that the disaggregation level is not enough to characterize uncertainty, but that there is a large regional variation. As a consequence, uncertainties should be evaluated in each MFA study to check whether or not road freight is reliable enough depending on the question tackled. Data reconciliation techniques that couple transport data with production, transformation and consumption data seem well adapted to take advantage of available trade data while still taking its (lack of) precision into account, as shown by the authors in a previous article (Courtonne et al., 2015).

Uncertainty propagation: studying wheat supply areas of French regions

Another common way of using transport databases is to estimate the origin or the destination of products (see, e.g., [START_REF] Kastner | Tracing distant environmental impacts of agricultural products from a consumer perspective[END_REF][START_REF] Billen | The food-print of paris: long-term reconstruction of the nitrogen flows imported into the city from its rural hinterland[END_REF][START_REF] Courtonne | Environmental pressures embodied in the french cereal supply chain[END_REF] to name only a few). In this section, we analyze the case of supply areas.

Following [START_REF] Kastner | Tracing distant environmental impacts of agricultural products from a consumer perspective[END_REF], we define a matrix R whose terms R ij represents the

Product disaggregation

Geographical disaggregation

France France

All Agro-products In these relations, I is the identity matrix; p the vector of regional productions; Z the transport matrix (with Z ij the exports of country j to country i); I a vector of ones so that ZI is the vector of total imports for each region; and x 1 a diagonal matrix whose ith diagonal elements is x 1 i . Note that term R ij takes into account an infinite regression of imports and exports between all regions (e.g., region j exports to region k which in turn exports partly to region i while importing its own supply from other regions, etc), under an assumption of perfect blend8 .

For the study of uncertainty propagation we use Monte-Carlo simulations and only consider uncertainties of domestic road freight statistics9 . For each simulation, road freight data (symbolized by the r superscript on matrix Z) are generated and satisfy the four following constraints:

• all terms must remain positive,

• random draws of trade between two regions are generated from a Gaussian distribution centered on the estimated value and within the 99% confidence interval (3 sigmas).

• total imports and total exports of a region computed with the random draws of interregional trade must be within the 99% confidence interval of the estimated total imports and total exports

• total domestic trade computed with the random draws of inter-regional trade must be within the 99% confidence interval of the estimated total domestic trade.

The distributions mean value are extracted from the TRM survey extrapolated values and the confidence interval from our error analysis. These constraints are necessary due to the fact that aggregated data is more reliable than disaggregated data. They translate into the following inequalities:

• For each couple of regions (i, j), Z r ij 0, with Z r the random draw of road freight, 3) . material flow studies criteria: the subsample size must be above 35 and the uncertainty below 40%. It also highlights extrapolations that are based on less than 50 trucks or whose uncertainties are above 20%. The uncertainty of the total in Sweden is about four times arger than in France, the latter being itself about twice as large as in Germany. Although a more comprehensive study would be necessary, these first results suggest that the conclusions drawn from case studies in France are likely to be valid in other European countries.

• |Z r ij Z 0 r ij |  3 (0) ij with Z r 0 the initial road freight data, of estimated standard deviation (0) , • |(Z r I) i (Z r 0 I) i |  3 (1) i , • |(I t Z r ) j (I t Z r 0 ) j |  3 (2) j , • |I t Z r I I t Z r 0 I|  3 (

Conclusion

This article addresses the complex and technical issue of uncertainties of domestic road freight data in the context of material flow studies. Since uncertainties on are not currently computed by the French statistics office, we have conducted our own uncertainty analysis of the sampling procedure performed in France, and proposed a model to estimate the resulting errors, based on available predictor variables, the subsample size or the number of observations. We also proposed a computation rule to assess uncertainty reduction when averaging over n y years. Results suggest that conducting MFA studies on period of several years instead of a single year would lead to more reliable results. For instance, we can expect a 3-year average to reduce the uncertainty of road freight by 30%.

Turning to specific material flows, we first analyzed the impact of domestic road freight uncertainties on the EW-MFA of the Bourgogne region. On this example, we showed that the relative uncertainty of the DMC index (Domestic Mass Consumption) is between 2 and 3 times higher than that of the DMI index (Domestic Mass Input). Results should therefore be interpreted with caution, especially when comparing subnational territories (for instance, eurostat nuts 2 and nuts 3 levels). We illustrate the data disaggregation effect on the case of agro-products, and then the propagation effect of determining regional supply areas for wheat. Results show it is not possible to assert up to which disaggregation level the data can be exploited: computing uncertainties should be done on every flow studied (which justifies the need for reliable and easy-to-implement computation rules). Of course, uncertainties are generally lower when large quantities are involved, however this is not always true. We indeed show that the subsample size (or the number of observations) is a much better predictor than the total tonnes estimated.

Although the analysis is conducted for the French domestic transport survey, many conclusions are likely to be valid in other European countries since they all make use the same kind of surveys for assessing road freight. The basic comparison conducted at the national level for the main product categories between France, Sweden and Germany tends to confirm this hypothesis.

Future perspectives would include conducting similar analysis in other European and non-European countries, implementing the models developed in this article in new regional material flow studies, and finally, conducting uncertainty analysis on other data sources used in MFA (production data, custom data...), when feasible.

With the large amounts of data and computational power available nowadays, it is tantalizing to elaborate evermore sophisticated tools without taking the time to question to what extent they provide useful new contributions to our knowledge and understanding. Analyzing uncertainties helps putting such results in perspective, avoiding premature conclusions, pointing to current lack of information, in line with this famous quote from [START_REF] Read | Logic: Deductive and Inductive[END_REF]: "it is better

Part one recap

The first part was devoted to:

• Situating our methodological developments in comparison with existing approaches of supply chain analysis (Chapter 2).

• Presenting the bases of the SC-MFA model (Chapter 3). Important features include the data reconciliation process, that exploits information on data sources' uncertainty, the downscaling process, that allows us to provide simultaneous and comparable assessment on all sub-territories, and the process of uncertainty propagation, based on Monte-Carlo simulations, allowing us to display confidence intervals on Sankey diagrams. Data is organized in the form of Supply and Use Tables (SUT) and submitted to the constrained optimization presented in Eq. ( 3.3) of the article. While such data reconciliation is a common process in MFA, we propose to use it at a greater quantitative scale. For instance, the multi-regional model handles about 15,000 variables for characterizing productions and consumptions in each of the 22 French regions as well as inter-regional and international trade.

• Applying the model on the French cereal supply chain: we obtained SC-MFAs for all French regions, that underline regional specialization strategies in a striking way. We further tested the downscaling process down to the department and ScoT levels (Isère department and Grenoble area), and showed what simplifications had to be made.

• Presenting an example of uncertainty assessment with what we consider the weakest link of local MFA studies: domestic road freight statistics (Chapter 4). We provide a simple model linking sample sizes with confidence intervals. A conclusion is worth noting, and probably applies beyond the case of France: uncertainties can be significantly reduced Chapter 4. Uncertainties of domestic road freight statistics: insights for regional material flow studies when a study is carried out on a multi-year period (for instance, uncertainty reduction for a 3-year average was estimated to 30%).

As pointed out in Chapter 3, we consider material flows as a basis for further analysis that includes environmental and socio-economic aspects associated to territorial supply chains. Part II is dedicated to this endeavor.

Part II

Coupling material flows with environmental and socio-economic aspects

Chapter 5

Formal links between methods aiming at tracing flows

This chapter serves as a preliminary to the coupling of the SC-MFA model with environmental pressures. As we saw in the introduction, we are particularly interested in building environmental footprint accounts from the producer's and consumer's perspectives. Here, we introduce formal methods for tracing physical flows, be it between regions or between economic sectors:

• In order to get used to the type of reasoning mobilized in this section, we start by detailing how one can formally trace the geographical origin or destination of a single product,

• We then present two common frameworks, Input-Ouput Analysis (IOA) and Absorbing Markov Chains (AMC) that help to efficiently organize data; we provide proofs of these frameworks' classical interpretations,

• We show the links between IOA and AMC using Leontief's minimal example (a twosectors economy, Leontief 1970),

• Finally, we briefly discuss how the Supply Use Tables (SUT) used in the SC-MFA model can be adapted to fit the IOA and AMC frameworks.

Tracing the origins and destinations of a single product

When tracing the geographical origin of a product, one refers to the origin at the first order when one only considers its last loading area, to the origin at the second order when one considers the transit that may have occurred before this last loading, and so on. Thus, the origin at the infinity order corresponds to the product's production area. The order is denoted k in the matrix formulation of this infinite order (k = 1) that is exposed below. Let us first introduce some definitions and notations:

• The expression "the part of quantity X..." always refers to an absolute quantity; the expressions "the fraction of quantity X..." and "the proportion of quantity X..." always refer to percentages.

• n: number of regions.

• I: identity matrix of size (n, n).

• 1: column vector of ones of contextual size (used for line or column summation of vectors and matrices).

• M t : transposed of any vector or matrix M .

• V : the diagonal matrix obtained from any column vector, i.e., Vij = V i ij where ij is the Kronecker delta symbol.

V = V • 1 and V t = 1 t • V .
• T : (n, n) matrix of trade between regions, T ij represents the amount of good transported from region i to region j, intra-regional flows (diagonal elements) are omitted.

• C: (n, 1) vector of consumption in each region,

• P : (n, 1) column vector of production in each region.

• S: (n, 1) column vector of total supply (production plus imports ) in each region:

S i = P i + X j T ji , S = P + (1 t • T ) t .
• U : (n, 1) column vector of total use (consumption plus exports ) in each region:

U i = C i + X j T ij , U = C + T • 1.
• X and X: (n, 1) vector and (n, n) diagonal matrix representing the proportion of direct local supply in each region:

X = P Ŝ 1 , X i = P i S i .
• Y and Ŷ : (n, 1) vector and (n, n) diagonal matrix representing the proportion of direct local consumption in each region:

Ŷ = Ĉ Ŝ 1 , Y i = C i S i .
• A: (n, n) matrix with null diagonal terms, such that A ij is the proportion of supply in region j directly coming from region i, with j 6 = i:

A = T Ŝ 1 . or in coordinate form, A ij = T ij /S j .
The column sum of each column of (A + X) is equal to one (as it corresponds to the total supply of the corresponding region):

1 t • (A + X) = 1 t ,

Tracing the origins and destinations of a single product 105

• Ã: (n, n) matrix with null diagonal terms, such that Ãij is the proportion of supply of region i directly going to region j, with j 6 = i:

à = Ŝ 1 T, so that à = Ŝ 1 • A • Ŝ and Ãij = T ij /S i .
The row sum of each row of ( Ã + Ŷ ) is equal to one (as it corresponds to the total use of the corresponding region):

( Ã + Ŷ ) • 1 = 1. • R (k) : (n, n) redistribution matrices, defined such that P i R (k)
ij is the part of region j supply which one can trace as produced in i, by considering a maximum of k successive transport operations. This matrix relates the production row vector to the supply column vector. In other words,

P i R (k)
ij is the part of products P i in the supply S j that has undergone at most k inter-regional operations of exports or imports. R (k) ij can also be interpreted as the average number of times one unit of i has transited through j at order k; note that the same product unit can be exported and reimported, which is to say R ij may be greater than one 1 . R (k) is the redistribution matrix of order k; R (1) is the redistribution matrix after an infinite series of inter-regional exchanges.

• O (k) : (n, n) defined such that O (k)
ij is the fraction of region j supply coming from the production of region i, at transport order k. It embodies the information of R (k) in fractional form:

O (k) ij = P i R (k) ij /S j . O (1) ij
is the fraction of region j supply produced in region i at infinite order.

• (k) : (n, n) matrices linking productions and consumptions at transportation order k.

More specifically

(k)
ij is the part of production P i that is consumed in region j after undergoing at most k transport operations. Similarly,

(1) ij gives the contribution of P i to C j at infinite transportation order. By construction, and in the absence of stock variation,

P i = P j (1) ij and C j = P i (1) ij .
One can compute R (k) and R (1) by induction, with the help of a perfect blend hypothesis. This hypothesis states that the proportion of production going to local consumption (which is unknown) is the same as the proportion of total supply going to local consumption (which is known). The same applies to the proportion of production directed to exports. The mathematical meaning of this statement is made explicit in figure 5.1.

For the sake of clarity and precision, the induction reasoning is presented in coordinate form, and then stated in matrix form. To alleviate notations, it is often conventional to omit summation signs over repeated indices; for example, for a matrix M connecting to vectors V 1 Time is conspicuously absent from this definition. A reimported product unit can only have been exported at an earlier time. Trade is usually monitored for a given time period, typically a year. over this period, only a finite number of imports and exports has taken place. The underlying approximation can be justified in the following way. First, the number of multiple imports and exports of the same product unit has a smaller and smaller probability at each successive order, as indicated by the decreasing magnitude of the k order trade flow calculated below so that only the first few orders matter (generally the first two). Second, trade flows today are similar to the flows from earlier time periods (stationary hypothesis). In this approximation, summing to all orders has little effect on the result and provides simple closed form formulae. and

W : W i = P j M ij V j = M ij V j .
This convention is used below to derive Eq. ( 5.1) and is given up afterwards.

The induction starts with a tautological recursive substitution2 :

S i1 = P i1 + X i2 T i2i1 = P i1 + X i2 S i2 T i2i1 S i2 = P i1 + X i2 " P i2 + X i3 T i3i2 # Ãi2i1 = P i1 + P i2 Ãi2i1 + S i3 Ãi3i2 Ãi2i1 = P i1 + P i2 Ãi2i1 + P i3 Ãi3i2 Ãi2i1 + • • • + P i k 2 Y j=k Ãijij 1 +S i k+1 2 Y j=k+1 Ãijij 1 . (5.1)
This is where the perfect blend assumption comes in to interpret the tautology: all terms represent part of the production that is exported. For example, under this assumption, P i2 Ãi2i1 is the part of the production of region i 2 that is exported to region i 1 . Indeed, as there is no preference in the origin of the product for their exportation, the exported production is proportional to what production represents in the exporting country's supply; the same conclusion holds as well for T i3i2 Ãi2i1 , which embodies the part of the importations of i 2 in its exportation to i 1 . Consequently, all the P ij terms in the preceding sum represent the contribution of region i j to the supply of region i 1 . This is the central result of this analysis. The preceding relation can be put in vector form as

S t = P t • " I + k X q=1 Ãq # + S t • Ãk+1 .
(5.2)

This implies that

R (k) = I + k X q=1 Ãq = I + k X q=1 ⇣ Ŝ 1 • A • Ŝ⌘ q , R (1) = ⇣ I Ã⌘ 1 = ⇣ I Ŝ 1 • A • Ŝ⌘ 1 .
where the limit k ! 1 has been taken to obtain the last equality.

108

Chapter 5. Formal links between methods aiming at tracing flows One can recast Eq. ( 5.1) to obtain the O (k) and O (1) matrices. Indeed, as

P i k Q 2 j=k Ãijij 1 = X i k Q 2 j=k A ij ij 1 S i1 , Eq.
(5.1) implies that (no summation over repeated indices)

O (k) ji = X j ji + X j " k X q=1 A q # ji , O (1) ji
= X j ji + X j [I A] 1
ji . These relations are more compactly written in matrix form as (with the convention that

A 0 = I) O (k) = X • " k X q=0 A q # , O (1) = X • [I A] 1 , (5.3)
Let us now turn to the connection between consumption and production. This is again achieved with the help of the perfect blend assumption, which implies:

(k) ij = O (k) ij C j .
(

) ij = O (1) ij C j . 1
(5.4)

Remember the closing relation:

P i = X j (1) ij = X j O (1) ij C j , P = O (1) C.
Note that at any order k, one can make an approximation [derived from Eq. (5.

2)] and use formula (5.6) to link productions and consumptions:

P = O ⇤(k) C, with
(5.5)

O ⇤(k) = O (k) + A k+1 , O ⇤(k) = X • " k X q=0 A q # + A k+1
For instance, at order 1 (meaning only products that have been transported one time before being consumed have been traced back to their real area of production):

O ⇤(1) = X • [I + A] + A 2 = X + XA + A 2 .
Eq. 5.6 is in fact the matrix formulation of the formula proposed by [START_REF] Billen | Calcul des aires d'approvisionnement à partir de la base de données SitraM du transport de marchandises[END_REF], and since then implemented in a number of French studies [e.g. Le Noë et al. ( 2016)]. In many cases, this approximation is indeed justified as O ⇤(1) ⇡ O (1) . In our study, we will however use the infinite order directly since it does not bring any computational overhead.

The same general relation between productions and consumptions can also be obtained directly in matrix form3 . This way of proceeding is a lot quicker but less intelligible at first.

From the equality of supply and uses, S = U = C + T 1, one can express the production vector as:

P = P • 1 = X • Ŝ • 1 = X • C + X • T • 1 = X • C + X • T • ⇣ Ŝ 1 • Ŝ • P 1 • P ⌘ • 1 = X • C + X • A • X 1 • P.
Then:

(I X • A • X 1 ) • P = X • C, (I A) • X 1 • P = C, P = X • [I A] 1 • C O (1) ij
being defined as the proportion of supply of j produced in i but also as the proportion of consumption of j produced in i (due to the perfect blend hypothesis), we have:

P = O (1) C, with O (1) = X • [I A] 1 (5.6)
which is consistent with Eq. ( 5.3). Now, we can define the destination matrix D (1) , where D

(1) ij is the proportion of production i consumed in j. Using Eq. ( 5.4) and remembering that ij is the production of i consumed in j, we have:

(1) ij = O (1) ij C j , D (1) ij = (1) ij /P i = O (1) ij C j /P i .
Or in matrix terms:

(1) = O (1) Ĉ, D (1) = P 1 (1) , D (1) = P 1 X • [I A] 1 Ĉ, D (1) = Ŝ 1 • [I A] 1 Ĉ.
And eventually, since

[I A] 1 = Ŝ • h I Ãi 1 • Ŝ 1 : D (1) = h I Ãi 1 Ŷ . (5.7)
TO SUM THINGS UP, matrix O (1) , where O

(1) ij is the proportion of supply (or consumption) of region j produced in i, is defined in Eq. (5.6), matrix D (1) , where D

(1) ij is the proportion of region i production consumed in region j, is defined in equation (5.7) and:

(1) = O (1) Ĉ = P D (1) where (1) ij is the production of region i consumed in region j.

Hopefully, this rather heavy section helped the reader to get used to the type of calculation used to trace flows. It is directly related to the formalism of IOA and AMC, which we will now present.

Input-Output Analysis

General formulation: quantity vs. price IO models

Introduced in their modern form by Wassily Leontief, Input-Output Tables (IOT)4 depict the links between factors of production, economic sectors (intermediate consumption) and final demand5 . As emphasized by [START_REF] Duchin | Input-output economics and material flows[END_REF], one can build two IO models based on these relationships: a quantity model and a price model: "the quantity model follows the supply chain, for an individual product or an entire bill of goods; the price model makes it possible to track the value chain for the same final deliveries". The following material presents the core of IO theory needed for this thesis. More details can be found in [START_REF] Miller | Input-output analysis: foundations and extensions[END_REF].

In order to describe the two IO models, we introduce the following notations6 :

• n is the number of economic sectors,

• 1 is a summation vector (of ones) of contextual size,

• M is the diagonal matrix formed from vector M : Mij = ij M i , • Z is the (n,n) matrix of intermediate consumption with Z ij the quantity of sector i production used by sector j. Each row i of Z can be quantified in the most natural unit (e.g. tonnes of wheat, tonnes of pig iron, kWh, ...or dollars when the product mix is too heterogeneous7 ),

• Y is the (n,1) vector of final demand for goods and services produced by economic sectors; each term Y i is expressed in the same unit as row Z i , • X is the (n,1) vector of total output per economic sector, X i =

P j Z ij + Y i , or in matrix form X = Z • 1 + Y , • A = Z • X 1 is the (n,n) matrix of technical coefficients, with A ij = Z ij /X j
the amount of sector i production directly consumed by sector j per unit of sector j output,

• P is a (n,1) vector of unit prices for each economic sector,

• V is a (n,1) vector of added value per unit of each sector's output.

The quantity model aims at explaining outputs from all sectors based on the level of final demand. It is classically derived as follows:

X = Z • 1 + Y X = A • X • 1 + Y = A • X + Y X = (I A) 1 • Y (5.8)
The price model aims at explaining the unit price of a particular good (or service) based on the level of value-added of each sector contributing directly or indirectly to the supply of this good. For deriving the price model, we start by writing that the added value of a sector is equal to the turnover of this sector (the money made from selling production) minus all the expenditures on intermediate consumption (NB: we note M t the transposition of matrix M):

V i • X i = P i • X i X j P j • Z ji V i • X i = P i • X i X j P j • A ji X i V i = P i X j P j • A t ij V = P A t • P • 1 = (I A t ) • P P = (I A t ) 1 • V (5.9)
Finally, one can derive from Eqs. (5.8) and (5.9) that:

P t • Y = V t • X
This means that the total value-added of the economy is equal to total final expenditures8 . Let us now introduce factors of production. Again, these are present in the quantity and in the price model: in fact, value-added is used to pay each production factor (labor, capital, land, natural resources etc.). We define the following elements:

• m is the number of production factors,

• F is a (m,1) vector of production factors with F i the amount of production factor i used by the whole economy. Each element of F can be expressed in the most natural unit (e.g., tonnes of ressources, number of working hours etc.),

• f is a (m,n) matrix of production factors per unit of output with f ij the quantity of production factor i used per unit of output of sector j,

• ⇡ is a (m,1) vector of unit prices for each factor of production.

We can then extend the quantity and price models to production factors:

F = f • X F = f • (I A) 1 • Y (5.10) V i = X j ⇡ j • f ji V = f t • ⇡ P = (I A t ) 1 • f t • ⇡ (5.11)
And from Eqs. (5.8) and (5.11) comes:

P t • Y = ⇡ t • f • X = ⇡ t • F
meaning total final expenditures are paying for total use of production factors.

The interest of Eqs. (5.8), (5.9), (5.10) and (5.11) is not readily obvious. Indeed, total outputs, unit prices, total use of production factors (vectors X, P and F ) are known from the start. These models are however very enriching for two reasons:

• Forecasting. Under the assumption that the economic recipe (structure) does not change, one can forecast how the use of production factors will evolve (e.g., number of job creations) consecutively to a change of final demand; with the price model, one can similarly estimate how prices of products will evolve following a change of unit prices of production factors.

• Analyzing the current situation. These models allow analytical accounting, that is, allocating a global quantity to a series of elementary processes. In doing so they help identify critical links in the economy (in our case, critical links related to environmental pressures).

In this thesis, we only concentrate on the second point. Coming back to Eq. (5.8), we can for instance compute matrix X whose ijth term represents the production of sector i used to satisfy final demand for sector j:

X = (I A) 1 • Y X = (I A) 1 • Ŷ
Here, it is noteworthy that X • 1 = X, however X 6 = X. In the next section, we show ways of further decomposing the links between production and consumption.

Taylor decomposition of (I A) 1 and Structural Path Analysis

Since A • X = X Y , the column sum of each row of matrix A is lesser or equal to one and at least one row is strictly inferior to one: 8i, P j A ij  1 and 9k, P j A kj < 1. This last condition simply means that final demand Y is strictly positive for at least one economic sector. These conditions imply that: lim n!1 A n = 0. One can therefore use the Taylor series decomposition of matrix (I A) 1 , often refered to as the Leontief matrix and noted L:

L = (I A) 1 = 1 X k=0 A k = I + A + A 2 + • • • + A n + . . .
Eq. (5.8) can then be rewritten as:

X = Y + A • Y + A 2 • Y + • • • + A n • Y + . . .
This formulation is interpreted as follows: in order to deliver quantities of Y to final demand, one must at least produce Y (order 0); the production of Y in turn requires intermediate consumptions of A • Y (order 1), and therefore the production of A • Y , which in turn requires the intermediate consumption of

A • A • Y = A 2 • Y (order 2), .
.. and so on. On the right-hand side of the equation, matrices correspond to successive orders (layers) of production where flows are traced upstream (direct inputs, inputs for inputs, inputs for inputs for inputs etc.) as the power of A increases, and eventually vanish.

We can also decompose matrix f • X, whose ijth term provides the quantity of production factor i directly and indirectly used to satisfy final demand for sector j:

f • X = f • Ŷ + f • A • Ŷ + f • A 2 • Ŷ + • • • + f • A n • Ŷ + • • •
Each term of the right-hand side of the equation then corresponds to direct uses of production factors (at order 0, 1, 2 etc.). Finally, using the notation9 T (f ) k = fk , one can track which sector used production factor k at each order:

fk • X = fk • Ŷ + fk • A • Ŷ + fk • A 2 • Ŷ + • • • + fk • A n • Ŷ + • • •
The ijth term of matrices fk • A n • Ŷ is the quantity of production factor k directly used by sector i at order n, in order to ultimately satisfy final demand for sector j.

The latter formulation already provides a fine understanding of the links between production factors (for our concerns, environmental pressures) and final consumption. However, it is possible to go one step further by decomposing the ijth terms of matrices A n . This is what is called Structural Path Analysis [SPA, (Peters and Hertwich, 2006b)]:

I ij = ij A ij = A ij A 2 ij = X k A ik • A kj . . . A n ij = X k1 X k2 • • • X kn 1 A ik1 • A k1k2 . . . A kn 2 kn 1 • A kn 1 j
A Structural Path describes a particular succession of processes that leads to embody of certain quantity of production factor k in final demand:

f ki • Y i (5.12) f ki • A ij • Y j (5.13) . . . f ki • X k1 X k2 • • • X kn 1 A ik1 • A k1k2 . . . A kn 2 kn 1 • A kn 1 j • Y j
Paths of type (5.12) are interpreted as follows: final demand Y i for sector i requires the production of Y i units by sector i, for which the sector uses f ki • Y i units of production factor k. Paths of type (5.13) are interpreted as follows: final demand Y j for sector j requires the production of Y j units of j, in turn requiring the production of A ij • Y j units of sector i, for which sector i uses f ki • A ij • Y j units of production factor k. And so on. In practical uses, structural paths are ranked according to their values, which makes it possible to identify which paths contribute the most to the use of a production factor.

Absorbing Markov Chains

Markov chains

An introductory example: weather forecast

In a given city, the weather can only take two forms: it can be sunny or rainy. After a one year (365 days) observation, one has counted 265 sunny days and 100 rainy days. Among the 265 sunny days, 215 were followed by another sunny day and 50 by a rainy day. Among the 100 rainy days, 50 were followed by a sunny day and 50 by another rainy day as the following table shows: (m) the matrix encompassing the probabilities to have sunny or rainy weather on day n + m knowing only the weather on day n. By definition M (1) = M and, for instance, the probability to have a rainy day on day n + 1 knowing there is a sunny day on day n is:

Day n /
P (Day n+1 = rain | Day n = sun) = M (1)
sun,rain = M sun,rain

We now wish to compute the probability to have a rainy day on day n + 2 knowing there is is sunny day on day n. Two courses of events can lead to this situation: Day n+1 can be either sunny or rainy. Mathematically, this translates into: Following the same computation steps, one can readily show by induction reasoning that for any positive integer m, M (m) = M m . Moreover we know that M m converges because M is a regular stochastic matrix 10 . Since this limit M 1 exists, we can write:

P (Day n+2 = rain | Day n = sun) = M (
M 1 .M = M 1 M 1 .(M I) = 0
And M 1 can be computed by solving the system of equations (all terms of matrix M 1 .(M I) must be null). We obtain the following matrix:

Day n / Day n+1
sun rain sun 0.73 0.27 rain 0.73 0.27

Each term ij represents the probability of having weather j on Day n+1 knowing that the weather on Day n was i. We can see that the type of weather on Day n does not influence the result. The interpretation of this matrix is quite logic: according to the model, the probability of having a sunny day in a far future is independent of today's weather and is merely the probability of having a sunny day, nothing else considered (e.g. 265/365); the same of course goes for rainy days as well.

General formulation

The theory of Markov chains is presented, e.g., in [START_REF] Kemeny | Finite Markov chains[END_REF]. In what follows, we present what is needed for this thesis purposes.

A Markov chain is a random process that undergoes transitions from one state to another on a state space, that is, on the set of values the process can take (in our previous example, {sun, rain}). A process is characterized by:

• a state space,

• a transition matrix describing the probabilities of particular transitions,

• an initial state (or initial distribution).

10 A real square matrix is stochastic if its rows or columns are each summing to one. Square matrix A is regular if there exists an integer k>0 with all A k ij terms >0.

Here, we call the transition matrix P (M in the previous example). P i j represents the probability of being in state j at step n + 1 knowing that the process is in state i at step n. Following the probabilities' definition:

P ij 0 X j P ij = 1
The Markov process is formally described as a sequence of random variables (row vectors) X (n) indicating the probabilities of being in each state at step n (implying that

P i X (n) i = 1)
, where X (n+1) depends only on X (n) and on the transition matrix P : n) .P Induction reasoning readily shows that:

X (n+1) = X (
X (n) = X (0) .P n
where X (0) is a column vector describing the initial state of the system. Finally, the theorem of stochastic matrices indicates that if P is regular (P moreover being stochastic by construction), then the Markov sequence converges (the system eventually reaches a steady-state):

lim n!1 X (0) .P n = X (1) with X i X (1) i = 1
In our previous example, we for instance computed that, whatever the initial state:

X (1) = 0.73 0.27

Absorbing Markov Chains

General formulation

This section is derived from the book by [START_REF] Kemeny | Finite Markov chains[END_REF]

P = ✓ s n s s S 0 n s R Q ◆
S is the transition matrix between ergodic states, R is the transition matrix from transient to ergodic states and Q is the transition matrix between transient states. Note that the definition of the equivalence class of transient states implies that12 , lim n!1 Q n = 0. Furthermore, "if a state is the only element of an ergodic state, then it is called an absorbing state". In other words, a particular state i is called an absorbing state if an only if:

P ii = 1 P ij = 0 8j 6 = i
The canonical form of P can then be rewritten:

P = ✓ s n s s I 0 n s R Q ◆
Under this form, computing the powers of P is straightforward:

P n = ✓ s n s s I 0 n s (I + Q + ... + Q n ).R Q n ◆
As we saw before, P n ij can be interpreted as the probability for the process to be in state j if it started in state i and underwent n transitions. Since lim n!1 Q n = 0, we can compute the infinity order:

P 1 = lim n!1 P n = ✓ s n s s I 0 n s (I Q) 1 .R 0 ◆ Let us call N the matrix (I Q) 1
. The interpretation of P 1 is (i) that there is a probability of one for the process to end up in an absorbing state and (ii) that (N.R) ij is the probability for the process to end up in absorbing state j if it started in transient state i. This important result will be proven in two other ways in a moment. Before, we wish to provide an interpretation of matrix N by proving N ij is the average number of time the process is found in transient state j if it started in transient state i.

Let us call n

ij the random variable corresponding to the number of times the process is in transient state j if it started in transient state i. Let us also define u (k) ij the random variable worth 1 when the process is in state j after k transitions and 0 otherwise, with again a start in 118 Chapter 5. Formal links between methods aiming at tracing flows state i. Finally, we note E(X) the expectation of random variable X. We then have:

n ij = 1 X k=0 u (k) ij E(n ij ) = E( 1 X k=0 u (k) ij ) = 1 X k=0 E(u (k) ij ) E(n ij ) = 1 X k=0 (1 P k ij ).0 + P k ij .1 = 1 X k=0 P k ij E(n ij ) = 1 X k=0 Q k ij = (I Q) 1 ij = N ij
which proves our initial assertion. Let us now define B ij the probability that a process starting in transient state i ends up in absorbing state j. The probability of being captured in a single step is

P ij = R ij .
If that does not happen, the process can either end up in another absorbing state (in which case it will never reach state j) or go to transient state k. In this latter case, the probability it will end up in absorbing state j is by definition B kj . Therefore:

B ij = P ij + P ik .B kj B = R + Q.B B = (I Q) 1 .R = N.R
An alternative way of proving this relies on the following observation: each time the process is in transient state k, it has a P kj = R kj chance to be absorbed in state j. Given N ik represents the average number of times a process starting in state i passes through state k before being absorbed, this translates into:

B ij = X k N ik .P kj with k in the set of transient states B ij = X k N ik .R kj B = N.R

Interpretation in industrial ecology

Industrial ecology studies the circulation of material and energy flows through human societies, with a perspective of reducing throughput (upstream resource extraction and downstream emissions to nature). As we saw in the introduction, virtual flows linked to the consumer's responsibility cannot be measured; only physical flows linked to the producer's responsibility can be.

The purpose of the MFA process described in Chapter 3, was precisely to assess the physical flows linked to the extraction, transformation and consumption of a specific material.

Q = 0 B B B B B B B B @ a b c d e f h a 1 b 1 c 1 d 1 e 1 f 0.4 h 1 C C C C C C C C A R = 0 B B B B B B B B @ g i a b c d e f 0.6 h 1 1 C C C C C C C C A N = 0 B B B B B B B B @ a b c d e f h a 1 1 1 1 1 0.4 b 1 1 1 1 0.4 c 1 1 1 1 0.4 d 1 1 1 0.4 e 1 1 0.4 f 1 0.4 h 1 1 C C C C C C C C A B = 0 B B B B B B B B @ g i a 0.6 0.4 b 0.6 0.4 c 0.6 0.4 d 0.6 0.4 e 0.6 0.4 f 0.6 0.4 h 1 1 C C C C C C C C A
Finally, following the proofs provided in the previous section, we will from now on directly use the following results:

• It is interesting to put the AMC problem in canonical form (thus defining matrices Q and R),

• The ijth term of Matrix N = (I Q) 1 represents the average number of time one unit of i passes through j before being embodied in an absorbing state (usually a final consumption),

• The ijth term of Matrix B = N.R represents the fraction of one unit of i that ends up embodied in absorbing state j.

Linking IOA with AMC

The main motivation of this section is to apply IOA and AMC on a simple example [START_REF] Leontief | Environmental Repercussions and the Economic Structure: An Input-Output Approach[END_REF] in order to illustrate the links between the two. In particular, [START_REF] Duchin | Embodied resource flows in a global economy[END_REF] state that "the explicit exposition in Peters and Hertwich (2006b) makes clear that the SPA paths [structural paths deriving from IOA] bear no direct relation to the AMC network that joins origin and destination nodes", which can be misinterpreted as a close relationship indeed exists between IOA and AMC. y-products (as well as cernpaid-for natural inputs) o the network of physical vern the day-to-day operaic system. The technical een the levels of desirable tputs can be described in oefficients simi'lar to those structural i'nterdependence lar branches of production s a matter of fact, it can facture, and Households. Each one of the two industries absorbs some of its annual output itself, supplies some to the other industry and delivers the rest to final consumers -in this case represented by the Households. These inter-sectoral flows can be conveniently entered in an input-output table. For example: Numbers of figure 5.3 can be interpreted as follows: among the 100 bushels of wheat produced, 45 serve intermediate consumption (25 for agriculture and 20 for manufacture), and 55 are destined to final consumption. We define the following notations:

• Z is the matrix of intermediate consumption,

• Y is the vector of final demand,

• X is the vector of production (total output),

• A = Z. X 1 , is the matrix of technical coefficients (representing the economic "recipe").

We saw that:

X = Z.1 + Y = A.X + Y
and that the Leontief matrix L is defined by:

X = L.Y with L = (I A) 1
L ij is the production of sector i needed to sustain one unit of final demand of sector j. Xij = (L. Ŷ ) ij is the production of sector i needed to sustain final demand of sector j.

We now extend the model to environmental pressures. These can either be resource use or emissions of pollutant: in both cases, these can be seen as production factors (they play a role similar to labor or capital). In the following, we take the example of resource use and we define the following elements:

• f is a row vector representing the intensity of resource use per unit of production in each sector; here it is considered as input data,

• F = f. X is a row vector with F j representing the total use of resource by sector j, • m = f.L, is a row vector with m j the amount of resource needed to sustain one unit of final demand of sector j,

• ' = m. Ŷ , with ' j the amount of resource needed to sustain final demand of sector j,

• F tot = '1 = F.1, with F tot the total amount of resource extracted and consumed13 .

In our example, results are the following: For later purposes, we extend every matrix to incorporate the resource sector:

Z = ✓ 25 20 14 6 ◆ Y = ✓ 55 30 ◆ X = ✓ 100 50 ◆ A = ✓ 0.
Z ext = ✓ 0 F 0 Z ◆ Y ext = ✓ 0 Y ◆ X ext = ✓ F tot X ◆ A ext = ✓ 0 f 0 A ◆ L ext = ✓ I m 0 L ◆ 5.4.

Basic AMC notations and application to the same example

Based on results from section 3, we directly compute matrices Q, R, N and B. Remember that the proportions of direct flows among the transient states (trade between industries) are represented by matrix Q, and those from transient to absorbing states (final consumption) are represented by matrix R.

Q = Ā with Ā = X 1 Z = X 1 A X R = X 1 Ŷ Q • 1 + R • 1 = 1 N = 1 X k=0 Q k = (1 Q) 1 = (I Ā) 1 = X 1 L X B = N • R
Remember that the term B ij is the proportion of sector i eventually embodied in final product j. We then define the following elements to consider environmental pressures (again, here we only consider a single resource14 ):

• f = F/F
tot is a row vector with fj the proportion of total resource extraction directly used by sector j,

• ↵ = fN = m X/F
tot is also a row vector, with ↵ j representing the average number of time one resource unit passes through sector j before being embodied in final consumption,

• = fNR = fB = ↵R = m Ŷ /F
tot is also a row vector, with j the proportion of resource eventually embodied in final consumption of sector j. Note that, as for the IOA case, we can incorporate the resource sector directly in the matrices:

Q ext = ✓ 0 f 0 Q ◆ = X ext 1 A ext X ext R ext = ✓ 0 R ◆ N ext = (1 Q ext ) 1 = ✓ I ↵ 0 N ◆ = X ext 1 L ext X ext B ext = ✓ B ◆
Now that basic vectors and matrices have been defined and interpreted, we can build correspondences between the two approaches.

Upstream and downstream perspectives

We schematize the national economy of Leontief's example in figure 5.4. It is noteworthy that flows a and b correspond to the producer's point of view, while flows c and d correspond to the consumer's point of view. Corresponding formulas are presented in table 5.1. These formula show that the IO model can be seen as "demand-driven": one starts from intermediate or final consumption (Z or Y) and multiplies it by coefficients accounting for upstream resource requirements. On the contrary, the AMC model appears as "resource-driven": one starts from the total resource extraction (F tot ) and applies transition coefficients to account for the fact that the resource flows from sectors to sectors until final consumption.

Point of view IOA AMC Production a = F1 = f1X1 b = F2 = f2X2 a = Ftot f1 b = Ftot f2 Consumption c = '1 = m1Y1 d = '2 = m2Y2 c = Ftot 1 d = Ftot 2
In their article, [START_REF] Skelton | Mapping flows of embodied emissions in the global production system[END_REF] propose an alternative representation of the system, by decomposing production layers 15 . They argue this representation is useful because it provides intermediate points of view between production and consumption. We use it to represent our problem (figure 5.5). The authors already provide the expression of each flow in the IOA framework. We start by expressing them in the AMC framework (table 5.4).

Figure 5.5: Flows of resources from consumption, through production layers, to original production. Light shades correspond to direct resource use by sectors and dark shades to resources embodied in products. For instance, in order to provide product 1 to final consumption (flow 1), sector 1 directly uses resources (flow 6) but also requires inputs from sector 1 and sector 2 that embody a certain amount of resources (flows 7 and 8) and so forth. refers to the kth row of matrix M, that is, a row vector.

Flow IO AMC Value 1 '1 = m1Y1 '1 = Ftot 1 42.62 2 '2 = m2Y2 '2 = Ftot 2 17.38 3 F1 = f1X1 F1 = Ftot f1 50 4 F2 = f2X2 F2 = Ftot f2 10 5 f2Y2 F2R22 = Ftot
Finally, we provide the link between representations from figures 5.4 and 5.5. If P L k i represents the amount of resources embodied in the production layer of sector i at order k (shown in figure 5.5) and F low ij and Node i correspond to what is shown in figure 5.4, then:

1 X k=0 F low P L k+1 i >P L k j = F low ij = total resources embodied in f lows f rom sector i to sector j, 1 X k=0 P L k i = Node i = total resources embodied in sector/node i.
As a proof, we sum the interlayers flows between sectors i and sector j. Again, we note A j: the jth row of matrix A:

m i A ij Y j + 1 X k=0 m i A ij A j: A k Y = m i A ij (Y j + A j: X) = m i A ij X j = m i Z ij = F low ij
We see that providing different representations of the same object enables a better understanding of its functioning. Depending on the question tackled, one representation may be better suited. We want to end this section with the correspondence between structural path analysis in IOA and AMC 16 . As explained by Peters and Hertwich (2006b), these structural paths pro-5.5. Transforming SUT into a single square matrix 127 vide the detailed linkage between production and consumption activities. In Leontief's example we saw that the final consumption of 55 bushels of wheat required the use of 42.62 units of resource. As explained in section 2.2, Structural Paths (SP) in fact correspond to the finest decomposition of these 42.62 units. The order of the SP corresponds to the production layer where the initial resource extraction occurred. SPA are often expressed using IOA notations, but not, to our knowledge, using AMC notations. We show the equivalence between the two in table 5.5.

SPA order IO AMC Application 0 fiYi fiXi/XiYi = FiRii 8i 1 fiAijYj fiQijXi/XjYj = FiQijRjj 8i, j 2 fiAijA jk Y k fiQijQ jk Xi/X k Y k = FiQijQ jk R kk 8i, j, k ... ... ... ... Total mY = Ftot Ftot sum of

all possible paths

Table 5.5: Classical SPA in IOA: IO and AMC formulation. Again, we note that paths must be interpreted upstream in the IOA formulation and downstream with the AMC formulation.

Transforming SUT into a single square matrix

In the course of the presentation of the SC-MFA model (Chapter 3), we showed the Supply-Use Tables (SUT) framework was very well suited to organize MFA data. SUT, however, are not square matrices, which is a requirement when one wants to undertake IOA or AMC (because of matrix inversion). To make this transformation, a first option is to move from product-byindustry matrices to product-by-product (M p ), or industry-by-industry matrices (M i ). The construction of these matrices (as well as underlying hypotheses) is discussed in chapter 5 of [START_REF] Miller | Input-output analysis: foundations and extensions[END_REF]. However, matrices M p and M i contain less information than the original SUT. In order to conserve all the information, it is possible to build either of the two following matrices:

M ip = ✓ industries products industries 0 S t products U 0 ◆ M pi = ✓ products industries products 0 U industries S t 0 ◆
This is the option chosen in the next Chapter.

The concepts presented in this chapter will be implemented in Chapter 6 to trace cereal flows and associated environmental pressures. As we hope we achieved to show, there is a direct correspondence between IOA and AMC, so either framework could have been used. However, using AMC seems more natural when the main concern is to trace flows Abstract. France is the second largest exporter of cereals in the world. Although the cereals supply chain is an asset for the country's economy and employment, it is at the same time responsible for a number of pressures on the local and global environment including greenhouse gases (GHG) emissions and stresses on water quality and quantity. This article aims at evaluating this situation from an environmental point of view by linking productions occurring in French regions with consumptions occurring in France and abroad. Based on previous work on Material Flow Analysis, we use an Absorbing Markov Chain model to study the fate of French cereals and link worldwide consumptions to environmental pressures along the supply chain, that is, induced by production, transformation or transport. The model is based on physical supply and use tables and distinguishes between 21 industries, 22 products, 38 regions of various spatial resolution (22 French regions, 10 countries, 6 continents) and 4 modes of transport. Energy use, GHG emissions, land use, use of pesticides and blue water footprint are studied. Illustrative examples are taken in order to demonstrate the versatility of the results produced, for instance: Where and under what form does local production end up? How do regions compare relatively to their production and consumption footprints? These results are designed to be a first step towards scenario analysis for decision-aiding that would also include socio-economic indicators. Examples of such scenarios are discussed in the conclusion.

Introduction

The producer-centric approach to environmental impacts of economic activities was historically the first developed. [START_REF] Lenzen | Shared producer and consumer responsibility ? Theory and practice[END_REF] suggest it may be because questioning consumer preferences was not in line with a free-market philosophy. A complementary explanation is that the producer's responsibility is the most easily and objectively traceable as it concerns flows that can be physically observed on site; on the contrary, a series of allocation hypotheses are needed in order to trace consumer's responsibility. In today's economy, intensively relying on international trade, environmental accounts from both perspectives are a necessity to guide decision-making and prevent a simple externalization of impacts. In the past two decades, an important research effort was put on the development of Input-Output Analysis (IOA) in order Chapter 6. Environmental pressures embodied in the French cereals supply chain to associate final consumption expenditures of households and administrations with the worldwide production of goods and services they trigger. Of all environmental pressures, greenhouse gases (GHG) emissions were the most studied (Peters and Hertwich, 2006a) [START_REF] Wiedmann | A carbon footprint time series of the UK -results from a multi-region input-output model[END_REF], although research also targeted water use [START_REF] Guan | Assessment of regional trade and virtual water flows in china[END_REF], land use [START_REF] Yu | Tele-connecting local consumption to global land use[END_REF] or material flows [START_REF] Bruckner | Materials embodied in international trade: Global material extraction and consumption between 1995 and 2005[END_REF] to name only a few. Socio-economical aspects were also studied [START_REF] Simas | Labor embodied in trade[END_REF]. The second path of research to link producer's and consumer's responsibilities is the coupling of Material Flow Analysis (MFA) with Life Cycle Assessment (LCA), or more simply with ratios of pressure intensity [START_REF] Rochat | Combining material flow analysis, life cycle assessment, and multiattribute utility theory[END_REF]. This is for instance the approach followed in the classical calculation of the Ecological Footprint [START_REF] Wackernagel | National footprint and biocapacity accounts 2005 -the underlying calculation method[END_REF]. Each method having its own drawbacks (typically, trade of services is not accounted for in the MFA-based approach, while IOA can sometimes lead to questionable results [START_REF] Kastner | Cropland area embodied in international trade: Contradictory results from different approaches[END_REF]), the choice between the two relies on the research question and on data availability. Our study is based on supply chain material flows because of our focus on the regional level and of the level of detail we aim at1 .

A supply chain is by definition a group of sectors organized to produce, transform and distribute specific goods to consumers. It is therefore an obvious object of study when it comes to analyzing the links between production and consumption. [START_REF] Leigh | Industrial ecology, industrial symbiosis and supply chain environmental sustainability: a case study of a large UK distributor[END_REF] propose a literature review on environmental approaches to sustainable supply chain management, that includes environmental management, design for environment, product stewardship, green purchasing, reverse logistics, recycling, reuse and remanufacturing. This body of literature studies the supply chain from a company's perspective. In a complementary way, the present work adopts a territorial point of view and is primarily intended for institutional decision makers at regional and national levels. [START_REF] Cazcarro | Environmental footprints and scenario analysis for assessing the impacts of the agri-food industry on a regional economy[END_REF] propose a similar perspective by focusing on footprints and scenario analysis of the agro-industry of a Spanish region. They underline the importance of articulating regional and national strategies, stressing Spanish regions have major competences regarding the local economy and environment. While France remains more centralized than Spain, the jurisdiction of local territories tends to expand. [START_REF] Calame | Essai sur l'oeconomie[END_REF] insists on the pivot role territories and supply chain could play in a transition to sustainability at local, national and international scales, benefiting from both horizontal (territorial coherence) and vertical (chain of production) integration. Moreover, they argue that these two actors are well adapted to a cooperative vision of the economy.

The present article is the second step of a project aiming at analyzing local supply chains from an economic, social and environmental perspective for decision-aiding. Here, our goal is to analyze environmental pressures along supply chains, that is from the producer's to the consumer's viewpoint, to see what pressures are internalized or externalized by French regions and foreign countries. This article follows a study which produced Material Flow Analysis (MFA) on every regional level by downscaling the national MFA (Courtonne et al., 2015). We shortly present these results in the methodology section as they are the starting point of the present work.

Although the methodology developed here could be applied to any supply chain or region, we implement it on the case of the French cereals supply chain. Cereals are, in terms of weight of production the most important agricultural good in France. The supply chain is a significant contributer to the national economy with a turnover of more than 50 billion euros and 500,000 jobs. It is also the largest contributer to the positive trade balance of the country's agro-industrial sector, along with wine (FranceAgriMer, 2012). Orientations for the development of the supply chain were recently proposed by the ministry of agriculture and confirmed this strategic role of exports. The model is focused on French regions: total productions, trade and consumptions of foreign countries are not studied, only the portion linked to the French supply chain is, that is, either imports of French products or exports of local production to France. According to FAO statistics, France was the 7 th largest cereals producer in the world in 2011 (after China, the United States, India, Russia, Indonesia and Brazil) but the 2 nd largest exporter (after the USA). Our study therefore encompass about 3% of global production and 11% of global trade of cereals.

We study five environmental pressures that are especially relevant for the cereals supply chain: energy consumption, GHG emissions, land use, use of pesticides and blue water consumption. Both global (for instance GHG emissions) and local (for instance use of pesticides) environmental pressures were included in order to aim at a holistic view of the situation. A recent assessment of the implementation of the Water Framework Directive in France revealed that rivers' contamination with pesticides was especially high in cereals-growing regions (SOeS, 2015a). With about 90 Mt CO 2 eq., agriculture is responsible for nearly one fifth of French greenhouse gazes emissions2 (SOeS, 2015b). Tranport and of transformation industries are also responsible for emissions through their use of energy. According to [START_REF] Ercin | The water footprint of france[END_REF], crop growing accounts for half of the French blue water footprint of production. Cereals represent 59% of this half, corn representing 50% on its own (the last 9% are shared between rice, wheat, triticale, barley and oats). Production of corn ranks first in the causes of water scarcity in the summer months in many regions, especially in Midi-Pyrénées, Aquitaine, Poitou-Charentes and Centre.

The first section is dedicated to the presentation of the methodology and of the datasources. We present the results in the second section laying the emphasis on the types of questions can be tackled with the model: What is the fate of the regional production? What are the supply areas of the regional consumption? What pressures are associated to each life-cycle stage? What pressures are embodied in a specific consumption? What are the production and consumption footprint of a region? What are the main paths between production and consumption? How do regions compare relatively to their per-capita footprint of consumption? We then discuss the limits and potential leads to improve the model. The concluding section summarizes the main features of the method developed for the present paper as well as some important findings, before outlining how such results can be used for actual decision-help, in particular through the discussion of energy transition and land use scenarios for France at the 2050 time horizon.

Materials and methods

Studying how environmental pressures flow from producers to consumers is done in 3 steps:

• Reusing and extending an existing MFA model at the level of French regions,

• Tracking flows downstream using an AMC model with transport sectors,

• Coupling material flows with associated pressures on the environment all along the supply Chapter 6. Environmental pressures embodied in the French cereals supply chain chain, that is pressures generated for the production of raw materials, pressures generated by transformation industries and pressures generated by freight.

Coupling of MFA with Markov chains modeling was for instance previously done by [START_REF] Eckelman | Markov chain modeling of the global technological lifetime of copper[END_REF] (for a discussion on the relationships between AMC, IOA and MFA see [START_REF] Eckelman | Exploring the global journey of nickel with markov chain models[END_REF]). This methodology can be applied to any type of product; here it is specifically applied to the French cereals' supply chain.

An MFA on cereals in every French region

We base the model on previous results of the authors (Courtonne et al., 2015). MFAs on the cereals supply chain in the 22 French regions were produced in the form of reconciled physical supply and use tables by downscaling the national MFA. 19 products (raw materials, intermediate and end-products) and 18 industries were taken into account. The period studied was the annual average between years 2001 and 2009 and is therefore the same in the present article. In this previous work, theses MFAs were limited to physical cereal flows, for instance flows of bread were considered because they physically embody cereal grains but flows of livestock products were left out, meaning that the model considered livestock consumption as a final consumption. This makes sense in a pure MFA study but becomes problematic when one is interested in studying and allocating environmental pressures: typically, husbandry regions would then have a high consumption footprint even if their animal products are consumed elsewhere. In order to overcome this issue, three animal products were included in this extension of the model: meat, milk (including milk products) and eggs. Balanced MFAs at the level of French regions were obtained using the methodology described in Courtonne et al. (2015) and data sources from the French Ministry of Agriculture, from customs data and from the SitraM database for inter-regional trade. All details regarding the classifications used are available in supplementary material.

An AMC model to track flows from producers to consumers

The next step is to study the fate of cereals products and the paths they take in the economy. Typical questions are: Where and under what form does a grain of wheat produced in region A end? What productions and transports were needed in order to consume 1 kg of bread in region B? Here, the two questions respectively adopt a downstream and an upstream perspective. The AMC model implemented is inspired by the one proposed by [START_REF] Duchin | Embodied resource flows in a global economy[END_REF]. The main difference is that we build the tables directly from our MFA data and not from Input-Output tables. A smaller difference is in the way we deal with transport sectors (we associate each transport flow with the product traded whereas they rather model the trade of transport services between regions).

Flows through a (spatialized) supply chain can be seen as changes of state of the quantities involved. After being normalized, they can be interpreted as transition probabilities. Note that the underlying assumption here is a perfect blend between local production and imports: without additional information we assume once a product is available in a region, its use is independent from its geographical origin. As explained by [START_REF] Duchin | Embodied resource flows and product flows[END_REF], "for any system represented by n states, the parameters of an AMC are the probabilities of directly transitioning from one state to another; they are contained in an n ⇥ n transition matrix M ". M ij describes the likelihood of transitioning from state i to state j. Therefore the sum of any row equals 1. State i is called an absorbing state if M

ii equals 1, meaning it can no longer be exited. In our model, this is the case for end-products that are consumed and for losses. The M matrix can be put into the following canonical form [START_REF] Kemeny | Finite Markov chains[END_REF]:

M = ✓ Q R 0 I ◆ (6.1)
In equation 6.1, Q ij represents the proportion of flows in transient state i directly moving to transient state j. This is the case when an industry supplies a product, when a product is used by an industry and when a product is exported from one region to another. Similarly, R ij is the proportion of flows from transient state i directly moving towards absorbing state j.

Below we give more details on the content on the Q and R matrices. We define the following elements:

• 1 is a summation vector (column vector filled with 1). Its size is contextual.

• n is the number of regions.

• p is the number of products.

• q is the number of industries.

• t is the number of transport modes.

• S r is the domestic supply matrix of region r of size (p,q).

• S r = S r 1 is a column vector representing the local supply of each product whatever the producing industry.

• (S r ) T = (S r ) T 1 is a column vector representing the total production of each industry of region r, whatever the product.

• U r is the domestic use matrix of region r of size (p,q).

• U r = U r 1 is a column vector representing the use of each product by industries of region r, whatever the consuming industry.

• E r,s vector of exports from region r to region s of size p.

• T r,s matrix of transport from region r to region s of size (t,p)

• T r = P s T r,s matrix of transport from region r to all other regions.

• T r = T r 1 is a column vector representing for each transport mode the total transport from region r.

• C r is the vector of consumption of region r of size p.

• Z r is the vector of total supply of region r of size q + p + t. Chapter 6. Environmental pressures embodied in the French cereals supply chain Vectors Z r are composed of 3 parts:

Z r = 0 @ 1 q Z r 1 p Z r 2 t Z r 3 1 A Z r 1 = h (S r ) T i Z r 2 = ⇥ S r + P s E s,r ⇤ = ⇥ U r + P s E r,s + C r ⇤ Z r 3 = ⇥ T r ⇤
Matrices T r,s are computed based on 3 elements:

• E r,s trade flows from region r to region s, not necessarily expressed in real weight, for instance we use the cereals grain equivalent unit, of size (p,1),

• w vector of conversion ratios from trade unit to real weight, of size (p,1),

• D r,s matrix representing distances of transport between regions, of size (t,p): each mode of transport is one row of the matrix and each product is a column. For international flows, we estimate the distance from/to the country of loading/unloading based on the mode of transport. Equation 6.2 therefore illustrates the properties of matrices D r,s for international transport. For domestic inter-regional flows, we exploit the SitraM database providing information both in tonnes and tonnes.kms for each good, mode of transport, origin and destination. Hence it is possible to compute average distances (tonnes.kms / tonnes) for each group defined by a good, mode of transport, region of origin and of destination. These distances are good estimates of distances from facilities to facilities.

The following properties only hold when r or s are foreign regions, they don't in the case of French interregional trade:

D r,s = D s,r D r,s m,j = D r,s m,k 8 products j, k (6.2)
The transport matrices, which show results in weight.distances (typically tonnes.kms) are then computed as follow (note that we use the hat symbol to refer to the diagonal matrix created from a vector):

T r,s = D r,s ŵ Êr,s

The Q and R matrices presented below are respectively of size (n.(q + p + t), n.(q + p + t)) and (n.(q + p + t), n.p). Q can be partitioned:

Q = 2 6 6 6 6 6 6 4 Q 11 . . . Q 1r . . . Q 1n . . . Q r1 . . . Q rr . . . Q rn . . . Q n1 . . . Q nr . . . Q nn 3 7 7 7 7 7 7 5
with

Q rr = 0 @ q p t q 0 ( Ẑr 1 ) 1 (S r ) T 0 p ( Ẑr 2 ) 1 U r 0 0 t 0 0 0 1 A 6.2

. Materials and methods

135

and with

Q rs = 0 @ q p t q 0 0 0 p 0 ( Ẑr 2 ) 1 Êr,s 0 t 0 ( Ẑr 3 ) 1 T r,s 0 1 A R is also partitioned R = 2
R rr = 0 @ p q 0 p ( Ẑr 2 ) 1 Ĉr t 0 1 A
Then two matrices of interest can be computed, N and B:

N = (I Q) 1 B = NR (6.3)
Each row i of matrix B can be interpreted as the fate of sector/product i. For instance, the B ij term is the proportion of i that is finally embodied in region-product j. As we will show it in the next section, it is interesting to aggregate the terms either by product type or by region. If we define the Z vector as equation 6.4, we can compute matrix ẐB, with the ij th term representing the amount of i finally embodied in region-product j. Finally, we can compute matrix L 3 as defined in equation 6.5 4 and its ij th term will be interpreted as the amount of i needed in order to consume one unit of region-product j.

Z = 2 6 4 Z 1 . . . Z n 3 7 5 (6.4) L = Ẑ B Ĉ 1 with C = 2 6 4 C 1 . . . C n 3 7 5 (6.5)
Table 6.1 presents the size of the main variables/matrices used.

3 We deliberately name this matrix L because it can be seen as an equivalent of the traditional Leontief matrix in IOA. 4 Elements equal to zero in vector C are replaced by ones in order to make Ĉ inversible ; the same is done on Z r vectors. This operation is purely technical and has no impact on the results. Chapter 6. Environmental pressures embodied in the French cereals supply chain Data sources to inform environmental stakes of the supply chain As explained in the introduction, we study five environmental pressures that are especially relevant for the cereals supply chain: energy consumption, GHG emissions, land use, use of pesticides and blue water consumption. [START_REF] Berger | Methodological challenges in volumetric and impactoriented water footprints[END_REF] show drawbacks of volumetric water footprints, arguing that numerically smaller footprints can cause higher impacts.

In particular they criticize the aggregation of green and blue water footprints by questioning the definition of water consumption. In this work, we build on previous diagnosis about regional water stress, and study the blue water footprint of cereals, that is the withdrawals of surface or groundwater. Table 6.2 presents the data sources used for estimating pressures from the producer's viewpoint.

Extension of the AMC model to environmental pressures Let ↵ be the number of environmental pressures under study, 5 in our case. We define matrix F so that F ij represents the direct emission of environmental pressure i by sector-region j. F i is the total environmental pressure i emitted, whatever the sector or region. Finally, f matrix is defined as:

f ij = F ij /F i .
We then extend our Q and R matrices as follow, in line with Duchin and Levine (2010):

Q 0 = ✓ ↵ dim Q ↵ 0 f dim Q 0 Q ◆ R 0 = ✓ dim R ↵ 0 dim Q R ◆ Z 0 = ✓ 1 ↵ F dim Q Z ◆
We compute matrices N 0 , B 0 the same way as explained above:

N 0 = ✓ ↵ dim Q ↵ I fN dim Q 0 N ◆ B 0 = ✓ dim R ↵ fB dim Q B ◆ The i th row of B 0 (i  ↵)
indicates in what consumption environmental pressure i is eventually embodied, summing all the paths taken from production to consumption. Similarly to IOA, it is however interesting to compute the main paths contributing to this sum, using the Taylor decomposition of matrix N 0 . We describe the algorithm used for this purpose in the Supplementary Material.

Results

In this section we present a range of questions than can be tackled with the model described above, stating each time what matrices are used. It is meant to be illustrative and therefore focuses on a few examples only. More comprehensive results are available in the Supplementary Material. The same methodology could be applied to other supply chains, territories and environmental pressures. We then discuss the limits of the model and some potential leads to improve it.

Studying the fate of a specific product As explained before, the model is focused on France and its main goal is to track resources and pressures downstream. In order to illustrate this, we show the fate of corn grown in the Midi-Pyrénées region. This example is of particular interest because water is becoming a major stake in this region both in terms of quality (in particular, pollution by pesticides) and quantity. We use matrix B to produce the results. They indicate that nearly two thirds of the corn is embodied in the consumption of foreign countries, pointing to the internalization of environmental impacts in Midi-Pyrénées. Figure 6.1 shows the regions of destination. It is also interesting to study under what form the corn is eventually consumed. 49% remains under the form of grain, meaning it is exported, lost or used for seeds. Animal products account for 48% of the total (43% for meat only, 4% for milk and 1% for eggs). Since the fate of exported grains is not modeled, this number is underestimated, given most of the exported corn is likely to be fed to livestock. Finally starch and canned corn respectively represent 2% and 1%.

Studying the supply area for a specific product Another way to exploit the results is to estimate supply areas for specific products. Starting from a final product, it is interesting to trace back earlier production stages and to compute average supply distances at each stage. This gives an idea of the degree of dependency of the region regarding the consumption of this final product. To illustrate this, we use matrix L along with distances matrices to analyze the supply of bread in the Provence-Alpes-Côte-d'Azur region (PACA). Figure 6.2 shows that the more we go back in the supply chain the further supply areas are located: average supply distances for bread, flour and wheat are respectively 55 km, 195 km and 470 km (distance is considered null for products originating from the PACA region itself).

Identifying the main life-cycle-steps producing environmental pressures Table 6.3 shows total amounts of pressures produced (whatever the region of production) and splits them among the production, transformation and transport phases using matrix F f. In all cases, the production phase clearly stands out as the most critical. Still, in the case of GHG, transformation and transport are significant with nearly one third of total emissions. Regarding the transport sector, road freight ranks first as GHG emitter (79% of the emissions with 28% of the tonnes kilometers), followed by sea freight (19% of the emissions with 66% of the tonnes kilometers). Domestic transport only represents 16% of total tonnes kilometers although it amounts to 64% of the tonnage traded. The production phase represents a larger part in energy consumption than in GHG emissions because of a biomass-based energy consumption at the farm, according to the LCA database. Regarding the blue water footprint of transformation region (for 14%). 13800 kcal are embodied in 1 kg of meat; by comparison, the caloric value of this kg of meat is about 2000 kcal. We compared pressures associated with Italian consumption with other regions and saw that indices do not vary a lot (generally more or less 10%) except for the ones related to blue water footprint and transport. This is explained by the fact that the production phase is the most significant one, as we saw above. The difference in blue water footprint intensities can be explained by the variability in cereal mix fed to livestock (corn being a lot more water-intensive than wheat).

Identifying the main paths linking production to consumption

We use a structural path analysis (SPA) algorithm, inspired by Peters and Hertwich (2006b), on matrix B in order to extract the main links between production of environmental pressures and final consumption of products. The algorithm is described in Supplementary Material. Table 6.5 presents the top five paths linked to GHG emissions as well as three other paths illustrating different emission patterns. The first 30 paths are linked to exports and contribute to nearly 10% of total GHG emissions of the supply chain. The largest path for freight emission is the one representing exports of corn from Aquitaine to Spain by road. The path of emissions due to the growing of wheat in Bretagne, to feed animals for meat consumption in Ile-de-France, is the main emission path related to French consumption. Finally the main path related to pressures occurring during the transformation step is the emission of craft bakeries in Ile-de-France for local consumption. The first 100 paths (listed in Supplementary Material) account for 17% of total emissions.

Building environmental accounts from the producer's and from the consumer's perspective For each region, we can build environmental accounts from the producer's (what is emitted/used by the productive activity of the region) and consumer's (what is emitted/used to satisfy the final consumption of the region) perspectives. For this purpose we respectively use matrices F f and F fB. For instance, results regarding the land use footprint indicate that Centre (FR) and Poitou-Charentes (FR) have the two largest footprints of production with respectively 1.25 Mha (12% of the total) and 720 kha (7%), whereas Ile-de-France (FR) and Italy have the two largest footprints of consumption with respectively 834 kha (8% of the total) and 741 kha (7%). These footprints can be seen as Ecological Footprints of cropland from the production Chapter 6. Environmental pressures embodied in the French cereals supply chain and consumption perspectives [START_REF] Wackernagel | National footprint and biocapacity accounts 2005 -the underlying calculation method[END_REF], although results are presented in real surface and not in surface of average bioproductive land. Of course, we can check that the total footprint of production is equal to the total footprint of consumption. Accounts for all regions and pressures are shown in supplementary material: it can be noted that rankings vary little except for the case of the blue water footprint, which is mostly driven by corn production and consumption.

Assessing net internalization of environmental pressures and identifying main trade partners at national and regional scales.

A net-export footprint can be computed as follows based on the production and consumption footprints: F ootprint net exports = F ootprint production F ootprint consumption . A positive value indicates that the region under study internalizes more environmental pressures than it externalizes and vice-versa. Results show that France is a net exporter of (that is internalizes) about 175 TWh of energy, 17.7 Mt CO 2 eq. of GHG emissions, 4.41 Mha of land, 8.98 kt of pesticides, 550 Mm 3 of blue water. In the case of land use, the main trade partners contributing to the net export balance are European countries (67%) followed by Africa (25%) and Asia (8%), net trade being almost negligible with north and south America and with Oceania. Finer resolution can be obtained by looking at regional results as shown in Figure 6.3, and is available in supplementary material.

Comparing environmental efficiency of different regions' consumptions

Knowing the population of each region, we can then estimate per-capita consumption footprints: detailed results are available in Supplementary Material. On average the French per-capita footprint linked to the cereals supply chain is about 3.1 MWh, 0.33 t CO 2 eq., 780 m 2 , 0.15 kg of active substance of pesticides and 20 m 3 of blue water. The two main French regions in terms of population are Ile-de-France and Rhône-Alpes (with respectively about 11.6 millions and 6.1 millions inhabitants in 2007). Looking at these two regions, per capita footprints are the same in the case of GHG emissions and the maximum difference is obtained in the case of blue water Chapter 6. Environmental pressures embodied in the French cereals supply chain with 12%. Given the differences may be in the range of the model's uncertainties, it would be premature to draw precise conclusions based on these results. However, they show French regions have relatively homogeneous footprints of consumption.

Limits of the model and perspectives of improvement

In this section, we discuss the limits of the model and some leads for future developments.

• The model is limited to the study of the cereals supply chain. For instance, soy cakes fed to livestock are not taken into account because they are oleaginous. Two levels of improvement can be targeted in the future to overcome this limitation. The first one is to apply the methodology on all the main agri-food supply chains (oleaginous, sugar, wine, fruits and vegetables, animal breeding) in order to have a comprehensive view on the food issue. The second one would be to extend the model to the main industrial supply chains (such as energy, wood, concrete, steel and chemistry). The obtention of such physical, highly desagregated supply/use table is of course a longer-term project.

• The model is focused on France. Foreign countries are only considered for their role of outlet or provider and their interior supply chain is not fully depicted; nor is trade between them. Including each country/continent's supply chain would be useful to track downstream flows to their final destination, although a priori it wouldn't be possible to reach the same level of disagregation as in the case of France. FAO statistics could be used to implement this idea.

• On a similar topic, the model could be compared and enriched with the works of [START_REF] Kastner | Tracing distant environmental impacts of agricultural products from a consumer perspective[END_REF] and [START_REF] Godar | Towards more accurate and policy relevant footprint analyses: Tracing fine-scale socio-environmental impacts of production to consumption[END_REF] that depict methods for enhanced tracing of international trade and subnational footprints.

• Intra-regional freight is not taken into account because of a lack of information: the distance between local crop fields and transformation industries in the same region is neglected, only inter-regional and international distances are estimated. The fact that French regions have developed specialization strategies, consequently relying a lot on inter-regional trade, makes it less problematic.

• Transport of consumers to local shops or to supermarkets is not considered. Rather than a technical impossibility, it was left out of the model because the authors did not find useful for policy-making to study the part of the travel to the supermarket that should be allocated to cereal products. It is however an important question once the scope of the study widens to the full basket of a household.

• Currently, part of the pressures related to inputs at the farm are not traced back to their geographical origin since LCA results are directly applied. This is for instance the case for GHG emissions occurring during the production of fertilizers, which may be located elsewhere.

• Uncertainties associated with MFA results were previously estimated. Adding confidence intervals to environmental pressure ratios would make it possible to compute interval of confidence of the model's outputs which would be useful for a better interpretation of the results. Work is underway to estimate the missing intervals of confidence.

Conclusion

The goal of this article was to show the potentialities of coupling supply chain MFA with AMC and environmental pressures. Adopting a downstream perspective through the use of AMC seems well-adapted to exporting regions. The implementation of the methodology on the case of French cereals leads to interesting results that could serve as a starting point for decision-aiding. The supply chain object is well adapted to understand what life-cycle stages (production, transformation, transport) are predominant regarding each environmental pressure: regarding GHG, it appears for instance that the transport of goods, mostly through road freight, is not negligible, which raises the question of fostering rail and river transport between French regions and between France and its direct neighbors. Given the relatively small variability of cultural practices in France, land use appears to be a good proxy of other pressures such as the use of pesticides. On the contrary, the blue water footprint is driven by corn production and therefore concentrates on specific regions. While previous studies have pointed out the major responsibility of corn production regarding water scarcity in these regions [START_REF] Ercin | The water footprint of france[END_REF], the analysis of the fate of corn production leads to two lines of thoughts. First, consumption of animal products is by far the main driver of production, and prospective scenarios of dietary changes should therefore be examined. Second, Spain appears as the main importer of French corn and consequently externalizes the associated pressures on the local environment: in particular qualitative and quantitative stresses put on water resources through the use of pesticides and irrigation. This situation points to a limit of the study: only one supply chain was taken into account so we lack information on "net trade of pressures" all activities considered. For instance, in return, France imports a lot of fruits and vegetables from Spain, grown in regions with even greater water-scarcity. Hence, a comprehensive view with a multi-supply chains approach is needed in order be more policy-relevant. Linking this study with recent works on Spanish agri-food industries and mutli-regional input-output tables is a promising perspective [START_REF] Cazcarro | Multiregional input-output model for the evaluation of Spanish water flows[END_REF][START_REF] Cazcarro | Environmental footprints and scenario analysis for assessing the impacts of the agri-food industry on a regional economy[END_REF].

The choice of a subnational spatial resolution was motivated by the existence of leverages of regional administrative levels but also by the potentialities it opens to analyze impacts of specialization strategies or to compare environmental efficiencies of regional consumptions. Given the model's uncertainties, results are not conclusive regarding inter-regional comparison of efficiencies except for the specific aspect of transport for which we observe a large variability of regional profiles. On the contrary, results are useful for the environmental evaluation of regional strategies, starting with the diagnosis. The level of detail of the model provides a concrete picture of each territory, all the more so as a finer spatial resolution is achievable. As stated in the introduction, the present work is part of a larger project aiming at the analysis of local supply chains from the environmental, economic and social points of view for decision-aiding. In this perspective the next step is to include socio-economical indicators (a minimum set of indicators being a labor footprint and an index on added value) to the model and to evaluate possible alternatives of development. Relevant areas of investigations related to cereals include the study of trade-offs of exports, adaptation to climate change (given water scarcity is planned to worsen in regions that are already enduring water stress) and trade-offs between food use and energy-use (for instance, bioethanol production has known a constant increase in recent years). The Afterres scenario [START_REF] Solagro | Un scénario soutenable pour l'agriculture et l'utilisation des terres en France à l'horizon[END_REF] envisions the future of land use in France in 2050 in concordance with the Negawatt scenario of energy transition [START_REF] Négawatt | Scénario négaWatt 2011 -dossier de synthèse[END_REF]. Changes in both modes of production and in modes of consumption are proposed. On the consumption Chapter 6. Environmental pressures embodied in the French cereals supply chain side, 3 actions are implemented: reduction of protein intake (currently in surplus), reduction of food waste and reduction of the proportion of animal proteins in the total intake. Concretely this translates into more direct cereal intake but eventually less cereals need for food purposes. On the production side, the scenario suggest a 50% proportion of organic agriculture by 2050, a division of corn export by two because of water stress and a partial reaffectation of arable land (mostly prairies) freed from animal production towards energy production. The work of regionalization of this scenario is in progress and it will eventually be useful for regional and national decision-makers to be able to compare this vision of the future with a business as usual scenario. The model and leads of development presented here are an important step towards this goal.

Introduction of Chapters 7 and 8

Understanding and quantifying what activities produce pressures on the environment and for the satisfaction of which end-consumers, was the main concern of our work. We saw the supply chain approach could in particular help identify what life-cycle stage (production, transformation, transport) should be targeted first to improve the overall situation. As underlined in Chapter 6 's conclusion though, measures implemented to reduce environmental footprints would also impact on local employment and distribution of wealth, positively or negatively. In a decision-aiding perspective, information on socio-economic aspects cannot be neglected. We do not attempt to develop new concepts on the subject. Rather, we wish to provide an overview of how the SC-MFA model could be coupled with existing economic and social models. Chapters 7 and 8 are dedicated to this endeavor. Chapter 7 focuses on linking MFA with economic modeling and Chapter 8 is studying how existing frameworks and theories stemming from social sciences could usefully complement MFA and also provide a better grasp on the issue of employment.

Chapter 7

Material flow analysis of the forest-wood supply chain: a consequential approach of log export policies in France

The article below is the result of a collaboration between the Laboratory of Forest Economics (LEF; INRA, AgroParisTech, Nancy) and the STEEP team (INRIA, Grenoble). The SC-MFA methodology was applied to the French forest-wood supply chain as part of a mission funded by the DRAAF Lorraine (regional direction of food, agriculture and forest of the Lorraine region) and directed by Mélanie Lucas. The demand was to "Assess and analyze wood flows in the Grand-Est area" which is composed of 5 regions (Alsace, Champagne-Ardenne, Lorraine, Bourgogne, Franche-Comté). The effort was concentrated on the six-month internship of Jonathan Lenglet (AgroParisTech), scientifically supervised by Sylvain Caurla (LEF) and us. The article itself focuses on the national scale and on the attempt to couple MFA with economic modelling. Regional results for Lorraine are however shown in Appendix of Chapter 7 as another illustration of the downscaling procedure.

Lenglet, J, Courtonne, J-Y, Caurla, S. Material flow analysis of the French forest-wood supply chain: a consequential approach of log exports policies.

Abstract. In the context of national policies for climate mitigation and energy transition, the forest-wood sector is drawing increasing attention, not only for energy wood but also for longer-life timber products. At the same time, part of the French timber transformation industry suffers from difficulties to adapt to recent changes on global markets, which translates into net exports of raw wood and imports of transformed products, detrimental to both the trade balance and the local creation of wealth. This article first aims at objectifying this situation by undertaking the first material flow analysis of the French forest-wood supply chain. We then evaluate the potential consequences of various scenarios of raw wood exports reduction policies, namely subsidies for consumption or transformation and taxation of exports, on both economic outcomes for the different actors and material flows. We thus provide an example of coupling material flow analysis with economic modeling in an attempt to move from the diagnostic phase to the assessment of possible actions within a decision-making perspective.

Introduction

For the last two decades, the forest sector has been increasingly involved in the climate mitigation policy portfolio. Since CO 2 emissions from wood combustion are considered to be null by the Kyoto Protocol (IPCC, 2006), climate policies in the forest sector have so far mostly favored the energy wood sector at the global level. For the last few years, however, the cascading use of wood products, defined by [START_REF] Sathre | Energy and carbon balances of wood cascade chains[END_REF] as the sequential use of a resource for different purposes, as the resource quality degrades over time on its path towards thermodynamic equilibrium, has been recognized as the first best option to take advantage of the entire mitigation potential of forests [START_REF] Bellassen | Carbon sequestration: managing forests in uncertain times[END_REF][START_REF] Sikkema | The GHG contribution of the cascaded use of harvested wood products in comparison with the use of wood for energy. A case study on available forest resources in Canada[END_REF][START_REF] Dornburg | Cost and co2-emission reduction of biomass cascading: Methodological aspects and case study of srf poplar[END_REF]. This implies the production of long-life wood products that sequester carbon over a long period of time [START_REF] Fortin | Quantifying the impact of forest management on the carbon balance of the forest-wood product chain: A case study applied to even-aged oak stands in France[END_REF][START_REF] Perez-Garcia | An assessment of carbon pools, storage, and wood product market substitution using life-cycle analysis results[END_REF][START_REF] Pingoud | Carbon dynamics in wood products[END_REF][START_REF] Profft | Forest management and carbon sequestration in wood products[END_REF]. These products generally come from extended-rotations forests that favor carbon sequestration in situ compared to energy-oriented types of management [START_REF] Liski | Which rotation length is favourable to carbon sequestration?[END_REF]. The use of wood as a replacement for other products then makes it possible to reduce carbon emitted at manufacturing stages [START_REF] Petersen | Environmental and economic impacts of substitution between wood products and alternative materials: a review of micro-level analyses from Norway and Sweden[END_REF][START_REF] Perez-Garcia | An assessment of carbon pools, storage, and wood product market substitution using life-cycle analysis results[END_REF]. Eventually, using end-of-life wood products as an energy source instead of landfilling makes it possible to avoid carbon emissions from fossil sources, via the energy substitution process [START_REF] Petersen | A comparison of avoided greenhouse gas emissions when using different kinds of wood energy[END_REF].

This transition from policies that stimulate energy wood sectors alone toward policies that promote the multipurpose cascading use of wood goes hand-in-hand with the promotion of roundwood products to tackle climate issues. Since official recommendations in France encourage the use of products made from roundwood, such as sawnwood, veneer and plywood, the question of the capacity of log provision has arisen [START_REF] Alexandre | Le bois, un matériau rare ? Vers une hiérarchie des usages du bois[END_REF]. This is all the more questionable given that wood is a material that requires a long time to grow and that global and national roundwood sectors have undergone several structural changes during the last two decades.

Indeed, the globalization of the wood products chain has shifted the centers of transformation in viex of shifting comparative advantages [START_REF] Uusivuori | Comparative advantage and forest endowment in forest products trade: evidence from panel data of OECD countries[END_REF]. In addition, the relaxation of trade and the containerization of transportation have dramatically facilitated the trade and exchange of raw and transformed products. Moreover, new engineered materials based on wood chips and fibers have emerged and lumber has lost its historic dominance as the primary raw product for secondary products [START_REF] Hansen | The global forest sector: Changes, practices, and prospects[END_REF].

These economic and technological changes have deeply transformed the French roundwood sector. Today, the country is a net exporter of roundwood and a net importer of processed wood products. This trade patterns is recognized as a source of value added loss and trade deficit [START_REF] Koebel | Productivity, resource endowment and trade performance of the wood product sector[END_REF][START_REF] Levet | Le commerce extérieur des produits bois : existe-t-il réellement un paradoxe français ?[END_REF].

Beyond these immediate economic implications, the current situation also raises mid and long-term issues. First, the mid-term efficiency rationale of the current situation is, to a large extent, due to the low transportation costs and the exclusion of environmental externalities in prices. These two factors may change in the future since transportation costs are expected to increase in line with fossil fuels depletion [START_REF] Capellán-Pérez | Fossil fuel depletion and socio-economic scenarios: An integrated approach[END_REF] and transportation may face a progressive inclusion of environmental externalities. Second, outsourcing by the manufacturing industry may decrease the economic resilience of national and sub-national forest sectors. Defining resilience as "the capacity [of a system] to absorb disturbance and reorganize while undergoing change so as to still retain essentially the same function, structure, identity, and feedbacks" [START_REF] Holling | Resilience and stability of ecological systems[END_REF][START_REF] Walker | Resilience, adaptability and transformability in social ecological systems[END_REF], lead us to assume that the loss of wood timber industries makes territories more vulnerable.

Relocating sawmill activities on the national territory can therefore be a solution to ensure the provision of sawnwood products in an efficient and resilient way. However this raises questions such as which sawmill industries should be relocated, to what extent and what would be the consequences over the rest of the wood sector, in terms of competition, trade-offs and/or synergies.

With this in mind, we strongly believe that any recommendation to relocate sawmill activities, either by stimulating private investments or by implementing public policies, should rely on a comprehensive pattern of wood harvests, flows and uses. The primary goal of this paper is therefore to assess wood product flows in a comprehensive manner, following their pathway from the time the wood is harvested in the forest, along the transformation process, and ending with the consumption of transformed products. We particularly focus on outgoing and ingoing flows. This endeavor typically falls in the field of Material Flow Analysis (MFA), that is, a systematic assessment of the flows and stocks of materials within a system defined in space and time (?). To our knowledge, so far, only [START_REF] Bais | Global patterns and trends of wood harvest and use between 1990 and 2010[END_REF] have so far extensively quantified wood flows at the global scale, suggesting that there are still considerable uncertainties about the extraction of wood at the global level and especially of woodfuels. Other identified wood flow studies have focused on regional levels (? [START_REF] Mantau | Wood flow analysis: quantification of resource potentials, cascades and carbon effects[END_REF], national levels [START_REF] Hekkert | Analysis of the paper and wood flow in the Netherlands[END_REF] for the Netherlands, ? for Japan, [START_REF] Piskur | Roundwood flow analysis in Slovenia[END_REF] for Slovenia, [START_REF] Knaggs | Estimated woodflow for the Republic of Ireland in 2007[END_REF] for Ireland, ? for China, METLA (2011) for Finland, [START_REF] Weimar | Der Holzfluss in der Bundesrepublik Deutschland 2009. Technical report, Methode und Ergebnis der Modellierung des Stoffflusses von Holz[END_REF] for Germany, [START_REF] Parobek | Analysis of wood flows in Slovakia[END_REF] for Slovakia), as well as on the European Union as a whole [START_REF] Mantau | Wood flows in Europe (EU27)[END_REF]. Such studies are currently lacking in France where no consistent and homogeneous accounts for wood product production and consumption exist at this time. Forest management and wood extraction are generally treated separately from wood transformation (which is itself organized into many different federations). Different units are used in official reports (cubic meters of roundwood, cubic meters of product, metric tons, number of units produced) making it difficult to cross-check the data. In addition, large uncertainties prevail in some existing databases, especially regarding woodfuels that are known to be largely under-reported in official statistics [START_REF] Chevallier | Etude de faisabilité pour l'évaluation des flux de matière de biomasse[END_REF]. This article is a first attempt to fill this gap and provide a comprehensive view of the flows in the French forest-wood supply chain. In order to reconcile data from various sources, we rely on the MFA framework depicted in ?, which uses the wood fiber equivalent (presented in Section 2) as a basic accounting unit.

The second goal of this paper is to assess the impacts of the relocation of sawmill activities on other forest sectors such as the fuelwood and pulp sectors, as well as on the economic outcomes for the sector agents. To address this issue, we couple the MFA with a partial equilibrium forest sector model, the French Forest Sector Model [START_REF] Lobianco | The importance of introducing spatial heterogeneity in bio-economic forest models: Insights gleaned from FFSM++[END_REF]Caurla et al., 2013,?;[START_REF] Lecocq | Paying for forest carbon or stimulating fuelwood demand? Insights from the French forest sector model[END_REF] and we explore the economic consequences of three policy options that reduce roundwood export.

By combining a MFA and a partial equilibrium framework, this paper makes it possible to bridge the gap between the diagnosis phase and the recommendation phase for policy makers through a multi-scenarios analysis. Indeed, as ? and ? recall, the impact of MFA on policy making is not clear since most studies stop at the diagnostic phase. We propose to go beyond the diagnosis in order to provide policy relevant information by using a partial equilibrium model that projects the evolution of the forest sector at the same scale and for the same prod-consequential approach of log export policies in France ucts as those described in the MFA. Compared to ? who focused on how different approaches (LCA, MFA and partial equilibrium model) independently contribute to elucidating a research question, we undertake the coupling of MFA with economic modeling. Note that in the title, we refer to this as a consequential approach in reference to consequential Life Cycle Assessment (LCA) that, contrary to attributional LCA, models economic links between processes and is therefore able to account for the indirect effects of a change. In practice, this generally translates into nonlinearities, because of the existence of thresholds or scaling effects.

The article is organized as follows. The first section is dedicated to the presentation of the data sources, hypotheses and methodologies used, both for the MFA and the parts dealing with economic prospectives. Results are presented and discussed in a second section before concluding on the main findings of the study and on future research perspectives within the context of a transition to sustainability.

Materials and methods

Material Flow Analysis (MFA)

Boundaries of the study

We focus on the upstream part of the forest-wood supply chain, which is the most relevant to our research questions. Firstly, this makes it possible to analyze to what extent the country is exporting raw products and importing products of first transformation. Secondly, it provides information on log outlets, a key question, for example, being: is there a reason to worry that firewood is cannibalizing log resources at the expense of the lumber industry? As a consequence, the model implemented does not aim to represent some second or third transformation industries such as the furniture industry. More precisely, our MFA covers all log products (distinguishing hardwood from softwood), wooden pallets, sawnwood, veneer, plywood and wood panels, as well as energy wood, sawmill residues, pulp and paper products and niche products such as wood staves. A full list of the products considered is presented in Table D.1 in the Supplementary Material. The geographic boundary of the study is metropolitan France.

Reference unit

To make the MFA consistent we need to define a homogeneous unit for the entire wood chain. This is all the more important given that wood products data are reported in various units. [START_REF] Bösch | Physical input-output accounting of the wood and paper flow in Germany[END_REF] note that when quantities of wooden products are converted into the same unit in order to compare them, the cubic meter of roundwood equivalent is often used. It is defined as the volume of roundwood necessary to make one unit of processed product. However, we share their opinion that it cannot be directly used in MFA studies since it leads to doublecounting of by-products such as sawmill residues. Using cubic meters or tonnes also raises consistency issues since other constitutive materials such as adhesives in panels or additives in paper products are then considered to be wood, whereas, volume changes due to drying would not be accounted for.

We therefore use the wood fiber equivalent as the reference unit. This unit was defined by [START_REF] Weimar | Der Holzfluss in der Bundesrepublik Deutschland 2009. Technical report, Methode und Ergebnis der Modellierung des Stoffflusses von Holz[END_REF] and used by [START_REF] Bösch | Physical input-output accounting of the wood and paper flow in Germany[END_REF]. The wood fiber equivalent (refered to as m3

[f] in the text) is the volume of the wood fibers that are contained in the product at the fiber saturation point [START_REF] Weimar | Der Holzfluss in der Bundesrepublik Deutschland 2009. Technical report, Methode und Ergebnis der Modellierung des Stoffflusses von Holz[END_REF]. For each wood-based product (e.g., fiber board, plywood, pulp), a specific conversion factor is calculated depending on its primary measurement units. A section of the Supplementary Material is dedicated to a presentation of the formula and hypotheses used for this unit, with Table D.1 providing conversion factors for each product studied. Although similar in principle, our theoretical formula slightly differs from the one provided by [START_REF] Weimar | Der Holzfluss in der Bundesrepublik Deutschland 2009. Technical report, Methode und Ergebnis der Modellierung des Stoffflusses von Holz[END_REF] in order to actually provide results expressed at the fiber saturation point. However, in practice, the lack of data (particularly concerning on moisture rates) leads us to use the same factors for many products.

Data sources

Table 7.2.1.3 summarizes the sources used to build the MFA model. Data is taken from a number of different sources, which makes it very unlikely that it will "fit" the mass conservation law. However, to take advantage of all of the information available, we used a data reconciliation technique inspired by ?.

Uncertainty of input data and period of study

Data quality is assessed either by directly retrieving precision indicators from the statistic sources, or, in most of the cases, on expert judgments based on the way data is built (source, type of survey or poll, scope of the study). Note that what matters the most for MFA results is the relative difference between data sources (e.g. source a is twice as precise as source b). Estimated 95% confidence intervals range from 1.4% (forest primary production) to 50% (wood logs used for individual heating, in official circuits).

Additionally, we chose to study the annual average between the years 2011, 2012 and 2013. This presents at least two advantages: first, it reduces the uncertainty of data from polls), and second, it allows us to neglect stock variations, which would be very difficult to quantify otherwise.

Supply and use tables and data reconciliation

Physical Supply and Uses Tables (SUT) have a long tradition of being used in the fields of ecological economics and industrial ecology ?. They consist of product-industry matrices indicating:

• which local industries and/or foreign territories are supplying the product to the studied system (Supply Table ),

• which local industries and/or foreign territories are using the product available in the studied system (Use Table ).

Data reconciliation is used to phase out inconsistencies. The model imposes mass conservation laws, which implies constraints on the supply-use tables. In particular, supply equals use constraints must be verified for each product and for each transformation industry (the materials that enter an industry must also exit this industry, regardless of the products they are embodied in) as well. Equations of the constraints are provided in the Supplementary Material. As we explained before, these constraints are unlikely to be met by input data so we resort to data consequential approach of log export policies in France reconciliation. While details are provided in supplementary material, the principle can be summarized as follow: in order for the constraints to be fulfilled, output data (results) are allowed to differ from input data but the less uncertainty there is about the input data the smaller the distance between output and input data will be. SUTs at the level of France are provided in the Supplementary Material both before and after the data reconciliation process (Tables D.1 and D.2).

Item

Uncertainty propagation

We use Monte Carlo simulations to evaluate uncertainties of output results. Each random draw corresponds to a set of input data. This set is composed as follows: for each input value, we assume a truncated Gaussian distribution (plus or minus infinity would have no meaning in our context) centered on this value, and whose standard deviation depends on the previously assessed uncertainty. We run the reconciliation model for each random set of input data and obtain the sets of output data. Uncertainties, presented in the form of 95% intervals of confidence, are computed by analyzing the dispersion of the distribution of each output variable.

French Forest Sector Model (FFSM)

An overview of the model

FFSM is a bio-economic recursive model of the French forest sector. The version used in this article is FFSM 1.0 (Caurla et al., 2013,?;[START_REF] Lecocq | Paying for forest carbon or stimulating fuelwood demand? Insights from the French forest sector model[END_REF], 1 . This version is composed of two modules: an inventory-based dynamics forest module (FD) and a partial equilibrium market module (MK). The FD module represents the dynamics of the French forests that accounts for natural growth and mortality (Colin and [START_REF] Chevalier | Rapport technique module biologique LEF[END_REF] and wood removals from human harvest.

The optimal harvest level is computed by the MK module on a yearly and regional basis, starting from 2006 as the base year. To do this, the MK module solves a partial equilibrium problem, annually taking the demands for transformed products, wood availabilities in forest, and the costs of transportation from one region to another into account, according to [START_REF] Samuelson | Spatial price equilibrium and linear programming[END_REF] spatial price equilibrium framework.

The model represents the demand of processed products: sawnwood (hard and softwood, respectively hereafter referred to as hsw and ssw), plywood (pw), fuelwood (fw), pulp, panels and the supply of raw products: roundwood (hard and softwood, respectively hereafter referred to as HRW and SRW) and industrial wood (IW). A Leontief function represents the transformation of raw products into processed products. The model considers sawmills and harvest residues as by-products of primary activities.

While interregional trade is modeled through the spatial price equilibrium framework, international trade is computed through an Armington framework assuming that domestic and foreign products are not fully substitutable. The international trade is modeled using exoge-1 The most recent version of the model (FFSM++; [START_REF] Lobianco | The importance of introducing spatial heterogeneity in bio-economic forest models: Insights gleaned from FFSM++[END_REF][START_REF] Lobianco | Accounting for active management and risk attitude in forest sector models. an impact study on French forests[END_REF]) involves a third module, referred to as the micro-based Area-Allocation module (AA) making it possible to project over longer horizons, and accounting for forest resource heterogeneity and the degree of forest owners expectations as well as their degree of risk-aversion. consequential approach of log export policies in France nous international prices derived from the FAO (2013) and elasticities of substitution between local and international products specifically estimated for FFSM in [START_REF] Sauquet | Estimating armington elasticities for sawnwood and application to the French forest sector model[END_REF].

Consistency with MFA and input-output calibration in FFSM

The number of products represented in FFSM is lower than in MFA analysis. To make the modeling framework consistent, results from MFA are aggregated to match the definition of products in FFSM. Input-output coefficients used in the Leontief function of FFSM are then calibrated using MFA results for each group of products. They are presented in Table D in the Supplementary Material.

Prospective: simulating policies to relocate sawmill activities

Several papers assess the impacts of export restrictions on global and national forest sectors. Using a global log-lumber trade model, Van [START_REF] Van Kooten | Global impacts of Russian log export restrictions and the Canada-U.S. lumber dispute: modeling trade in logs and lumber[END_REF] show that moving an export tax at the national level (Canada or Russia) has a small impact on the global forest sector welfare. Using data for the State of Washington, [START_REF] Johnson | Expanding U.S. log export restrictions: impacts on state revenue and policy implications[END_REF] suggest that domestic mills and consumers clearly benefit from the ban while the welfare of Japanese consumers and the export industry is reduced. The same conclusion holds in Van Kooten and Johnston (2014) for British Columbia (BC). They report that, while free trade of logs might maximize global wellbeing, it might also reduce the domestic welfare of economic forest sector agents. While these papers clearly suggest that export bans are beneficial to the domestic forest sector, neoclassical economy judges them inefficient at the global scale [START_REF] Goodland | If tropical log export bans are so perverse, why are there so many?[END_REF]. However, these studies focus on the impacts of a restriction without analyzing the different design of policy options to reduce export and their implications on forest sectors. This is precisely the aim of the prospective part of this paper. To do this, we tested three alternative policies. Two of them consist in subsidizing transformed products made of roundwood: Sub_C is a subsidy to domestic sawnwood and plywood consumption, while Sub_T is a subsidy to sawnwood and plywood transformation. The other policy, referred to as Exp, is an extra-cost to roundwood export. Sub_C and Sub_T differ from their transmission channels: while Sub_C acts through processed product consumers, Sub_T directly irrigates the upstream and the downstream of the roundwood sector through the reduction of transformation costs. Exp acts differently and models an extra cost for plant-health control and preventive treatment. Such a policy already exists for wood packaging material [START_REF] Strutt | Evaluating the impacts of an international phytosanitary standard for wood packaging material: Global and united states trade implications[END_REF] as a tool to limit the diffusion of pests and diseases. We assume that this policy costs 10 e/m3 which is close to the export tax equivalent imposed by Canada on its exports to the U.S. (Van Kooten and Johnston, 2014) and which is considered as plausible by the French government. In the model, this value leads to a reduction of roundwood log exports of 20% regarding a baseline scenario without policy. To make the comparison between policies meaningful, we based them on the same level of export reduction derived from the Exp policy result (-20% for roundwood, either hardwood or softwood). We calibrated the levels of subsidies Sub_C and Sub_T consistent with this objective by a trial and error process (55% and 110%, respectively).

Results

Wood flow analysis

MFA results are presented in two figures: Figure 7.1 provides a global view of the upstream part of the supply chain (forest stock, increment, harvest, self-consumption of households, etc.) and Figure 7.2 focuses on the transformation of lumber and pulpwood. Every flow comes with a figure that specifies the quantity of wood in m3(f). Confidence intervals are also represented as well as some quantities in a more intelligible unit, e.g., paper production is expressed in tonnes.

Six main outcomes stem from the diagrams. First, Figure 7.1 shows that, at the national level, the stock of standing wood is increasing since the total of harvested wood (including self-consumption) represents about half of the annual increment. Although this result is in line with figures published elsewhere (Colin and Thivolle-Cazat, 2016), it must be qualified since all biological production at the national level cannot be harvested. Indeed, some species or diameters do not have a commercial outlet and some areas, such as mountainous ones, are inaccessible. This can explain the paradoxical situation encountered in many French regions where forest stocks increase while wood harvest seems to reach a ceiling. In addition, as suggested by its wide confidence interval, the production of energy wood remains difficult to assess. The majority of energy wood flowing in anthropogenic activities is composed of self-consumption energy wood. These self-consumption volumes are estimated by [START_REF] Pouet | Etude sur le chauffage domestique au bois : marché et approvisionnement[END_REF] based on a poll taken on some 1,500 households. Even if the total household consumption probably gives a fair idea of the situation, quantifying the share of the different firewood supply chains is more difficult since some suppliers may have an interest in underreporting their sales. In addition, the core business of energy wood suppliers is often logging or sawmilling, which makes the identification of energy wood flows even more complex (INSEE, 2014).

Second, although the standing wood resource at national level is mostly composed of broadleaves (about 63% (FCBA, 2013)), it appears that HRW represents 9.5% of log volumes, wheareas SRW accounts for 28%. This result is explained by the higher adequacy of softwood with the process industry requirements. Indeed, sawmills consume about four times more SRW than HRW, and the panel and paper pulp industries nearly twice as much.

Third, France is a net exporter of logs. This is all the more true for hardwood. Exports represent 22% of total HRW and 7% of total SRW. France is also a net exporter of pulpwood since about 15% of the pulpwood harvest is exported.

Fourth, Figure 7.2 suggests that ssw represents the largest production in volume closely followed by panels production. Half of the sawmill residues are used in the pulp and panel industries as raw material, which reveals a well-established recovery chain and potential competition with new additional fuelwood demand. The pulp and paper sectors have a large recycling chain: more than 80% of papers consumed are sorted to be recycled, representing about 55% of the resources of the paper industry (expressed in volume of wood fiber equivalent). These sectors determine the economic value of the wood sector in France. It can be noted that France also exports large quantities of paper wastes that are therefore not valued in the country.

Fifth, Figure D.3 in the Supplementary Material shows that niche products such as stave woods and plywood, even if negligible from a volume point of view, remain important from a value-added perspective. Conversely, the weight of sawmill residues is strongly reduced. Note (f) and correspond to a one-year average during the period 2011-2013. consequential approach of log export policies in France that these niche products are mainly produced from HRW and could become interesting outlets from the point of view of export reduction. Sixth, from a trade balance perspective, we can notice that panels and paperboards are largely exported (resp. 60% and 54% of the total production is exported). Hardwood sawmilling is also a net exporter, which shows a possible commercial outlet for producing hsw in France for export. On the contrary, 28% of total ssw consumed in France is imported which shows an inadequacy between local supply and demand. Imported products are likely to be species and/or diameters that are not produced in France (even if data cannot corroborate this assumption).

These results mask important regional differences. For example, about half of the wood harvest takes place in only five regions (of the 22 French regions). These regions are not analyzed in this article, which focuses on diagnosis and prospective for the national forestwood supply chain, although they constitute major leads for future work. We will come back to this question in the conclusion.

Prospective

We assessed the impacts of the policies described above on two groups of economic indicators: (i) the variations in prices and quantities produced, consumed, imported and exported, and (ii) the budgetary cost and the variations in economic agent surpluses. Variations are given for the year 2020. Sankey diagrams outlining the potential impact of each policy on material flows are proposed in the Supplementary Material (Figures D.4,D.5 Exp acts via an extra cost on export without modifying domestic prices and domestic agents' behaviors. As a consequence, total roundwood production decreases because of export reduction but this does not lead to a rebound effect on the domestic market. Second, while Sub_C and Sub_T have almost the same impact on the production of raw products upstream, their impacts on consumption patterns differ. In fact, the impacts of Sub_C mostly depend on the price elasticity of the transformed product demand and the price elasticity of the primary product supply. Since the demand of hsw (-0.5) is more elastic than that of ssw (-0.4) and pw (-0.3) and the supply of HRW is more elastic than that of SRW (1.2 vs. 0.9), Sub_C has a relatively bigger impact on hsw than ssw. For its acts, Sub_T plays via the costs of transformation so that the higher the cost of transformation is, the higher the impact of Sub_T will be. This explains the higher impact on plywood (cost of transformation: 534 e/m3) than on hardwood sawnwood (268 e/m3) and on softwood sawnwood (48 e/m3). Third, although Sub_C and Sub_T are subsidies of the sawnwood and plywood sectors, they also impact fuelwood and, to a lesser extent, the pulp and panel sectors via the increase in production of sawmill residues. This implies a crowding-out effect with IW, which results in a reduction of IW production (-20% and -18%, respectively) that is not observed with Exp policy.

Regarding impacts on exports and imports, Table 7.3 shows that Sub_C increases imports of hsw, ssw and pw in a proportion depending on the price elasticity of the demand. Sub_C therefore creates an important windfall effect. On the other hand, Sub_T decreases imports of ssw and pw and does not affect imports of hsw. This is because Sub_T only acts on domestic production costs, which makes domestic products more competitive than foreign substitutes.

Chapter 7. Material flow analysis of the forest-wood supply chain: a consequential approach of log export policies in France 7.3.2.2 Variation of surpluses and budgetary costs Table 7.4 shows that while the two subsidies increase all surpluses except the surplus related to IW production Exp reduces surplus related to HRW/SRW productions, slightly increases surplus related to IW production and has no significant impact on surpluses related to consumption activities. In the case of Sub_T, the driver is the reduction of transformation costs that reduces the consumer price and increases the producer price and, as a consequence, increases both the quantities produced and consumed at the national scale. This results in overall gains in economic agents' surplus. In the Sub_C case, the consumer-perceived price is reduced which leads to a higher demand and, therefore, an increase in production upstream. In that case, however, part of the additional demand is fulfilled by imports, as shown in the previous section, which do not increase domestic agents' surplus. Both subsidies have a negative impact over industrial wood activities since they lead to an additional production of sawmill residues, leading to a crowding-out effect with industrial wood upstream.

Table 7.5 shows that while Sub_C is the subsidy leading to a higher welfare benefits, it is also the most expensive. When looking at the social costs, Sub_T performs better than Sub_C since Sub_T does not increase imports and does not not imply a windfall effect. Budgetary costs of Exp are 0 since FFSM does not take transaction costs into account.

Discussion about the results

Results show there is no first best policy option. From a policy-making perspective, the implementation of a policy to reduce roundwood export must consider the different levels of impacts, namely the welfare variations for each economic segment, the total welfare costs, and the total budgetary costs. Sub_C leads to the highest welfare gains for economic agents (except IW suppliers) but is the most costly for the government budget because of the windfall effect. Sub_T follows a comparable surplus gains pattern while being half as expensive. Exp policy is not beneficial to wood sector surplus but is the least costly if we assume that the transaction and functioning costs are covered by the payment made by roundwood exporters. In addition, it is the only policy in which the IW sector remains unchanged. According to these results, the only possible solution for (1) reducing the crowding out effect between sawmill residues and industrial wood competition with the pulpwood sector, and (2) increasing welfare surplus in the forest sector while (3) preventing a windfall effect would be to combine Exp with Sub_T. Figure D.7 in the Supplementary Material shows the effect of a range of combinations between these two policies on social cost. However, as outlined before, social cost is not the only criterion to be considered. The choice of a policy mix should imply a debate among all stakeholders impacted by the policy (e.g., including citizens paying for the potential subsidies). We believe that they alone can express which criteria matter the most and which efforts they are willing to make.

In addition, since FFSM has no endogenous growth module, it cannot represent the impacts of subsidies on capital accumulation. Yet, it is very likely that, in reality, when looking at the long term, the net social costs of policies would diminish over time as capital investments increase. At one point, the net social costs may even become negative.

Conclusion

Our paper fills two important gaps. It is the first in the literature to draw a comprehensive picture of wood flows in the upstream part of the wood sector in France that takes all available data sources into account. To do this, we built an MFA model using a reconciliation process and a homogeneous unit to make the different sources consistent and comparable while quantifying uncertainty. Second, it assesses the economic impacts of three policy alternatives to reduce exports of logs by using FFSM, a partial equilibrium model. Impacts on material flows are evaluated as well. By combining an MFA and an economic modeling framework, our analysis goes beyond diagnosis and proposes insights into policy-makers' recommendations.

We demonstrated the relevance of MFA to reconcile highly heterogeneous datasets. Since no common database exists in the forest-wood sector, these results offer a solid base for analysis and opportunities for development prospects. However, attention must be paid to the temporal aspects of the study. Our MFA provides a snapshot of the situation for a specific reference year and does not capture trends. For instance, concerns on raw wood leaks are not only due to current export levels but also, and maybe mostly, to increasing exports trends and sawmill shutdowns. Thus, it would be relevant to repeat the study according to a predetermined time-step (e.g., 5 years), using the same methodology. Comparison across time of wood flow dynamics may be encouraged as a tool to study the wood-forest sector's health and as a powerful monitoring instrument for policy makers. The systematic framework implemented here will hopefully foster this endeavor.

MFA results suggest that while broadleaves dominate conifers in French forests, production of HRW is three times lower than that of SRW. Meanwhile, exports represent 22% of the total HRW production but only 7% of SRW production. This leads to an apparent paradox: the resource is abundant and potentially under-harvested but the sector is unprofitable since part of the value added is created abroad. Nevertheless, the MFA suggests that both hsw production and niche products such as stave wood are a potential commercial outlet for domestic HRW. Yet, as long as the international demand for logs and especially broadleaf products is the driving force behind exports, production of HRW will be oriented toward exportation and investments in the sector will be postponed, exacerbating the trade balance deficit. With this in mind, as the second step of our analysis, we tested three policy options to reduce log exports: a subsidy to consumers, a subsidy to process industries and an additional costs to export due to phytosanitary control, which acts as a ban in the model. The potential effects of these policies help to specify several criteria of interest to aid the decision process: budget costs, welfare variation in the forest-wood sector and redistribution of this welfare among agents. These indicators could also serve to assess potential impacts on local employment given that labor intensiveness differs between sectors. Moreover, a healthier, more dynamic supply chain would arguably make it easier to reach national climate mitigation goals. These last two points would require more in-depth studies but seem crucial if we are to have a holistic view of the sector. While mono-criterion optimization approaches (e.g., optimizing cost-effectiveness) are often used to make policy recommendations, we believe that multi-criteria analysis would be better suited to study possible alternatives. This approach would go hand-in-hand with a decision process involving all of the stakeholders, that is, ideally, anyone affected by the decision, where they are asked what they value most and what compromises they are willing to accept and support.

Finally, we noted in the introduction that the forest-wood sector was an essential part of many regional economies and cultural identities. Although this was not the purpose of this article, we know that this sector is highly geographically heterogeneous. Therefore, similar studies at regional levels would be beneficial. Rather than a series of individual regional assessments, we would argue for a coherent multi-regional assessment, that is, disaggregating the national MFA and economic model to provide evaluations in all regions. Regional strategies, e.g., specialization strategies, could then be revisited both in terms of their internal effects and consequences on other regions. Interestingly, there is no guarantee that the same policy would be preferred, regardless of whether the focus is put on the national level or on the regional level. We think that a multi-regional approach will therefore be a major direction for future research.

Chapter 8

Territorial supply chains from a social sciences' perspective

In Chapter 7, we proposed an example of coupling SC-MFA with economic modeling in order to evaluate potential consequences of policy alternatives. This is one possibility of extending SC-MFA to economic aspects, but there are many others. First, one can make a distinction between establishing a diagnosis and exploring scenarios. Comparing Sankey diagrams of material and monetary flows for instance illuminates present (or possibly past) situations1 . Second, economic aspects can't be reduced to monetary flows. Economic theories are diverse and in some cases, separating economic from social and cultural aspects is simply impossible. For this reason, we wish to explore in this chapter what social sciences (as opposed to environmental sciences) can offer regarding the analysis of territorial supply chains. No case study was conducted on the matter in the course of the thesis, however, we find it useful to reflect on what could be undertaken in the future. Social sciences indeed provide a large set of theories for conducting systemic analyses of supply chains, that is, not only characterizing individual parts of the chain, but also the relationships between them, their links to governance institutions and to the environment. A first section is dedicated to the presentation of such grids of analysis, originating among other fields from management, economics and sociology. Believing that environmental issues are unlikely to be solved separately from social-economic ones, and aware that employment is, even more so in a time of crisis, a top concern for local decision-makers, we put a more practical emphasis on this question in a second section.

Complementarity of existing frameworks

At the start of our PhD, we participated in a one-week summer school2 dedicated to the field of territorial ecology3 . The group of academic attendees continued the work initiated during the school which eventually lead to the publication of a book (Buclet et al., 2015) dedicated to the formal presentation of methodologies and to their application to the town of Aussois, Savoie. Four aspects are mainly developed: the socio-ecological trajectory of the territory from the early 19 st century to today [START_REF] Barles | Aussois et la Maurienne, une approche par les trajectoires socio-écologiques, XIXe-XXIe siècle[END_REF], the systems of wealth creation on the territory and how they respond to people's needs (Buclet et al., 2015), the agri-food system [START_REF] Bonaudo | Le système agro-alimentaire, un découplage progressif de la production et de la consommation[END_REF], and the energetic metabolism of the territory (Courtonne et al., 2015). Although these four chapters aim at balancing quantitative and qualitative descriptions, the first two are more qualitative and the last two more quantitative. In the following, we draw many concepts from this essay, although also relying on alternative sources.

Elinor Ostrom's framework of social-ecological systems (SES), illustrated in figure 8.1, provides a global view of a bio-geo-physical unit and its associated actors and institutions and is therefore a relevant starting point [START_REF] Ostrom | A general framework for analyzing sustainability of socio-ecological systems[END_REF][START_REF] Mcginnis | Social-ecological system framework: initial changes and continuing challenges[END_REF]. The system is described by four main subsystems: a resource system (e.g. forest) contains resource units (e.g. trees) that may be used by actors (e.g. forest loggers) under certain conditions set by a governance system (e.g. property rights, sustainable management plans). Prominence is attached to the concept of action situation in which "actors in positions make choices among available options in light of information about the likely actions of other participants and the benefits and costs of potential outcomes" (McGinnis and Ostrom, 2014)4 . In accordance with this framework, [START_REF] Kébir | Ressource et développement : une approche institutionnelle et territoriale[END_REF] shows resources alone do not exist. An object (e.g. a particular material) becomes a resource once its potential has been revealed by a will of using it to a productive end (for instance, uranium ore was of little interest until the development of the nuclear industry). In this sense, resources are both a given and a construct: they are neutrally provided by the environment but their fate depends on what people do with it [START_REF] Kébir | Dynamique des ressources et milieux innovateurs[END_REF].

The SES framework would however benefit from an adaptation in order to be more relevant to supply chains. Supply chains are indeed both embedded in territories and a-territorial in the sense that they link different sectors in different territories together. Of course degrees of territoriality may differ for different supply chains, for instance short-circuits have deeper relationships to the territory than export oriented chains. Moreover, chains' functioning is influenced by local, regional, national, continental and international sets of rules and usually impacts both local and global environments. [START_REF] Debuisson | Les modes d'interaction pour une dynamique territoriale soutenable : un apport à l'écologie territoriale[END_REF] proposes a grid of analysis to study local supply chains, and local food chains in particular, in an attempt to identify obstacles and levers of action for territorial sustainable development strategies (table 8.1). The grid is divided in 3 parts. The first part aims at characterizing actors by their situation in the supply chain and their role and motivation (in this perspective, we will develop in a moment the concepts of power, legitimacy and interest). The second part is dedicated to collective action and qualifies modes of interaction (to what extent do actors share the same goals? ), membership to a type of economic sphere inspired by [START_REF] Polanyi | The great transformation: The political and economic origins of our time[END_REF] and [START_REF] Kolm | La bonne économie: la réciprocité générale[END_REF], entity sizes and scopes of influence, and finally type of proximity(ies) between actors: those can be close from a physical distance viewpoint, because they share similar cognitive frameworks (e.g. belong to the same networks, rely on the same technology) or because they share the same values and norms [START_REF] Pecqueur | Economie de proximités[END_REF]. Finally, the third part of the grid characterizes the environment (context) in which the group of actors operates and how it interacts with it, from a policy, social and ecological viewpoint.

Ecology and Society 19(2): 30 http://www.ecologyandsociety.org/vol19/iss2/art30/ Fig. 2. Revised social-ecological system (SES) framework with multiple first-tier components. Solid boxes denote first-tier categories. Resource Systems, Resource Units, Governance Systems, and Actors are the highest-tier variables that contain multiple variables at the second tier as well as lower tiers (see Table 1 for an updated list of second-tier variables within each of the top-tier categories). Action Situations are where all the action takes place as inputs are transformed by the actions of multiple actors into outcomes. Dashed arrows denote feedback from action situations to each of the top-tier categories. The dotted-and-dashed line that surrounds the interior elements of the figure indicates that the focal SES can be considered as a logical whole, but that exogenous influences from related ecological systems or social-economic-political settings can affect any component of the SES. These exogenous influences might emerge from the dynamic operation of processes at larger or smaller scales than that of the focal SES.

the highest-tier variables that contain multiple variables at the second tier as well as lower tiers. Action Situations are where all the action takes place as inputs are transformed by the actions of multiple actors into outcomes. Feedback occurs from action situations to each of the top-tier categories. The focal SES can be considered as a logical whole, but exogenous influences from related ecological systems or social-economic-political settings can affect any component of the SES. These exogenous influences might emerge from the dynamic operation of processes at larger or smaller scales than that of the focal SES.

Pictures are an incomplete representation of the full range of meaning intended to be included in a general concept, and we are concerned that our presentation of the SES framework may convey the mistaken impression that it is static in nature. The feedback paths (Fig. 2) suggest that the consequences of action situations may spread to any of the other top-tier variables, but our experience is that this interpretation is not immediately obvious to all observers. To be clear, we interpret all of the factors included in the top-tier categories (RS, RU, A, and GS in Fig. 2) to be, at least potentially, both inputs to and outputs from one or more action situations. Action situations take as inputs the values of the SES top-tier categories at time t and generate changed values of at least some of those factors at time t + 1.

Recognizing action situations

The IAD framework attaches prominence to the concept of an action situation in which actors in positions make choices among available options in light of information about the likely actions of other participants and the benefits and costs of potential outcomes. The initial versions of the SES framework (Ostrom 2007[START_REF] Ostrom | A general framework for analyzing sustainability of socio-ecological systems[END_REF] implicitly incorporated the action situation within the box labeled as interactions and outcomes (Fig. 2). Initial feedback on these versions of the SES framework suggested that the action situation needed to be explicitly denoted in the base figure .   Accordingly, Ostrom (2010) used the occasion of her Nobel Prize acceptance speech to change the label of the Interactions and Outcomes to also include the broader term Action Situations. This simple step cemented a close connection between decades of work on the IAD framework and the newly established SES trom, 2014). As the layers show, the main categories can be further detailed with "second-tier variables", e.g. economic trends, equilibrium properties of resource systems, number of resource units, actors' past experiences, government organizations, deliberation processes etc. The full list is proposed in appendix of the chapter (table E.2).

Exploring the dynamics of wealth creation systems, Buclet et al. (2015) additionally refer to the economics of convention [START_REF] Boltanski | Les économies de la grandeur[END_REF]. In this paradigm, interactions between individuals are not purely rational nor purely guided by self-interest: symbolic representations (conventions) also play a role in decision-making and coordination. These systems of legitimacy must be analyzed in order to better understand what drives coordination or hold it back. Moreover, the authors attach a lot of importance to the idea of "territorial capability" adapted from Amartya Sen's concept (Sen et al., 1999): favorable resources (in the wide meaning of the word) are not sufficient to reach well-being, one requires means to convert these resources into ends. In order to be even more supply chain specific, we now examine the study of [START_REF] Bassene | Organisation en réseau et durabilité systémique de deux filières alimentaires (riz biologique et petit épeautre en France)[END_REF] on two French food chains: organic rice and einkorn (petit épeautre). The authors attempt to characterize supply chains' "systemic sustainability", which is similar to the concept of resilience introduced in the previous chapter (the ability to absorb shocks while retaining the same functions and identity). After identifying the actors (producers, transformers, packers and distributers) and structure of each chain, they apply network analysis using the governance typology of [START_REF] Vurro | Shaping sustainable value chains: Network determinants of supply chain governance models[END_REF] 5 and the concept of "survivability" developed in [START_REF] Thadakamalla | Survivability of multiagent-based supply networks: a topological perspect[END_REF] 6 . Because these typologies alone are insufficient to answer their question7 they also qualitatively assess a set of economic, social and environmental indicators shown in table 8.2. Although these indicators are dedicated to food chains, they could be adapted to any other sector.

Finally, while the above frameworks refer to actors, we believe this notion is worth extend- ing to that of stakeholders. The term was popularized by [START_REF] Freeman | Strategic management: a stakeholder approach[END_REF] in the context of strategic management and defined as "any group or individual who can affect or is affected by the achievement of the organization's objectives". In this book, Freeman argues that firms' strategic decisions shouldn't only consider shareholders' interests but also that of stakeholders. The stakeholder model of the corporation proposed by [START_REF] Donaldson | The stakeholder theory of the corporation: Concepts, evidence, and implications[END_REF] illustrates this idea (figure 8.2). [START_REF] Donaldson | The stakeholder theory of the corporation: Concepts, evidence, and implications[END_REF] further examine justifications for this representation of the firm and distinguish descriptive grounds (the model is describing what a firm really is, i.e. a "constellation of cooperative and competitive interests possessing intrinsic value"), instrumental grounds (a mean to achieve a competitive advantage: "corporations practicing stakeholder management will, other things being equal, be relatively successful in conventional performance terms (profitability, stability, growth, etc.)") and normative grounds ("each group of stakeholders merits consideration for its own sake and not merely because of its ability to further the interests of some other group"). They ultimately find that this latter ground is fundamental8 . This being said, organizations cannot take into account all actors of their environment, they need to identify the most relevant ones. Precisely noting that there was no agreement on "'principles of who and what really counts", [START_REF] Mitchell | Toward a theory of stakeholder identification and salience: Defining the principle of who or what really counts[END_REF] proposed a typology to identify and prioritize stakeholders according to three key attributes: power, legitimacy and urgency. Power is the potential ability of an actor to impose its will to others9 . Legitimacy is the acknowledgment of a stakeholder by its peers. Urgency corresponds to the degree to which a stakeholder perceives its claims as important and requiring immediate attention. As shown in figure 8.3, a variety of stakeholder's profiles derives from these three attribute and for instance helps to identify pivot (or definitive) actors with all three attributes, but also dominant, dependant and dangerous ones. Those who do not possess any attribute should be excluded from concertation processes. In France, this typology was adapted to the study of governance and sustainability of industrial ecology projects [START_REF] Brullot | Stratégies d'acteurs et gouvernance des démarches d'écologie industrielle et territoriale[END_REF]. The objective being to identify actors that would be suited to actively support a project, the notion of urgency was replaced by interest (e.g. political, economic, environmental interest). Depending on the focus, the two typologies seem well suited to (i) prioritize who should be considered in the analysis and (ii) provide a first image of motivations, claims and power relationships10 . More generally, the notion of stakeholder is essential to sustainable development. As [START_REF] Boutaud | Le développement durable : penser le changement ou changer le pansement ?[END_REF] shows, sustainable development reshapes the idea of general interest by extending it in space and time. While general interest traditionally refers to present generations in a delimited community, sustainable general interest implies to consider the rest of the world as well as future generations, that is two additional groups of stakeholders. Of course finding ways of representing interests of future generation is not easy [START_REF] Bourg | Vers une démocratie écologique[END_REF]. We will see in Part 3 that participation can fulfill this role in some situations. Associations Employe C ommunities owned corporation. Although stakeholder concepts have been applied in other settings (e.g., government agencies and social programs), these situations are fundamentally different, and simultaneous discussion of a variety of possible stakeholder relationships leads, in our view, to confusion rather than clarification. The critical corporate stakeholder issues, both in theory and in practice, involve evidentiary considerations and conceptual issues (e.g., the meaning of property rights) unique to the corporate setting.

It is also worth noting at the outset that the extent to which the stakeholder theory is understood to represent a controversial or challenging approach to conventional views varies greatly among market capitalist economies. These differences are highlighted in a recent issue of The Economist (1993: 52):

In America, for instance, shareholders have a comparatively big say in the running of the enterprises they own; workers . . . have much less influence. In many European countries, shareholders have less say and workers more . . . [I]n Japan . . . managers have been left alone to run their companies as they see fit-namely for the benefit of employees and of allied companies, as much as for shareholders.

ALTERNATIVE ASPECTS OF STAKEHOLDER THEORY: DESCRIPTIVE/EMPIRICAL, INSTRUMENTAL, AND NORMATIVE

One of the central problems in the evolution of stakeholder theory has been confusion about its nature and purpose. For example, stakeholder theory has been used, either explicitly or implicitly, for descriptive purposes. Brenner and Cochran (1991: 452) offered a "stakeholder theory of the firm" for "two purposes: to describe how organizations operate and to help predict organizational behavior." They contrasted this "theory," [START_REF] Donaldson | The stakeholder theory of the corporation: Concepts, evidence, and implications[END_REF].

Going back to territorial issues, we now wish to explore a bit more the question of employment, given supply chains are an essential part of it.

Characterizing employment

We briefly introduce this section with thoughts on the situation of work in today's societies, then we present an overview of ways to assess the effect of public policy's on employment, on the example of climate policies. Finally, we propose an example of crossing economic, employment and material flow data in three sectors of the forest-wood supply chain in order to show how it can help characterizing the value chain. [START_REF] Méda | Le travail[END_REF][START_REF] Méda | Le travail, une valeur en voie de disparition ?[END_REF] show that, in western societies, social order is organized around work. Labor is both the main source of subsistence revenues and the main space for social relationships. Both free market advocates and marxists agree on this, the first because they view society as a mean of increasing production and trade and the latter because they view work as the basis

Latent Stakeholders

With limited time, energy, and other resources to track stakeholder behavior and to manage relationships, managers may well do nothing about stakeholders they believe possess only one of the identifying attributes, and managers may not even go so far as to recognize those stakeholders' existence. Similarly, latent stakeholders are not likely to give any attention or acknowledgment to the firm. Hence: Proposition la: Stakeholder salience will be low where only one of the stakeholder attributes-power, legitimacy, and urgency-is perceived by managers to be present.

In the next few paragraphs we discuss the reasoning behind this expectation as it applies to each class of latent stakeholder, and we also discuss the implications for managers. Dormant stakeholders. The relevant attribute of a dormant stakeholder is power. Dormant stakeholders possess power to impose their will on a firm, but by not having a legitimate relationship or an urgent claim, Figure 8.3: A typology of stakeholders. Source : [START_REF] Mitchell | Toward a theory of stakeholder identification and salience: Defining the principle of who or what really counts[END_REF].

of social allegiance. The author argues there is no philosophical ground to justify this central space of work other than an utilitarian conception of the world, in which the unemployed are perceived as useless weights. Work certainly produces wealth but forming a society is more than participating in the productive economy. Reducing its importance would leave room for other forms of relationships and involvements, political involvement in particular. These thoughts may be revisited in the perspective of a (wanted or unwanted) transition to postgrowth economies.

This being said, employment is currently a key issue for local decision-maker as it represents a large part of a territory's revenues11 and participates in its social dynamic. Policy choices on sustainability issues or therefore unlikely to be made without an assessment of their impacts on job creation. We now propose a description of ways to conduct such assessments, relying on a recent study on the effects of climate policies [START_REF] Quirion | L'effet net sur l'emploi de la transition énergétique en France : Une analyse input-output du scénario négaWatt[END_REF].

In this paper, Philippe Quirion undertakes the evaluation of the French négaWatt scenario of energy transition 12 . Here, we only focus on the way he situates it regarding other studies on the subject. Figure 8.4 illustrates nested scopes (and associated job creation/destruction mechanisms) that can be considered. The most restricted scope (blue frame), only considers direct job creation due to the implementation of a policy. The notion of net job creation appears in the next scope (red frame), by also considering direct jobs destruction (polluting activities that will disappear or at least decrease if the policy is implemented). This is however biased as it leads to favor higher cost technologies or organizational forms 13 . In his study, the author therefore extends the scope (violet frame) to account for the fact that ultimately households or companies have to pay for this extra-cost, therefore decreasing final demand for other activities. We saw in Chapter 5 how Input-Output Analysis makes it possible to estimate production factors (in this case labor) induced by a given level of final demand. Using this methodology, the net effect on job creation has been re-evaluated. Finally, macro-economic models can consider an even wider scope (green frame), for instance estimating the retro-action of a change in wages on labor demand. However, the author argues these models are less transparent and do not allow to have a detailed (sectoral) view on the system. French CO 2 emissions, without requiring carbon capture and storage technologies or new nuclear plants. 13 To produce the same amount of goods and services, in this case energy, more money has to be spent and,

given that wages represent the largest part of added value, this is likely to translate into more job creations.

Another way to see it is that sectors favored by sustainability policies are in general more labor-intensive than the ones which they substitute.

The main limit of these evaluations is that they use the current economic recipe (e.g. matrix of technical coefficient) to forecast future trends. Moreover, the uncertainty is high on the reallocation of households' and companies' final demands for each economic sector, as one could argue such scenarios go along with important changes in modes of consumption. As most forecasting endeavor though, the author points out that it must be considered in terms of comparison with the business-as-usual scenario, and also conducts sensitivity analysis on a few variables to study their effect on results.

Interestingly, Philippe Quirion and colleagues recently used a similar methodology to evaluate the impact on jobs of Solagro's Afterres 2050 scenario for a sustainable agriculture14 . This scenario (as well as its variants), is presented in Chapter 10 as we will use it in a deliberation role-play.

Finally, as we saw in table 8.2, employment should be assessed both in quantitative and qualitative terms. Beyond the number of jobs (which is of course an essential information), relevant evaluations would for instance include work drudgery, exposure to risks, precariousness, continuing training but also less tangible aspects as one's interest in a job and social representations on it.

We now turn to an example of crossing employment, turnover and biophysical data to show how it can help characterizing each sector regarding its material and labor intensiveness. We do so on the example of the French forest-wood chain: Table 8.3 is obtained by crossing economic data from the ministry of agriculture with the MFA presented in Chapter 7.

Although the table does not show it, the proportion of self-employment varies a lot depending on the sector: 57% for wood harvest, 6% for the first transformation, 8% for the second transformation and less than 1% in the pulp and paper industry. Column ke/1000 m3(f) provides order of magnitude of the economic efficiency of wood in terms of turnover. This conveys a clear idea of the value chain with more and more creation of wealth per unit of material throughput as one moves from harvest to first and then to second transformation. Note that the pulp and paper industry contains in itself first and second transformations and has the highest turnover to material throughput coefficient. The last column, employment per material throughput, is interesting as well. We can see, that although first transformation industries generate nearly 5 times as much value as harvest per material unit, their employment to material ratio is about the same. This can be explained by three factors: harvest also includes forest management that does not directly provide wood to the market, wages in transformation industries are higher than in harvest, and transformation is relying on more capital-intensive investments. The same conclusion can be drawn when comparing the second transformation with the pulp and paper sector: here, capital intensiveness is clearly the main factor explaining that the second transformation is more labor-intensive than the pulp and paper industry per material unit while simultaneously generating less value. Finally, the ratios of the first and second transformation clearly express the fact that the first transformation values the material while the second values work on the material. Note that all ratios presented here only reflect the current situation (degree of horizontal integration in each sector, degree of reliance on imports, available technology etc.) and could not be directly used to provide employment forecasts based on the evolution of physical flows. As we just saw, they can however help better understanding the current functioning of the value chain.

Sector

Employment Employment is computed as the addition of self-employment and employees. Ratios of turnover to material throughput an employment to material throughput are computed on this basis. The 1 st transformation sector includes sawmills, wood panels and plywood and the 2 nd transformation sector includes wooden frames and joineries, wood packaging, furnitures, wooden consumer goods. Numbers related to this sector may be a bit biased because some activities (e.g furniture) encompass other materials as well and are only partially part of the wood chain. The material throughput of each of these four sectors is computed by looking at their inputs (for 1 st tranformation, 2 nd transformation and for the paper industry) or outputs (for harvest). For the pulp and paper industry, we add up pulpwood, residues from sawmills, imported pulp, imported waste paper but not the amount of paper recycled from local waste (which would be double-counting).

Part two recap

The second part was devoted to extending the supply chain MFA (SC-MFA) model to environmental stakes and exploring possibilities of studying socio-economic aspects. More specifically:

• In Chapter 5, we presented methods aiming at tracing flows, both between regions and between industries. We demonstrated the links between Input-Output Analysis (IOA), Absorbing Markov Chains (AMC), and eventually with the Supply and Use tables (SUT) used to handle data in the SC-MFA model. Using Leontief's minimal example of a 2sectors economy, we illustrated that while IOA and AMC were equivalent, using the first was more natural for tracing upstream flows (from consumption to production), the latter being more natural for downstream flows.

• In Chapter 6, we extended the MFA study on the French cereal supply chain presented in Chapter 3 to environmental pressures (energy use and greenhouse gases emissions, land use, use of pesticides and blue water footprint). For this purpose, we extended the cereal model to meat, dairy and eggs products and used AMC to trace flows. The main goal was to build environmental footprint accounts from the producer's and consumer's viewpoints but we showed many other questions could be tackled by the model: What is the fate of a specific product? What are the supply areas of a given region for a given product and along the product's fabrication steps? What life-cycle phases (production, transformation, transport) are the most critical for each pressure? What pressures (e.g. land use) are virtually traded between regions? We pointed out the limits of this work and possible ways to overcome them; in particular, providing a detailed view of the whole agri-food sector and describing supply chains of other countries seems to be required in order to be more policy relevant.

• In Chapter 7, we developed in collaboration with the Laboratory of Forest Economics (LEF, Nancy), a SC-MFA model of the French forest-wood chain. One important goal was to objectify the importance of raw wood exports and put them in context with flows in the rest of the supply chain. LEF's partial equilibrium model (FFSM) was then applied in order to explore potential consequences of log export reduction policies on both the economy of the sector and material flows. Although the article is only focused on the national level, regional results were obtained as well and an example is given in supplementary material.

• Chapter 8 's purpose was to provide an overview of additional socio-economic aspects that could be studied on the basis of the SC-MFA model. To do so, we presented a set of frameworks originating from economics, sociology and management that could be adapted to the supply chain context, including Ostrom's framework of social-ecological systems, concepts applied in territorial ecology and stakeholders theory. In a decisionaiding perspective, we then focused on the issue of employment to understand how effects of public policies could be estimated and provide a first idea of how crossing material flow data with economic and employment data could help to better understand the value chain. In this perspective, Sankey diagrams comparing material and monetary flows offer a powerful representation, all the more so if one is able to spatialize them down to the city level.

Overall, in order to convey more synthetic results and discard information that is considered too uncertain, it would be useful to conduct a "fuzzification" process on current outputs from SC-MFA and environmental extensions. In particular, this will require to conduct sensitivity analyses (for instance more systematically testing different distance functions in the data reconciliation process). In turn, this could also provide ideas on how to simplify the model, thus making it more transparent, while retaining essential information.

Part III

Structuring public deliberation through multicriteria methods

Chapter 9

Principles of multicriteria decision-aiding, participation and deliberation

This chapter (as one can guess from the title) is mainly dedicated to the presentation of Multicriteria Decision-Aiding (MCDA), and to the concepts of participation and deliberation. After outlining the main decision models and theories, we describe each step of MCDA in a participatory context, with a special focus on multicriteria aggregation methods. We then discuss participation and controversies surrounding it before introducing the underlying principles of deliberative democracy that will guide us in the next chapter, for the design of a decision-aiding procedure.

A short introduction to decision theories

Deciding is choosing an action among different possibilities. This choice is based on the values, preferences and objectives of the decision-maker(s). From the 1950's, decision-making has become the subject of an academic discipline, at the crossroads of management, organizations' sociology and political sciences. The rational model has been revisited and other decision models have been developed. They underline the fact that decision-making processes are in no way neutral or objective (CEDIP, 2012).

In the rational model, the individual (homo oeconomicus), is able to rank its preferences transitively, to optimize its resources in order to maximize its satisfaction and to perfectly analyze its environment in order to anticipate the best decisions to make.

In the bounded rationality model, individuals cannot find a perfect solution, in the sense of satisfaction maximization, but only a satisfying solution. Indeed, the available information is imperfect (it contains uncertainties that are difficult to handle), the decision-maker has a limited capacity to integrate the information and finally actors may find themselves in situations of strategical interdependence. Only a limited number of actions is studied [START_REF] Simon | Models of Man[END_REF].

In the political model, the decision process is a cycle of bargains and negotiations between decision-makers. In order to reach their objectives, the latter can conceal or distort information.

In the garbage can model, decisions emerge from random encounters between a flow of problems, a flow of solutions, a flow of participants, and occasions to choose. The interest of this model is not to overestimate the rationality of actors. However, it is ill-suited for planned decision-making processes. deliberation Finally, in the cognitive hierarchy model, decision-makers are separated in 3 classes: "cognitive decision-makers" who make rational choices depending on objective information available to them, "affective decision-makers", who are more sensible to feelings than to facts, and "mix decision-makers". This model is widely used to study consumer behavior.

As we will see right away, the underlying decision model behind MCDA is the bounded rationality model, although all processes described above may also play a role at certain times. Transversely to these models, it is possible to decide alone or in a group. In this last case, one can distinguish between decision by delegation, for instance to an expert trusted by the group, decision by majority, implying a voting procedure, and finally decision by apparent consensus, which is less well know and will be presented in the second section.

Multicriteria decision-aiding in a multi-stakeholders context

Decision-aiding is defined by [START_REF] Roy | Aide multicritère à la décision : méthodes et cas[END_REF] as an activity serving action (personal translation): "The purpose of decision aiding is to identify part of an answer to questions asked by stakeholders in a decision process. Decision-aiding acts through the use of explicit but not completely formalized models. These partial answers inform the decision and recommend, or simply foster, a behavior increasing the coherence between the evolution of the process on the one hand and the objectives and systems of values the decision-maker is confronted to on the other hand ".

In this section, we wish to focus on a particular field of decision-aiding that makes use of multicriteria methods in a participatory context. The implementation of such methods requires several steps: (o) identification of the problem, (i) identification of stakeholders and determination of their involvement, (ii) determination of possible actions to address the problem, (iii) choice of evaluation criteria, (iv) indicators design, (v) evaluation of actions with the selected indicators, and finally, (vi) preference aggregation among criteria and among stakeholders. We will describe these steps shortly, but first, as the involvement of various stakeholders adds a layer of complexity to the process, we present the main grounds for choosing this path for sustainability issues.

Why foster participative processes?

Froger and [START_REF] Froger | L'aide multicritère à la décision participative : une démarche originale de gouvernance en matière de développement durable[END_REF] emphasize the incentives of top executives to include sustainable development in their decision processes through the example of the 1992 Rio Declaration on Environment and Development and the Agenda 21 initiatives. Two main reasons are advanced.

The first reason is of epistemic order and is related to problems complexity. Problems are complex because actions (or non-decisions) have delayed or remote consequences, because consequences are uncertain, and because of a network of inter-connections inside ecosystems but also, at all geographical scales, between the economic, social and environmental spheres. This complexity may be managed through the participation of different stakeholders, who address the problem together and justify their points of view based on their experiences and knowledge.

The second reason is of instrumental order. Sustainability issues are characterized by the presence of various stakeholders whose short-term interests diverge. Participation must then allow to make different judgments explicit; the objective is not necessarily to reconcile them, but to favor the acceptability of decisions. This seems all the more required as the traditional decision model for public projects, organized around the couple State/experts, has been increasingly questioned in recent decades. Part of the population challenges the legitimacy of the decisions taken by their political representatives, as recent confrontations about "useless imposed mega-projects" illustrate. While this is not a new issue1 , it becomes more acute in times of crises. Participation is then viewed mostly as a way to reduce the risk of conflict, although under adequate conditions, it can effectively favor the inclusion of various viewpoints, deliberation and transparency.

These reflections are directly linked to the concepts of governance, participatory democracy and deliberative democracy in the field of political science. Note that the definitions of these terms, in particular those of governance, vary in the literature. For example, [START_REF] Scorier | Démocratie managériale, démocratie délibérative et écologie politique[END_REF] distinguish them according to a hierarchy of public authorities' motivations (personal translations). Thus, "the objective of governance is not to make a legitimate decision, potentially respected by all, but rather to legitimize the actions of public authorities [...]. Governance motivates and empowers actors to achieve its ends", while "participatory democracy is a matter of consolidating the legitimacy of political decisions by involving non-elected citizens in the discussions". Finally, participation differs from the deliberative project, as proposed by [START_REF] Habermas | Au-delà du libéralisme et du républicanisme, la démocratie délibérative[END_REF]. If participation can be a way to anticipate or to defuse conflict, the deliberative project instead seeks to promote a critical activity. It is a matter of "refining understanding, decoding information, revealing strategies, manipulations and bargains between interest groups, to make room for a communication space where only the best argument prevails" (personal translation). In this sense, deliberative democracy can be considered as an ideal to strive for. We will come back to this in the second section. Let us now describe the main steps of MCDA.

Identification and involvement of stakeholders

As we saw in Chapter 8, the concept of stakeholder is much broader than that of actor. Future generations, who are directly affected by certain decisions but not involved in problems formulation or solving are a good illustration of the distinction between stakeholders and actors. [START_REF] Banville | A stakeholder's approach to MCDA -Document de travail[END_REF] propose to classify stakeholders according to two criteria: their relationship to the problem (are they influenced by the problem, do they influence it, or both? ) and their level of participation (direct or indirect participation in decision-making). Meanwhile, [START_REF] Mitchell | Toward a theory of stakeholder identification and salience: Defining the principle of who or what really counts[END_REF] propose an analytical framework based on three criteria: power, legitimacy and urgency2 .

Participatory decision corresponds to a situation involving several stakeholders: policy makers, experts, interest groups, public etc. It is not a mere consultation nor a negotiation, but a form of intermediate decision. As we have discussed above, the involvement of each stakeholder in the process is essential to achieve some legitimacy. This legitimacy is based on an implicit initial consensus: stakeholders agree to undergo the planned procedure for adopting a solution. deliberation This is the reason why it is important to clarify the power and mode of intervention of each stakeholder at the beginning. Not all (and usually very few) stakeholders have an ultimate decision-making power and they can play different roles. [START_REF] Keeney | Value focused thinking: a path to creative decision making[END_REF] proposes to differentiate between values and facts. [START_REF] Rousseau | La décision participative : une démarche pour gérer efficacement les conflits environnementaux -document de travail 96-24[END_REF] thus indicate that: "one can ask experts to make judgments based on facts (relations between causes and effects for example), but as experts, they do not bear the responsibility to make value judgments on behalf of the general population. Similarly, one shouldn't ask the public to speculate about complex systems". An expert can therefore help feed or animate the decision process but shouldn't act directly on the decision.

Construction of scenarios

Scenario planning emerged in the second half of the 20 th century with two main school of thought [START_REF] Lecourt | Philosophie prospective[END_REF] 3 . The American school emerged mostly under the impulse of the Rand Corportation4 and was mainly based on computation, statistics and deductive reasoning. The work undergone in The Limits to Growth [START_REF] Meadows | The limits to Growth[END_REF] is related to this branch. The French school of "la prospective" on the other hand, for instance represented by the works of [START_REF] Berger | L'attitude prospective[END_REF], [START_REF] Jouvenel | La démarche prospective. un bref guide méthodologique[END_REF] or DATAR (1975), was more qualitative, multidisciplinary, and aimed at exploring contrasted futures using hypotheses of trend discontinuation. To a large extent, this clear distinction no longer stands as most studies now use a mix of the two approaches. [START_REF] Kahn | Year 2000, A framework for speculation on the next thirtythree years[END_REF] define scenarios as "attempts to describe in some detail a hypothetical sequence of events that could plausibly lead to the situation envisaged ". [START_REF] Schwartz | Plotting your scenarios[END_REF] provide a complementary point of view by stating that: "Scenarios are narratives of alternative environments in which today's decisions may be played out. They are not predictions. Nor are they strategies. Instead they are more like hypotheses of different futures specifically designed to highlight the risks and opportunities involved in specific strategic issues". Scenarios can project past trends, leading to a probable future, they can explore possible futures starting from current trends but also from emerging changes, or they can provide a (positive or negative) normative vision of the future and backcast possible trajectories leading to this future.

Among other possibilities, [START_REF] Godet | La prospective stratégique pour les entreprises et les territoires[END_REF] propose a method based on the identification of core variables driving the evolution of the system. These can for instance be demography, economic and geopolitic context, technological progress, cultural evolution etc. In a second step, mini-scenarios are proposed by participants for each of these variables, for instance the coming of an economic crisis or in contrary of an unexpected technological innovation. Scenarios are then formed by combining the mini-scenarios together and seeing if it is possible to make sense of them (which is of course not the case for all combinations). This methodology, has the advantage of structuring the process and fostering creativity. Of course it is possible to use it only as a starting point of a more thorough reflection.

In this context, participation is valuable as it helps gathering a large variability of knowledge and viewpoints. One can also point out that debates occurring during this phase can be the base of future collective action. Finally, for the interest of the MCDA process (and of the decision-makers), it is useful to provide contrasted scenarios rather than lighter and darker shades of a central scenario.

Choice of criteria

The choice of criteria and corresponding indicators is a key step in the process and must be conducted in a transparent manner. Criteria determination can be considered in two complementary ways. [START_REF] Keeney | Decisions with multiple objectives: preferences and value tradeoff[END_REF] assume that certain stakeholders, for instance project promoters, can easily explain their point of views by referring to their objectives, since actions were motivated by these objectives. On the other hand, [START_REF] Roy | Méthodologie multicritère d'aide à la décision[END_REF] stresses that other stakeholders can better explain their perspectives by referring to the consequences of the actions when they are affected by these consequences. It is therefore important to take into account these two methods (objectives and consequences) to ensure that one has properly addressed the interest of each stakeholder.

Design of indicators

OECD (2008a) proposes a practical manual for the design of composite indicators in which important factors that must be taken into account when selecting indicators are listed. These are relevance, simplicity, reliability (and sensitivity to change), political bias5 , feasibility in terms of timeliness and data collection, and contribution to a coherent and comprehensive view.

Regarding this last factor (global contribution), the European Environment Agency suggests to classify indicators according to the DPSIR framework (Drivers, Pressures, State, Impacts, and Responses). Under this framework, adapted to the environmental issues, drivers (e.g. economic activities) produce pressures (e.g. greenhouse gas emissions) that change the state of the system (e.g. the chemical composition of the atmosphere). This produces a series of cascading effects, often undesirable (e.g. climate change will cause a rise in sea level and population migration).

Policymakers must then take measures (responses) in order to target each of the previous steps (develop plans to adapt to climate change impacts, encourage businesses and households to emit less carbon etc.). Starting from the DPSIR framework, one can build efficiency indicators. for instance, the energy efficiency of the economy can be measured by dividing the quantity of goods and services (driver indicator) by energy consumption (pressure indicator). possible compensation phenomena between incomparable issues. This leads us to address the multi criteria aggregation methods in the following paragraph.

Multicriteria aggregation

Overview of multicriteria analysis

The two major multi-criteria approaches, compensatory and non-compensatory, directly derive from the work of Condorcet and Borda on electoral processes. The latter are besides considered to be the founders of social choice and rational choice theories [START_REF] Gaertner | A Primer in Social Choice Theory: Revised Edition[END_REF]. Before presenting these branches, two conclusions are worth noting. On the one hand, the final decision is partly conditioned by the voting system chosen. On the other, [START_REF] Arrow | Social choice and individual values[END_REF] demonstrates that it is impossible to aggregate multiple preferences into a single collective preference endowed with all desirable characteristics (universality, unanimity, independence of irrelevant alternatives) without using the dictatorship of one viewpoint6 . Therefore, there is no universal procedure. A voting or multi-criteria decision procedure must be formulated considering the context and the objectives, and focus on certain features at the expense of others. There is a direct link between a voting procedure and a multi-criteria decision: alternatives to assess in a multi-criteria procedure can be likened to candidates and the criteria to voters.

Compensation refers to the existence of trade-offs, that is, the possibility of offsetting a disadvantage on some criteria by a sufficiently large advantage on another criterion. Compensatory methods commonly begin by aggregating and then compare. The most widely used one is the weighted arithmetic average. However, this technique tends to favor extreme alternatives at the expense of balanced alternatives (in terms of their performance on each criterion). In this regard, the geometric mean is less compensatory than the arithmetic mean as it tends to favor balanced alternatives. Utility functions such as the Multi Attribute Utility Theory (MAUT) are a generalization of these compensatory methods.

In certain circumstances, allowing compensation between criteria may not be wanted because criteria are incomparable. For example, in the family of environmental criteria, local and global pollution can be considered incomparable. Similarly, in a perspective of strong sustainability, one cannot compensate weak environmental performance with good economic performance. The non-compensatory methods begin by comparing and then aggregate. Most often, the comparison step is characterized by a pairwise comparison of alternatives, as in the PROMETHEE and ELECTRE methods. Some methods authorize vetoes (acceptability thresholds). Non-compensation is eventually based on two scales of distinct values: a scale of preference and a scale of rejection. These methods enable a clearer analysis of possible choices, eliminate certain alternatives, but generally do not generate a transitive preference relation among the different alternatives: some can be considered incomparable. The decision then has to be justified by the greater attachment to a system of values over another. deliberation 9.2.6.2 A didactic example with Lara, Pablo and Juan: Weighted average, AHP and Promethee

The goal here is not to present all existing multi-criteria methods, nor to study them from a mathematical point of view. In order to do that, the reader can for instance refer to [START_REF] Ishizaka | Multi-Criteria Decision Analysis, Methods and Software[END_REF]. Rather, we want to apply three different methods on a single example stripped down to the bare minimum in order to show the importance of the choice of the method and of its parameters. By doing so, we point out the distinction between methods that allow compensation between criteria and methods that don't.

The problem A school wants to select the best student between Pablo, Lara and Juan (3 alternatives) given their grades in French and Maths (2 criteria). The following table summarizes their performance in those subjects:

2 means to efficiently organize public debate. The goal is for each participant to have a deeper view of the problem discussed: he/she should be able to better justify his/her own preferences (that may evolve during the process), to understand more clearly the positions of others, and finally, to identify the possible lock-in(s) (interactions or judgment traps) that prevent to reach a decision that is acceptable for all involved parties. In this perspective, the decision that will be taken at the end of the process is less important than the process itself.

For instance, since we are dealing with complex systems, new information may appear in the future that is in contradiction with the original decision. If the original decision was taken unilaterally and in opacity, it will be hard to quickly converge towards a new decision whereas if a transparent multi-stakeholder framework was already implemented, the new information can be integrated quickly in the decision process.

Multi1criteria!

The goal here is not to present all the existing multi-criteria methods, nor to study them from a mathematical point of view. In order to do that, the reader can for instance refer to [START_REF] Ishizaka | Multi-Criteria Decision Analysis, Methods and Software[END_REF]. Rather, we want to apply three different methods on a single example stripped down to the bare minimum in order to show the importance of the choice of the method and of its parameters. By doing so, we point out the distinction between methods that allow compensation between criteria and methods that don't. Compensability refers to the existence of trade-offs, i.e. the possibility of offsetting a disadvantage on some criteria by a sufficiently large advantage on another criterion (OECD, 2010).

The!problem!

A school wants to select the best student between Pablo, Lara and Juan (3 alternatives) given their grades in French and Math (2 criteria). The following table summarizes their performance in those subjects: 0 would be the worst possible grade and 10 the best possible grade.

Methods!with!compensation!

2.2.1. Weighted!average! The weighted average is the most common/natural method to solve this kind of problem. Coefficients (weights) are chosen for French and Math (i.e., for each criteria), a weighted Zero would be the worst possible grade and 10 the best possible grade.

Methods with compensation

Weighted average

The weighted average is the most common/natural method to solve this kind of problem. Coefficients (weights) are chosen for French and Maths (i.e., for each criteria), a weighted average is computed for each student (i.e., for each alternative) and the students are ranked based on this single indicator. Each coefficient can take all the values from 0 to 1, under the constraint that the sum of all coefficients must be equal to 1.

The figure below shows that whatever the coefficients chosen, Juan will never be selected as the best student (arrows represent the coefficients in French and Maths).

average is computed for each student (i.e., for each alternative) and the students are ranked based on this single indicator. Each coefficient can take all the values from 0 to 1, under the constraint that the sum of all coefficients must be equal to 1.

The figure below shows that whatever the coefficients chosen, Juan will never be selected as the best student (arrows represent the coefficients in French and Math).

The weighted average penalizes balanced profiles because it allows full compensation between criteria: poor Math skills can be compensated by excellent French skills. In many cases, this is not a desired property, so decision-makers should be aware of it. For instance, here, the school may want to select someone that has (at least) an average level in French and Math.

Remark: the weighted average does not always eliminate balanced profile; for example, if Juan has 7 in both Math and French, it dominates both Lara and Pablo for equal weights. However, it has a strong tendency to do so as can be seen from the fact that 7 is already a high grade.

AHP!(Analytical!Hierarchy!Process)!

AHP is well adapted to human thinking. Therefore its results are more likely to reflect the judgments of the decision-makers. Indeed, it uses pairwise comparisons to assess:

-how well each alternative performs against each criteria ; in this step, the available information on alternatives (qualitative or quantitative, in our case, the grades in French and Math) are used to produce a relative scoring of alternatives for each criteria ; the score is relative to the other alternatives it is compared with, -How important is each criteria; this step leads to the choice of the relative weight of each criteria.

The weighted average penalizes balanced profiles because it allows full compensation between criteria: poor Maths skills can be compensated by excellent French skills. In many cases, this is not a desired property, so decision-makers should be aware of it. For instance, here, the school may want to select someone that has (at least) an average level in French and Maths. Of course, the weighted average does not always eliminate balanced profile; for example, if Juan has 7 in both Maths and French, Juan dominates both Lara and Pablo for equal weights. However, the weighted average method has a strong tendency to do so as can be seen from the fact that 7 is already a high grade.

If the school really wants to select someone with sufficient French and Math proficiency, but does not really seek excellent skills in these subject matters, the scores of pairwise comparisons could look like this:

It is worth noting that those comparisons are not necessarily fully consistent from a purely rational point of view (no transitivity property) because each comparison is conducted independently. For instance, it is not impossible to have the following judgment for alternatives A, B, C: A > B, B > C and C > A. An index of consistency has to be computed (Saaty, 1987), and it may not be a good choice to keep using AHP if this index is too high.

The comparison scores are then put in a matrix form.

Final (relative) scores are computed (blue column) as the principal right eigenvector of the matrices. Those scores can be interpreted as relative preference intensities: for instance, here

If the school really wants to select someone with sufficient French and Maths proficiency, but does not really seek excellent skills in these subject matters, the scores of pairwise comparisons could look like this:

If the school really wants to select someone with sufficient French and Math proficiency, but does not really seek excellent skills in these subject matters, the scores of pairwise comparisons could look like this:

It is worth noting that those comparisons are not necessarily fully consistent from a purely rational point of view (no transitivity property) because each comparison is conducted independently. For instance, it is not impossible to have the following judgment for alternatives A, B, C: A > B, B > C and C > A. An index of consistency has to be computed (Saaty, 1987), and it may not be a good choice to keep using AHP if this index is too high.

The comparison scores are then put in a matrix form.

Final (relative) scores are computed (blue column) as the principal right eigenvector of the matrices. Those scores can be interpreted as relative preference intensities: for instance, here we can conclude that, regarding French, Pablo is preferred 0.59/0.36 = 1,64 times over Juan and 0.59/0.05 = 11.8 times over Lara.

It is worth noting that those comparisons are not necessarily fully consistent from a purely rational point of view (no transitivity property) because each comparison is conducted independently. For instance, it is not impossible to have the following judgment for alternatives A, B, C: A>B, B>C and C>A. An index of consistency has to be computed (Saaty, 1987), and it may not be a good choice to keep using AHP if this index is too low. The comparison scores are then put in a matrix form.

It is worth noting that those comparisons are not necessarily fully consistent from a purely rational point of view (no transitivity property) because each comparison is conducted independently. For instance, it is not impossible to have the following judgment for alternatives A, B, C: A > B, B > C and C > A. An index of consistency has to be computed (Saaty, 1987), and it may not be a good choice to keep using AHP if this index is too high.

The comparison scores are then put in a matrix form.

Final (relative) scores are computed (blue column) as the principal right eigenvector of the matrices. Those scores can be interpreted as relative preference intensities: for instance, here we can conclude that, regarding French, Pablo is preferred 0.59/0.36 = 1,64 times over Juan and 0.59/0.05 = 11.8 times over Lara.

The second step consists of choosing weights for each criteria. With only two criteria (French and Math), there is little interest in using AHP for defining weights. It however becomes very useful when there are 3 or more criteria. In this case, similarly to what is presented above, pairwise comparisons have to be conducted on the criteria (for instance what is the decision maker's preference between French and Math, French and History, Math and History…), Final (relative) scores are computed (blue column) as the principal right eigenvector of the matrices. Those scores can be interpreted as relative preference intensities: for instance, here we can conclude that, regarding French, Pablo is preferred 0.59/0.36 = 1,64 times over Juan and 0.59/0.05 = 11.8 times over Lara.

The second step consists of choosing weights for each criteria. With only two criteria (French and Maths), there is little interest in using AHP for defining weights. AHP becomes very useful, however, when there are 3 or more criteria. In this case, similarly to what is presented above, pairwise comparisons have to be conducted on the criteria (for instance, What is the decision maker's preference between French and Maths, French and History, Maths and History? ), using the same scoring scale (from 1 to 9). The final weights are obtained by the principal right eigenvector of the new matrix.

The figure below shows the intervals of coefficients where each candidate can be selected (numbers are rounded for simplification): we can see that if the school is seeking a balanced profile, it will choose balanced coefficients in French and Maths, i.e. close to 0.5. This corresponds to the domain of value where Juan is ranked first. 5 using the same scoring scale (from 1 to 9). The final weights are obtained by the principal right eigenvector of the new matrix.

The figure below shows the intervals of coefficients where each candidate can be selected (numbers are rounded for simplification): we can see that if the school is seeking a balanced profile, it will choose balanced coefficients in French and Math, i.e. close to 0.5. This corresponds to the domain of value where Juan is ranked first.

In the case of coefficients 0.5 in French and Math, the following representations can be used:

Using AHP allowed the decision-maker to better express his preferences, comparatively to the weighted average method. However the method still has a few drawbacks:

-Even in the most favorable case (coefficients of 0.5 in French and Maths), Juan is not selected with a strong preference intensity: 0.36/0.32 = only 1.1 times as much as Pablo or Lara. The table below gives the final (weighted) relative scores of the students with these coefficients. This is explained by the fact that AHP still allows compensation between criteria.

-The final ranking provided by AHP is sensitive to the alternatives originally considered. For instance, in the last example, Juan is preferred to Pablo but it may happen that starting the procedure again with another new candidate, Ines, will lead to an inversion of this ranking: Pablo being preferred to Juan. This property is of course not intuitive and not desirable. Consequently, if one uses AHP, we would advise to first consider all possible alternatives, and then restart the process with a reduced number of alternatives (the ones which scored the highest) to see if their relative ranking is modified or not.

In the case of coefficients 0.5 in French and Maths, the following representations can be used: using the same scoring scale (from 1 to 9). The final weights are obtained by the principal right eigenvector of the new matrix.

The figure below shows the intervals of coefficients where each candidate can be selected (numbers are rounded for simplification): we can see that if the school is seeking a balanced profile, it will choose balanced coefficients in French and Math, i.e. close to 0.5. This corresponds to the domain of value where Juan is ranked first.

In the case of coefficients 0.5 in French and Math, the following representations can be used:

Using AHP allowed the decision-maker to better express his preferences, comparatively to the weighted average method. However the method still has a few drawbacks:

-Even in the most favorable case (coefficients of 0.5 in French and Maths), Juan is not selected with a strong preference intensity: 0.36/0.32 = only 1.1 times as much as Pablo or Lara. The table below gives the final (weighted) relative scores of the students with these coefficients. This is explained by the fact that AHP still allows compensation between criteria.

-The final ranking provided by AHP is sensitive to the alternatives originally considered. For instance, in the last example, Juan is preferred to Pablo but it may happen that starting the procedure again with another new candidate, Ines, will lead to

Using AHP allowed the decision-maker to better express his preferences, comparatively to the weighted average method. However the method still has a few drawbacks:

• Even in the most favorable case (coefficients of 0.5 in French and Maths), Juan is not selected with a strong preference intensity: 0.36/0.32 = only 1.1 times as much as Pablo or Lara. The table below gives the final (weighted) relative scores of the students with these coefficients.

5

Using AHP allowed the decision-maker to better express his preferences, comparatively to the weighted average method. However the method still has a few drawbacks:

-Even in the most favorable case (coefficients of 0.5 in French and Maths), Juan is not selected with a strong preference intensity: 0.36/0.32 = only 1.1 times as much as Pablo or Lara. The table below gives the final (weighted) relative scores of the students with these coefficients. This is explained by the fact that AHP still allows compensation between criteria.

-The final ranking provided by AHP is sensitive to the alternatives originally considered. For instance, in the last example, Juan is preferred to Pablo but it may happen that starting the procedure again with another new candidate, Ines, will lead to an inversion of this ranking: Pablo being preferred to Juan. This property is of course not intuitive and not desirable. Consequently, if one uses AHP, we would advise to first consider all possible alternatives, and then restart the process with a reduced number of alternatives (the ones which scored the highest) to see if their relative ranking is modified or not.

This is explained by the fact that AHP still allows compensation between criteria.

• The final ranking provided by AHP is sensitive to the alternatives originally considered. For instance, in the last example, Juan is preferred to Pablo but it may happen that starting the procedure again with another new candidate, Ines, will lead to an inversion of this ranking: Pablo being preferred to Juan. This property is of course not intuitive and not desirable. Consequently, if one uses AHP, we would advise to first consider all possible alternatives, and then restart the process with a reduced number of alternatives (the ones which scored the highest) to see if their relative ranking is modified or not.

Methods without compensation (outranking): the example of Prométhée Outranking methods do not lead to the same type of results as compensation methods. The main advantage is that they don't reduce the problem to the comparison of a single indicator.

For instance, Prométhée leads to two different rankings of alternatives: one ranking according to preference intensities and a second ranking for rejection intensities. This is a way of simplifying the problem while still reflecting the preferences and values of decision-makers. The main drawback however is that some options can appear at the end of the process as incomparable: in the general case, outranking methods will not produce a complete ranking of alternatives.

In the following, we illustrate this by using the Prométhée method on our basic example.

Similarly to AHP, Prométhée uses pairwise comparisons, to compare alternatives relatively to each criteria. The scale is the following: 6

Methods!without!compensation!(outranking):!the!example!of!Prométhée!

Outranking methods do not lead to the same type of results as compensation methods. The main advantage is that they don't reduce the complexity of the problem to the comparison of a single indicator. For instance, Prométhée1 leads to two different rankings of alternatives: one ranking according to preference intensities and a second ranking for rejection intensities. This is a way of simplifying the problem while still reflecting the preferences and values of decision-makers. The main drawback however is that some options can appear at the end of the process as incomparable: in the general case, outranking methods will not produce a complete ranking of alternatives. In the following, we illustrate this by using the Prométhée method on our basic example.

Similarly to AHP, Prométhée uses pairwise comparisons, to compare alternatives relatively to each criteria. The scale is the following:

If we still take the example of a school looking for balanced profiles, the following scores may follow from the pairwise comparison process:

From this, we can compute average preference and rejection intensities for each alternative and criteria as show in the next figure :   1 Outranking methods are used worldwide, but have been mostly developed by the French school. Hence the French spelling of Prometheus.

If we still take the example of a school looking for balanced profiles, the following scores may follow from the pairwise comparison process:

Methods!without!compensation!(outranking):!the!example!of!Prométhée!

Outranking methods do not lead to the same type of results as compensation methods. The main advantage is that they don't reduce the complexity of the problem to the comparison of a single indicator. For instance, Prométhée 1 leads to two different rankings of alternatives: one ranking according to preference intensities and a second ranking for rejection intensities. This is a way of simplifying the problem while still reflecting the preferences and values of decision-makers. The main drawback however is that some options can appear at the end of the process as incomparable: in the general case, outranking methods will not produce a complete ranking of alternatives. In the following, we illustrate this by using the Prométhée method on our basic example.

Similarly to AHP, Prométhée uses pairwise comparisons, to compare alternatives relatively to each criteria. The scale is the following:

If we still take the example of a school looking for balanced profiles, the following scores may follow from the pairwise comparison process:

From this, we can compute average preference and rejection intensities for each alternative and criteria as show in the next figure :  From this, we can compute average preference and rejection intensities for each alternative and criteria as shown in the next figure: 8 strongly rejected). In this case, we can conclude that Juan is preferred over Pablo and Lara and the decision is easy to take for the decision-maker.

It is interesting to see that Juan is not strongly preferred but rather substantially less rejected than the other two options.

Weights of 0.8 in French and 0.2 in Maths. The choice of this coefficients means that the school attaches more importance to French than to Math. This question is independent from defining a scale of values for each criteria (e.g. saying that the difference between grades 10 and 6 is less important than the difference between 6 and 2). In this case, the output will look like this: Pablo and Juan are both better choices than Lara (in the case of this particular choice of coefficients of course…), however they are incomparable: Pablo is preferred to Juan but Juan is less rejected than Pablo. The interest of such a result for decision-making may not be obvious in this simple example but it gets clearer when the complexity increases:

-it makes it possible to reduce the number of considered alternatives (for instance, Lara would be rejected here), -it summarizes all the criteria in only two rankings which are easy to interpret (preference and rejection intensities) ; note that it is possible to substract rejection from preference to end up with a single indicator (here, Pablo and Juan would score 0.3 and Lara -0.6), but in this case, the interest of non-compensation methods is lost, -it is possible to study further incomparable alternatives by for instance adding new criteria or applying another method to them. Don't lose sight of the fact that the main goal of multi-criteria methods is not to so much to select the best alternative as to organize the discussions and to help the decisionmaker to formalize his/her values. Many other methods exist and none is ideal. What matters is to be aware of the consequences of the choice of methods and parameters, and to conduct the process in a transparent way.

Multi1stakeholders!

Pablo and Juan are both better choices than Lara (in the case of this particular choice of coefficients of course), however they are incomparable: Pablo is preferred to Juan but Juan is less rejected than Pablo. The interest of such a result for decision-making may not be obvious in this simple example but it gets clearer when the complexity increases:

• It makes it possible to reduce the number of considered alternatives (for instance, Lara would be rejected here),

• It summarizes all the criteria in only two rankings which are easy to interpret (preference and rejection intensities); note that it is possible to substract rejection from preference to end up with a single indicator (here, Pablo and Juan would score 0.3 and Lara -0.6), but in this case, the interest of non-compensation methods is lost,

• It is possible to study further incomparable alternatives by for instance adding new criteria or applying another method to them.

One shouldn't lose sight of the fact that the main goal of multi-criteria methods is not to so much to select the best alternative as to organize the discussions and to help the decision-maker to formalize his/her values. Many other methods exist and none is ideal. What matters is to be aware of the consequences of the choice of methods and parameters, and to conduct the process in a transparent way. 9.2.6.3 MCDA on environmental issues and a few empirical lessons [START_REF] Huang | Multi-criteria decision analysis in environmental sciences: 10 years of applications and trends[END_REF] conducted a scientific literature review of multi-criteria methods applied to environmental issues, analyzing over 300 papers pubished between 2000 and 2009. They emphasize that there has been a significant growth in environmental applications of MCDA over the last decade.

In particular, the graph on figure 9.3 shows which methods were most commonly used depending on the environmental stake under study. Interestingly, the authors also point out that a large majority of Asian and North American papers use the AHP method whereas the method mix is a lot more balanced in Europe. This is consistent with the influence of the French school of multicriteria analysis, in particular regarding the promotion of outranking methods.

Continuing with empirical lessons, CLG (2009) highlight some good-practices in MCDA:

• The objective of the process should be explicitly stated at the beginning: does one want to select the best option, to select a short list of alternatives, to rank all alternatives? Indeed, depending on the objective, judgments from stakeholders may vary, Chapter 9. Principles of multicriteria decision-aiding, participation and deliberation 13 addition, the papers were also classified by the MCDA methods used in the analysis (analytic hierarchy process, multi-attribute utility theory, and outranking). The results suggest that there is a significant growth in environmental applications of MCDA over the last decade across all environmental application areas. Multiple MCDA tools have been successfully used for environmental applications. Even though the use of the specific methods and tools varies in different application areas and geographic regions, our review of a few papers where several methods were used in parallel with the same problem indicates that recommended course of action does not vary significantly with the method applied.

The graph below is also extracted from their paper. It shows which methods were most commonly used depending on the environmental stake under study.

As mentioned above, this graph shows that there are other methods besides AHP and Prométhée, especially MAUT (multi-attribute utility theory) which allows compensation between criteria and ELECTRE that belongs to the outranking methods.

Behzadian et al ( 2010) proposed a literature review on application cases of the Prométhée methodology. The three main types of applications that emerge are: -location of facilities or infrastructures (location of a landfill, path of a (rail)road…), -choice of a technical solution (choice between various soil remediation techniques, choice between construction materials), -choice of a policy mix (mix of taxes, subsidies, regulations to answer an environmental issue). • It can be useful to start the MCDA process from the beginning of the project, because the first discussions may point to missing data for decision-making,

• MCDA is meant to be an iterative process: the result should not be expected in the first go. One should leave time to explore the model fully. The authors specify that: "MCDA is a divide and conquer strategy in the sense that a complex issue is subdivided into parts that are easier to deal with separately, and the theory is used to reassemble the parts. The resulting high-level view typically reveals new features that were not observed in the individual parts. [...] If the results of the modeling don't feel right, explore the discrepancies. [...] Create different displays, conduct sensitivity analysis on weights to help participants to gain a better qualitative feel for the issues and to increase their confidence in the decision",

• The MCDA model should not be over-complicated,

• MCDA does not give the answer to a problem, subjective judgments are necessary inputs to the modeling. Making decisions in necessarily a human function,

• Time should be devoted to the design of the final output of the process. Graphs can be useful but words should not be neglected in order to convey the subtlety of the results. Sensitivity analysis enables the results to be couched as conditional conclusions: "If you believe this, this and this, then [A] is best, but if you believe that, that and that, then [B] is best". They conclude that: "This approach highlights the key value judgments, providing realistic freedom of choice, within bounds, for the decision-maker ". Participation refers to the involvement of non-decision makers and non-experts in a decision process, most frequently, members of the civil society. The incentives to implement participatory processes clearly increased in the context of sustainability issues, but participation was already put forward in other contexts long before the Rio conference. The controversies it generates haven't changed much as one can notice in an article by [START_REF] Arnstein | A ladder of citizen participation[END_REF]. As Arnstein provocatively puts it: "The idea of citizen participation is a little like eating spinach: no one is against it in principle because it is good for you. Participation of the governed in their government is, in theory, the cornerstone of democracy -a revered idea that is vigorously applauded by virtually everyone. The applause is reduced to polite handclaps, however, when this principle is advocated by the have-not blacks, Mexican-Americans, Puerto Ricans, Indians, Eskimos and whites. And when the have-not define participation as a redistribution of power, the American consensus on the fundamental principle explodes [...] ". Considering that a typology was needed to differentiate empty rituals of participation from real citizen power, he proposed a "Ladder for Citizen Participation" displayed in figure 9.4, and used it to characterize examples of federal social programs in the late 60's USA: urban renewal, anti-poverty, and Model Cities. He distinguishes eight levels of increasing participation. Manipulation (1) as well as Therapy (2) refer to uses of participation as pretexts for power-holders to "educate or cure the participants" and strengthen their authority. Informing (3), Consultation (4) and Placation ( 5) are refered to as degrees of "tokenism" (i.e. the practice of making no more than a minimal gesture): citizens can express their opinion, be heard or even advise but they don't have any decision power. Upper in the ladder, citizens gain power on some aspects of the decisions: in Partnership (6), they can negociate with powerholders and in Delegated power (7) and Citizen control (8), "have-not citizen obtain the majority of decision-making seats, or full managerial power ". Of course, participation can arise disbelief and hostility in people that have felt manipulated. This is all the more true in a context where citizens increasingly question the legitimacy of their deliberation representatives, while at the same time losing interest in politics [START_REF] Van Reybrouck | Contre les élections[END_REF]. Giving up on participation is however not a real option for anyone who believes in democracy. The question is then to be able to spot and expose nonparticipation and to imagine conditions that could be favorable for both participants and decision-makers. As we already highlighted, engaging in transparent processes is a start for people to regain confidence.

At the beginning of the chapter, we provided insights on the differences between participatory and deliberative democracy. The first can be seen as concrete and instrumental. The latter first and foremost has normative grounds, that we will now present.

Deliberative democracy

A procedural legitimacy

What is it that makes a political decision legitimate? This is the question tackled by Bernard Manin in his 1985 article Volonté générale ou délibération ? [START_REF] Manin | Volonté générale ou délibération ?[END_REF] 7 . Reflecting on the notion of justice and on the possibility to define universal social rules, he begins by examining what he considers the most commonly accepted source of legitimacy: unanimity. A decision is legitimate in so far as all individuals support it.

In this view, for radical liberals, "security is the only acceptable political principle" as individuals seek to pursue their own interests "in peace" with the least possible constraints. The State shouldn't set rules influencing material conditions since definitions of well-being vary from one individual to the other. However, Manin points out that "for individuals whose incomes and actual circumstances are below a certain threshold, [the right to pursue one's objectives without constraints], simply loses its meaning.", which disqualifies liberal theories' claim of universality.

Democratic theories in fact do not only think in terms of legitimacy but also in terms of efficiency. The majority principle is precisely introduced as a way to reach decisions. However, one must keep in mind that: "The majority will is not intrinsically legitimate, it is legitimized because one decides to confer upon it all attributes of unanimous will ". Only utilitarian theories can consistently justify it as they seek to maximize happiness for a majority of people, be it at the detriment of a minority. These views however seem morally unacceptable to Manin.

Universalistic theories, notably that of Rousseau and Rawls seek to prove universal principles exist such that unanimity and justice can be reached. In Rousseau's writing, individuals abiding by the general will are only obeying themselves (even if they are not aware of it), since their predetermined will is by nature congruent with the general will. In this view, debate can only distort individual wills, for instance because of rhetorical abilities of certain speakers, and twist the general will (which is then refered to as the will of all ). Rawls puts the underlying intuition of Rousseau's social contract in a different perspective. His Theory of Justice [START_REF] Rawls | A theory of justice[END_REF] states that under circumstances where individuals wouldn't know their position in society (the "veil of ignorance"), they would naturally advocate that (i) "each person [should have] an equal right to a fully adequate scheme of equal basic liberties which is compatible with a similar scheme of liberties for all " and (ii) that "Social and economic inequalities are to satisfy two conditions. First, they must be attached to offices and positions open to all under conditions of fair equality of opportunity; and second, they must be to the greatest benefit of the least advantaged members of society.". According to Manin, however, this second principle cannot be recognized as universal as it implies a dissymmetry between two groups of individuals.

More deeply, in agreement with Simon's bounded rationality model, he argues that people do not have a priori predetermined preferences on all subjects: "When individuals have to make a decision about society, it is absolutely unreasonable to assume they possess all necessary information. [...] It is through collective deliberation and individual pondering that incomplete information [...] are clarified without however reaching completeness.". Moreover, "it is unrealistic and illigitimate to assume individuals have from the start a coherent set of preferences [...]. Through deliberation and the exchange of arguments, individuals become aware of internal conflicts related to their own desires".

It is in fact a preconceived idea that the only source of political legitimacy is the will of individuals. Manin's central thesis is that: "The legitimate decision is not the will of all, but the one resulting from the deliberation of all; it is the process of will formation which confers legitimacy to the result, not the predetermined wills. Such a principle is both individualistic and democratic.". It is democratic in the sense that one assumes all can participate in the deliberation process, and individualistic because everyone freely makes up his mind on one option or another.

Deliberation is a rational argumentative process where opposing visions attempt to convince one another. However, setting out arguments does not mean demonstrating a truth and people are free to accept or reject them. Therefore deliberation cannot lead to "necessary and universally accepted truths". However it helps reassess one's preconceived ideas, for instance, in view of new information on potential consequences of actions.

He suggests that the deliberative process ends with a vote, when wills have formed. Only at this moment is the majority principle justified because "the support of the greater number of people reflects the superior strength of one argumentation relatively to others". However, one must also acknowledge that reasons for supporting other options exist, even though minorities defending them were less convincing this time. This is an important point as it contributes to a balance of power: "A will that faces no obstacle deliberates less on what it decides and justifies its decisions less".

In conclusion, Manin clarifies that fundamental values such as human rights, or the ability for all to participate in political life, retain superior legitimacy and could not be questioned by deliberation results. A more recent article of [START_REF] Habermas | Au-delà du libéralisme et du républicanisme, la démocratie délibérative[END_REF], precisely dedicated to the issue of conflict between human rights and popular sovereignty, advocates that deliberative democracy overcomes this contradiction. In this context, rights would not be constraints, but on the contrary, the expression of democratic self-governance.

Manin described one possible way to reach a decision, voting; we will now describe the other, apparent consensus, which we also find relevant to our analysis.

Apparent consensus

The various aggregation methods used in multi-criteria/multi-stakeholders analysis all amount to a particular choice of voting procedure. They are legitimate in as much as voting procedures are; and once one has noticed that election results depend on the procedure, one usually looks at them with some reasonable suspicion. This being said, it is important to note that voting deliberation is but one of two ways to reach a decision, the other being what has been dubbed "apparent consensus" by the French political scientist that pointed out its relevance in modern democratic deliberation processes [START_REF] Urfalino | La décision par consensus apparent : nature et propriétés[END_REF]. Apparent consensus refers to a decision reached by a political body (e.g., a village assembly, or a shareholders' meeting), when nobody finds it useful, constructive or profitable to further argue for or against the said decision. It does not mean that unanimity has been reached. And it is not either a majority rule: there is no denying of the rights or opinions of a minority in this process, and usually no oppression of the minority by the majority; furthermore, it may happen that the decision actually reflects the preferred choice of a minority, if it is also the least rejected option of the majority or of the largest but conflicting groups of influence. Apparent consensus also implies that good arguments may win, not simply the most authoritative ones, which does not imply that some people in the assembly are not more influential than others, only that there influence is perceived as legitimate. Of course, this also implies a level of honesty in at least a majority of participants, and at least some willingness to make one's opinion evolve in the discussion process at the light of important/relevant arguments. Apparent consensus is reached in several steps. A first round of discussion on the issue at stake is organized by the discussion leader, who also at some point summarizes the options and opinions expressed thus far and sketches a possible decision or line of action. A second round follows if participants are not satisfied with the first sketch, leading to another summary and proposed option, and so on until apparent consensus as defined above is reached. Several remarks are important here:

• The role of the discussion leader is critical, both in the way he fosters discussions and opinions, and in the way he is able to recast what has been said in summarized form, or in different forms etc.

• Multi-criteria and multi-stakeholder decision analysis methods provide a powerful way to help achieving this purpose, and in organizing debates towards reaching apparent consensus, if feasible.

• Scientists do not only act here as experts of the Multi-Criteria Analysis (MCA) methods used in the process, but also ideally must provide alternative ways of enlarging or focusing the debate, present alternative options, etc; they should also be able to recast the problem in different forms for MCA analysis, either by capturing from the discussion forgotten criteria or forgotten options, or by pointing them out from their somewhat external point of view. This may be used either as a substitute for the discussion leader if the scientists are experienced enough in leading this type of discussion and can maintain a neutral stand with respect to all options, or instead, as an important expert help to the discussion leader, who should in any case be proficient in negotiation/mediation/deliberation techniques.

• If apparent consensus cannot be reached, then one needs to resort to a final voting procedure; the procedure is usually chosen by apparent consensus. Note also that indicative votes can also be made at various points in the course of the discussion in order to make further progress towards apparent consensus.

The widespread use of voting procedures in democratic countries is motivated by the huge amount of people involved in the decision process, and by the large geographic extent of modern countries with respect to, e.g., the original democracy of the Greek polis (Athens in particular, whose constitution we know thanks to Aristotle). However, the second method (apparent consensus) is the method of choice in quite a number of traditional societies on the one hand, and quite a number of associations or political bodies in the modern world on the other. In public decision-making, the number of stakeholders rarely exceeds a dozen or so; therefore apparent consensus should be aimed at first, and formal votes used only as a last resort and with proper preliminary discussion of the voting procedure to be applied. When apparent consensus is reached, participants feel much more implicated in the decision process, and as a consequence are usually much more committed to the decision reached as it is perceived as the best outcome considering all constraints, even if it is not their preferred option, except for those stakeholders whose agenda is not to reach a common decision, of course.

Chapter 10

Proposition of a multicriteria deliberation-aiding procedure

Now that underlying principles (and controversies) of participation, deliberation, decisionaiding and multicriteria analysis have been presented, we will reflect on the way they could be assembled in a deliberative decision-aiding procedure. Starting from thoughts on science in policy and from different typologies of decision-making contexts, we clarify the scope of our research question by defining deliberative multicriteria procedures in contrast with optimization and technical multicriteria strategies. We analyze several outranking methods to understand their essence and see how they could be adapted to our needs. We then propose a decision-aiding procedure built around a deliberative multicriteria framework, called Satisfaction-Regret III.

Finally, the soon-to-come experiment of the method on the case of the Afterres 2050 agricultural scenarios is outlined.

A typology of decision-making contexts and possible decision-support tools

The following reflections attach much importance to analyzing decision-making contexts. Whether they attempt to characterize possible roles of scientists in society, to describe decision-making styles or classify decision-support tools, they make use of the same two attributes: the level of consensus among stakeholders and the degree of uncertainty.

10.1.1 Science in policy [START_REF] Pielke | The honest broker: making sense of science in policy and politics[END_REF] analyses four idealized roles scientists can play in society:

• The pure scientist focuses on his research with no consideration for its use and no connection with decision-makers,

• The science-arbiter seeks to focus on issues that can be resolved by science (positive issues in opposition to normative issues) and accepts the role of expert to answer specific questions raised by decision-makers,

• The issue advocate seeks to participate in the decision-making process and aligns himself with specific interest groups,

• The honest broker of policy alternatives participates in decision-making by "clarifying and, at times, seeking to expand the scope of choice available to decision-makers". In other words, its role is not to decide what choices should be taken but to indicate possible choices and constraints associated to them.

might determine whether a particular situation is characterized by a broad values consensus or fundamental conflict.

It is easy to conflate scientific uncertainty with political uncertainty, and then to suggest that a reduction in the former compels a reduction in the latter (Chapter 5). Understanding the relationship of different conceptions of uncertainty can help to make sense of different perspectives on the role of science in decision-making. Sometimes scientific research actually increases uncertainty, at least on the time scales of policy-making. This chapter explains different conceptions of uncertainty, how political uncertainty is related to scientific uncertainty, and how scientists might determine whether a particular situation is likely to have scientific or political uncertainty resolved through research.

More broadly, expectations that consensus on science can lead to a consensus in politics have their roots in the "linear model" of the relationship of science and society (Chapter 6). The linear model Of course, these roles are idealized, in the sense that one is unlikely to be found all the time in the same role. The author for instance often uses the expression stealth advocacy to refer to scientists who present themselves as neutral but are in fact, consciously or unconsciously, using science to promote their political views. Moreover, there is no good or bad role in absolute, for instance, issue advocacy can be useful in democratic functioning as far as it is recognized as such. Roles are however more or less suited to decision-making contexts defined by the degree of consensus and uncertainties, by the connection to policy and by the will to widen or reduce the scope of choices. This is what is illustrated in figure 10.1.

In the continuity of the Honest broker of policy alternatives, [START_REF] Edenhofer | Cartography of pathways: A new model for environmental policy assessments[END_REF] propose a model for solution-oriented assessments called "the pragmatic-enlightened model " (PEM). Starting from the question "How can assessments of environmental policy issues be policy-relevant without being policy-prescriptive? ", they propose to overcome the dichotomoy between technocratic responses, which suppose science can be value-free, and democratic participatory models, where the role of researchers is often unclear. The PEM model "suggests that after researchers and stakeholders have jointly framed the problem, they explore the objectives, means and consequences. [...] The public debate on alternative policy pathways, as well as policy decisions and implementation by policymakers are outside the assessment-process per se. Next, there is a scientific ex-post evaluation of the actual means-consequences, which is also the starting point for a new assessment cycle". This implies that at least some PEM elements seem robust and are not confined to the proponents of pragmatist philosophy. However, the major difference from most existing approaches (exceptions include, for instance, Lasswell, 1951;Habermas, 1971;Dunn, 2012;Douglas, 2009) is the systematic idea of a Siebenhu ¨ner, 2003;[START_REF] Pielke | The honest broker: making sense of science in policy and politics[END_REF], let alone a broad range of practical means-consequences, seems to be a misguided conception of values. Either values are regarded as subjective and irrational and to be avoided in assessments whenever possible, or researchers, to some extent depending on their discipline, have very strong opinions about them (e.g., in terms of policy narratives) and regard them as fixed criteria, i.e., as Fig. 2 -The PEM model. The PEM as a model for solution-oriented assessments suggests that after researchers and stakeholders have jointly framed the problem, they explore the objectives, means and consequences. The two white boxes indicate steps in the policy process that are outside the assessment-process per se, such as public debate on alternative policy pathways, as well as policy decisions and implementation by policymakers. Next, there is a scientific ex-post evaluation of the actual means-consequences, which is also the starting point for a new assessment cycle. While the first two parts of the thesis aimed at problem analysis (and to a lesser extent at envisioning potential consequences of actions), this chapter is dedicated to the public debate phase, and more specifically aims at providing tools to structure it.

At this point it is useful to highlight that the underlying conviction of our research team1 is that scientists should be more involved in political debates on the sustainability issues that they otherwise analyze, not to act as decision-makers, but rather as honest brokers of policy alternatives helping to structure research questions with a double objective in mind:

• Research questions, although retaining their own justified logic, should not ignore realworld problems and the way to manage them,

• Conversely, helping decision-makers to become more aware of the depth of the issues they handle.

Governance

In an article on "innovation" and "powerlessness" of environmental governance, [START_REF] Theys | Environmental governance: from innovation to powerlessness[END_REF] introduces the concept of "govemability" that "emphasizes the specificity of situations and the probability, in the face of these more or less complex specific situations, of finding both efficient and acceptable solutions". He adds: "Certain situations are both intrinsically and politically manageable. Others are not, or cannot be except at the price of considerable difficulty and effort.". There is therefore no universal governance tool and one should recognize difficult situations, for instance characterized by an ill-structured problem, lack of immediate practical solutions or of mobilizing project, or lock-in of a major actor: in such cases conditions for "good governance" are not fullfiled and need to be built. In the same spirit, [START_REF] Godard | Stratégies industrielles et conventions d'environnement: de l'univers stabilisé aux univers controversés[END_REF] distinguishes decision-making in a stabilized and in a controversial world. In the first case agents are informed by scientific knowledge relevant to action (e.g. causality chains are understood) and what is at stake is rather economic effectiveness and equity. On the contrary, in the second case, some key stakeholders are missing, scientific knowledge is more controversial and visions of the world and of the future compete. Similarly, [START_REF] Mény | Politiques publiques[END_REF] propose a typology of programmed, negotiated, pragmatic and chaotic processes depending on the degree of certainty and the degree of agreement on values between actors (chaotic processes corresponding to high uncertainty and value conflict). These are presented in more details in appendix in figures F.1, F.2 and F.3. According to Jacques Theys, four conditions are needed in order to overcome the previously stated difficulties and reach a good environmental governance: a methodological condition (making governance procedures more transparent and efficient), a political condition (restore the balance of power between actors), an institutional condition (redistribute the power between the representative government and participatory governance) and a cultural condition (promoting "cognitive democracy").

Our work precisely focuses on the first (methodological) condition. Before going further an important point should be highlighted. As [START_REF] Faucheux | Au-delà de la prospective technologique-une gestion démocratique des déchets est-elle possible ? FCBA[END_REF] put it, "'democratic debates and stakeholders dialogs cannot eliminate complexity, uncertainty or conflict [...]. Disagreements will always appear regarding inappropriate or unbalanced representations and abuse of power. Nevertheless deliberative processes can be used to facilitate the construction of a clear image of merits and drawbacks of alternatives.". We adopt a similar view, considering that the primary goal of deliberation shouldn't be to reach (or expect) consensus but to structure controversies. This is not to say that consensus is not desirable, just that it may not occur even under favorable conditions.

Decision-support tools

We now wish to study the constraints brought by the decision contexts to the relevance of tools used to support decision-making. We underlined in the previous chapter that multicriteria analysis seemed well suited to tackle the challenges of strong sustainability, that is highlighting trade-offs between non-compensatory effects. However, given the numerous case studies on the subject, we felt the need for making explicit what approaches seemed the closest to our concerns.

To do so, we rely on the definitions of finality, goal, objective and means provided by [START_REF] Maystre | Aide à la négociation multicritère: pratique et conseils[END_REF] in their book Aide à la négociation multicritère (Multicriteria negociationaiding). According to them, finality refers to a fundamental idea, stated generally enough for everyone to make sense of it (e.g. preserving the environment). A goal is also a general statement, but more concrete, that contributes to this finality (e.g. preserving water bodies from pollution). An objective has an operational meaning, refers to an action defined in space and time (e.g. creating a waste landfill facility in a given region). Means are what are needed in order to implement the objective 2 . They underline that in their case studies, they assume people share the same finality and goal (which explains why they meet). They may have different opinions on objectives, and most certainly diverge on the means (which is why they call it a negotiation) 3 . We translate these concepts on a scale of technicality and values displayed in figure 10.3, mean being the closest to technicality and finality the closest to values. Based on these possible levels of value conflict, we propose a flowchart on figure 10.4 that distiguishes 2 The authors note that these definitions are relative and sliding: for instance a given objective can be a mean to an objective of higher level (creating one facility is a mean to reach the regional objective of volume of waste treatment capacity) .

3 They finally point out that starting a meeting by explaining this terminology may foster the group's dynamic and facilitate the work on scenarios and criteria design. Optimization. When there is a relative consensus on values, the question is rather to optimize a criterion under a set of constraints. In mathematics, the area studying the evolution of dynamic systems under constraints is known as viability theory (?). Taking the example of fisheries, one can for instance look for trajectories satisfying both revenue and fish stock constraints. Cost-efficiency analysis, for instance assessing climate mitigation and adaptation plans, also falls in this category of relative consensus. Here the engineering tool is at the core of the decision-making process.

Technical multicriteria. As pointed out by [START_REF] Maystre | Aide à la négociation multicritère: pratique et conseils[END_REF], other situations are characterized by a consensus on a general objective but possible disagreement on the priorities to set. This case is the most often encountered in multicriteria analysis studies. Typically, multicriteria methods are applied in three main fields [START_REF] Behzadian | Promethee: A comprehensive literature review on methodologies and applications[END_REF]:

• Choosing a technical solution (e.g. between different waste treatment alternatives, soil remediation techniques, construction materials...),

• Choosing the location of an infrastructure (e.g. a wind park, a high speed railroad...),

• Choosing a policy mix to tackle a particular environmental issue (e.g. regarding air quality, mixes of taxes, subsidies, norms, urban planning etc.).

This of course requires a consensus on finalities and goals among stakeholders. For instance, citizen opposing the construction of a highway or railroad because they deny its public utility4 , won't agree to participate in a process where the scope of alternatives is reduced to the choice of a location. Of course, technical multicriteria strategies are also designed to favor discussions among stakeholders (and some authors suggest this is their main objective5 ) but they always give a large place to the tool itself. Indeed most tools are complex and stakeholders require time to apprehend them.

Deliberative multicriteria. The more the decision is complex to make, either because of high uncertainties or because the stakes are high and generate conflicts, the more technical tools must give way to other animation techniques. We define deliberative multicriteria tools as artefacts aiming at reproducing the principles of multicriteria methods but keeping technicality to a minimum in order to leave more space for other forms of discussion. Taking too much time to fill a tool's parameters may indeed be perceived as inappropriate. Also, in this view, using qualitative assessments may be encouraged. Typically, one could imagine a confrontation of views on an infrastructure project based on the evaluation of economic, social, local and global environmental impacts.

Other tools and strategies. Finally, we are only stating the obvious by saying that multicriteria methods are not adapted to any kind of debate. On figure 10.4, we use a criterion relative to the problem's structuring to make this distinction. Indeed, a lot of questions couldn't (reasonably) be structured in the form of criteria assessment and any attempt to do so would certainly sound trivial (examples of this include most societal debates such as death penalty, euthanasia, gay marriage etc.).

Transversely to this scale of value conflicts, we find it useful to integrate a scale of uncertainty. Indeed, as uncertainties increase facts tend to give way to values and technical tools arguably become less appropriate and accepted by stakeholders. We summarize these thoughts in figure 10.5.

In the course of this section, we may have given a false impression that one strategy is better than another, that deliberative multicriteria should be preferred to technical multicriteria, but this isn't was is meant here. We merely wish to highlight the fact that tools need be adapted to contexts. In the following we explore possibilities for deliberative multicriteria tools and start by presenting what we consider an existing example of it.

Deliberative multicriteria tools

The REEDS lab6 has developed a tool called KerDST (KerBabel optimization, technical and deliberative multicriteria methods. The x-axis can also be interpreted as the degree of the problem's structuring and the y-axis as the level of stakes. This representation is directly inspired by the one used by [START_REF] Funtowicz | Science for the post-normal age[END_REF] to situate post-normal science relatively to other problem-solving strategies. the following five steps [START_REF] Chamaret | KerDST: The kerbabel on-line deliberation support tool. Centre of economics and ethics for environment and development[END_REF]:

1. Identify the problem, 2. Organize the problem: identify actors, options and quality/performance issues (criteria), 3. Mobilize tools for representation (indicators, maps, models), 4. Multi-criteria and multi-actor deliberation about actions to undertake, 5. Discussion, validation, communication of results, 6. Back to step 1.

During step 4, stakeholders express individually how they think scenarios perform relatively to each criterion. They can either use a three-color code (green for good performance, yellow for mediocre, red for unacceptable), use a color and add a comment to explain it or attribute a color to each indicator relevant to the criterion (when these indicators are available) and weigh them. Each cell of the deliberation matrix is therefore partly or entirely colored in green, yellow or red, reflecting the judgment of actor y on scenario z relatively to criterion x, as figure 10.6 shows.

In practice, this leads to representation such as figure 10.7a. Then, criteria, actors or scenarios can be aggregated using a weighted average to lead to a more synthetic representation 10.7b and the facilitator can iteratively show aggregated and disaggregated results to outline the view of each actor. Other options can of course emerge during the deliberation in which case it is possible to add it to the matrix.

This tool has been used in many studies in the past decade. In particular, [START_REF] Remvikos | L'interface science/décision au travers d'une évaluation multicritères et multi-acteurs du plan régional pour la qualité de l'air en Ile-de-France[END_REF] evaluated different air quality strategies for the Parisian region, Da Cunha (2010) studied alternative agricultural futures (in the Parisian region as well), and [START_REF] Brou | Potentialités et perspectives d'un outil d'évaluation multi-acteur et multicritère des projets d'exploitation des ressources naturelles[END_REF] analyzed possible natural resources management plans, more specifically for mine and forestry projects in Africa.

We share with this approach the goal to use multicriteria as a deliberation tool. This method is simple enough to be transparent for actors. However, this simplicity is achieved through the use of weighted average aggregation which we wish to avoid for reasons stated in the previous chapter. Simply put, we wish to propose a synthetic view on the problem using properties of outranking methods. Their underlying principles seem well-adapted to sustainable development issues. For instance, it is important to account for non (or partial) compensation and to be able to pinpoint incomparable scenarios and associated trade-offs. Additionally, both the majority principle and the respect of minorities principle are usually implemented in the methods. Electre and Promethee, the two most widely used outranking methods, have robust foundations, however we judge them too technical for our purpose. The choice of an artefact is important (e.g. the deliberation matrix in the case of KerDST) and we believe the quadrant displayed in figure 10.8, based on the measure of satisfaction and regret intensities, could be adapted to facilitate the debate. It is in particular inspired by Promethee's positive and negative flows 7 . In a nutshell, the method proposed transforms multiple criteria into a couple of criteria (satisfaction and regret), that carry important information for reaching a decision. Indeed, apparent consensus implies that a solution rejected by a stakeholder is rejected by the whole group. As we will see, satisfaction can be related to the majority principle and regret to the respect of minorities.

Interestingly, cognitive psychology shows human beings are generally more sensitive to losses than to gains. [START_REF] Kahneman | Thinking fast and slow[END_REF] for instance illustrates it with this simple example: "You are offered a gamble on the toss of a coin. If the coin shows tails, you lose $100. If the coin shows heads, you win $150. Is this gamble attractive? Would you accept it? ". Experiments show that most people refuse such proposition because they fear losses more than they value gains. We believe we can extend this observation to satisfaction and regret, that is to say, most people are more sensitive to regret than to satisfaction. In practice, this means that in a weighted average, scenarios that perform very bad on one or more criteria are not penalized enough compared to what people think of them.

In the next, section, we will therefore examine how Promethee and Electre (versions I and III) capture the concepts of satisfaction and regret. In the course of or research we also found a less well-known method precisely called Satisfaction-Regret [START_REF] André | L'analyse multicritère de projets d'éducation à l'environnement: un outil de gouvernance participative en région Corse[END_REF]. We will therefore also study its properties and see how it can be adapted.

Keep in mind that the decision-aiding procedure we envision is structured in two main steps: (i) each individual stakeholder evaluates scenarios using a multicriteria method (the purpose of section 10.13 is to select this method) and (ii) these evaluations are shared between all participant and are used to structure the deliberation process (this point will be tackled in section 10.4).

Satisfaction and Regret

Satisfaction and Regret in four outranking methods

The flowcharts presented here are based on methods description by numerous sources, including [START_REF] Figueira | Electre methods[END_REF], [START_REF] Lenca | Aide multicritère à la décision -méthodes de surclassement[END_REF], [START_REF] André | L'analyse multicritère de projets d'éducation à l'environnement: un outil de gouvernance participative en région Corse[END_REF]. Before analyzing the methods, we provide a quick definition of the outranking principle. Option a outranks option b (aSb) if it is judged at least as good as b and if there is no important reason to think otherwise. From there:

• if aSb and bSa, then a is prefered to b (aP b),

• if aSb and bSa, then a and b are indifferent (aIb),

• if ā Sb and bSa, then b is prefered to a (bP a),

• if ā Sb and bSa, then a and b are incomparable (aRb).

Figure 10.9 contains a table summarizing these relations.

In Electre I (figure 10.9), the notion of satisfaction appears in the concordance index for pairwise comparison of alternatives. The majority principle is applied (sum of weights of criteria where a is better than b). This relation is binary: a criterion gives all its weight or none of it to the index. The notion of regret appears in the discordance index of pairwise comparison of alternatives. The respect of minority principle is applied: final discordance corresponds to the worst under-performance of a compared to b, even if it occurs on a criterion of low weight. However, regret does not increase even if a similar under-performance is found on another criterion.

Performance matrix: each scenario is evaluated relatively to each criterion.

: performance of scenario a for criterion j.

Weighting of each criterion.

: weight of criteria j.

For each ranked couple of scenarios (a,b), the hypothesis "a outranks b" (aSb) is tested, i.e. "a is as least as good as b".

Concordance index Normalised sum of weights for criteria favorable to scenario a:

Discordance index Among criteria favorable to b, choose the largest divergence and divide by the notation scale. In Electre III (figure 10.10), satisfaction is found as in Electre I in the concordance index. In this case however, the criterion-specific preference intensity is no longer binary but can take values between 0 and 1. Regret appears in the term penalizing concordance, thus forming the outranking credibility index: several criteria can contribute to it, although their number is necessarily limited (as described by set V ). Notions of satisfaction and regret are also present in the production of two distinct rankings at the end of the process: a ranking by weakness and one by strength. These are absolute intensities and no longer refer to other alternative. In its principles, this approach is close to Promethee's positive and negative flows. [START_REF] Schärlig | Pratiquer Electre et Prométhée, un complément à Décider sur plusieurs critères[END_REF] considers Promethee (presented in figure 10.11) as a simplification of Electre III. A notable difference however is that it does not implement a discordance index: the outranking index is only based on concordance. This simplification is (partially) justified by the fact that concordance computed with Promethee is more strict since one asks the question 'To what extend is a better than b?, instead of 'To what extend is a at least as good as b?. Figure 10.12 summarizes this difference by presenting the concordance index c(a, b) in doted line for Electre III and in solid line for Promethee. Note that due to the absense of discordance in Promethee, it is not possible for two scenarios to be incomparable if they are the only two scenarios compared. Indeed, one can easily show that in this case + (a) = (b) (NB: the notations are defined in figure 10.11):

+ (a) = 1 n 1 X x X k P k (a, x).w k = 1 n 1 X k P k (a, b).w k = 1 n 1 X x X k P k (x, b).w k = (b)
This means that the positive flow is always identical to the negative flow (i.e. a and b are always comparable):

+ (a) > + (b) ) (b) > (a) + (b) > + (a) ) (a) > (b) + (a) = + (b) ) (b) = (a)
This is rather a counter-intuitive result as the fact that two scenarios are incomparable shouldn't depend on other alternatives.

Coming back to our main focus, the notion of satisfaction is present both in the pairwise comparison of alternatives in the ⇡(a, b) term and in absolute in the positive flow + (a). Weights of criteria are considered in both cases. It is worth noting that for the computation of ⇡(a, b), there is no distinction between criteria where b largely outperforms a and criteria where b is only a little better than a (this will be however accounted for in ⇡(b, a)). Regret is found in the term (a). Note that Promethee also proposes (but it isn't mandatory) to aggregate + (a) and (a) using an arithmetic mean, suggesting satisfaction and regret have equal importance and can be mutually compensative.

As explained earlier, a method called Satisfaction-Regret (S-R) already exists, although it has been very little used to our knowledge. It is presented in [START_REF] Oberti | Extension des modèles Satisfaction -Regret par la définition d'une structure de quasi-ordre valué[END_REF] and [START_REF] André | L'analyse multicritère de projets d'éducation à l'environnement: un outil de gouvernance participative en région Corse[END_REF] and we propose a flowchart description of it on figure 10.13. It is usually based on a discrete, qualitative evaluation scale, although it is not a requirement. This method does not do pairwise comparisons in order to compute satisfaction and regret. Rather, each action is compared to an ideal scenario. This ideal scenario is defined by performances equal to criteria weights. For instance if a participant responds True to the assertion Criterion x matters then the ideal scenario will have to perform well on this criteria. For the satisfaction index, the authors propose to use a Maximum (S-R version I) or a Median (S-R version II) operator. However this goes against the majority principle which implies to take criteria weights into account (as in Electre or Promethee). For the regret index, the distance to the ideal is measured on each criterion, then partial regrets are aggregated in a global regret index using the operator Maximum (S-R version I) or Median (S-R version II, in which case the respect of minority principle no longer stands). Satisfaction and Regret can be aggregated (the authors suggest using Min(satisfaction,non-regret)), however the interest of the methods is precisely to put the emphasis on this distinction.

Satisfaction-Regret III

The S-R methods have many strengths : they keep things simple while retaining the essential idea of regret, they do not necessitate pairwise comparisons and are therefore less timeconsuming, and finally they use a qualitative scale. We find this last property interesting because it is both a way of handling uncertainties, and a way of putting the focus on judgment values rather than on numbers. Following our remarks on S-R I and S-R II regarding principles we wish to respect, we propose to implement the following modification, therefore leading to... a SR-III method:

• Regret is computed with the Maximum index (as in SR-I), in order to implement the respect of minorities principle,

• Satisfaction is computed as the Weighted Median of partial (criterion-specific) satisfactions, in order to satisfy the majority principle.

The small example below illustrates this in the case of 3 scenarios (a, b, c) and 3 criteria (x, y, z).

As shown in figure 10.13, the first step is to define a qualitative evaluation scale from False to Right. It is possible to choose coarser or finer subdivisions and here we use a limited scale: False (F) -Rather False (RF) -As True As False (ATF) -Rather True (RT) -True (T). Then we have to fill a qualitative performance matrix. Remember that the ijth term of this matrix corresponds to the evaluation of scenario i performance on criterion j and that the assertion made is: "Performance of scenario i is good on criterion j".

SATISFACTION-REGRET I

Figure 10.13: Flowchart of the Satsifaction-Regret I (S-R I) methods. The variant of S-R II is made explicit in the dotted rectangle. Note that the two rectangles at the bottom (partial preorder and complete preorder) correspond to two possible alternatives to rank scenarios: one partial ranking and one complete ranking. Of course, the interest of the method lies in the fact that one can differentiate satisfaction from regret, so a complete aggregation is not advised.

x y z a 10 9 2 b 7 7 5 c 9 5 4 At this stage, all the information needed for the computation of the satisfaction and regret indices has been gathered. Partial regrets, global regrets and global non-regrets are shown in table 10.4. If on criterion j, scenario i performs better or as good as the ideal scenario (which performances are defined by criteria weights), then the partial regret r ij is worth False. Otherwise partial regret corresponds to the distance between the two.9 .

Partial and global satisfactions are shown in table 10.5. For each scenario and each criterion, partial satisfaction refers to the minimum between the weight of the criterion and the scenario's performance on this criterion. For computing the global satisfaction (weighted median of partial satisfactions), we start by writing the worst partial satisfaction a number of times equal to the weight of the corresponding criterion, then the second worst and so on. We use the following convention linking qualitative criterion weight and number of repetition: False=0, Rather False=1, As True As False=2, Rather True=3, True=4.

We can finally position actions (a, b, c) on the Satisfaction -Regret diagram as shown in figure 10.14. As in any multicriteria method, conducting sensitivity analysis can help assess the results' robustness. For instance, the satisfaction indexes of a and c could probably be evaluated as True with little change in the parameters.

Partial regrets

Global

A procedure for deliberation-aiding

There are three ways of envisioning multi-stakeholders multicriteria processes:

• Option 1: One can start by aggregating individual preferences and then deliberate in group (multicriteria then multi-stakeholders),

• Option 2: Each stakeholder chooses the parameters for the multicriteria method, then the deliberation is organized around the average result, also analyzing dispersion of viewpoints,

• Option 3: Stakeholders deliberate on the parameters of the multicriteria method (simultaneous multicriteria and multi-stakeholders).

Option 3 is not desirable in our context as there would be a risk to confiscate the debate on value at the profit of a technical debate. Moreover, it would be difficult for stakeholders to apprehend the true consequences of a choice of parameter on the final decision. Option 2 is for instance what is proposed by [START_REF] André | L'analyse multicritère de projets d'éducation à l'environnement: un outil de gouvernance participative en région Corse[END_REF], using the most severe and the most favorable evaluations to present results, and [START_REF] Proctor | Deliberative multicriteria evaluation[END_REF], that use the mean and standard diversion to convey the idea of agreement or disagreement. We are rather interested in each individual stakeholder expressing its viewpoint and making his/her values explicit, which is why we choose Option 1.

Following [START_REF] Proctor | Deliberative multicriteria evaluation[END_REF], we propose a decision-aiding procedure going from problem identification to the implementation of the multi-stakeholder multicriteria method. As we will see we propose two possible outcomes: either apparent consensus is reached or we use a voting procedure. Note that our starting hypothesis is that we are in a situation of concertation, meaning stakeholders are encouraged to express their viewpoints and propose an agenda but don't have the final say. Such situations are common in real life, for instance when a group is asked to write a White Paper. Even if decision-makers are not forced to follow instructions, they have incentives to do so, especially if the group deliberation process was conducted transparently. As figure 10.15 shows, this is a 10 steps procedure, that we will now describe.

The first 6 steps are classical and were already discussed in the previous chapter: problem identification, identification of stakeholders, presentation of the process and agreement on collective rules of participation10 , co-elaboration of scenarios and of criteria to assess those scenarios, choice or design of indicators to feed the criteria and eventually construction of a performance matrix. Of course, these steps already imply a form of deliberation in order to agree on what aspects should be considered. At this point, we propose to use the Satisfaction-Regret III method to structure the debate. Step 7 (elicitation of satisfactions and regrets) is performed with each stakeholder individually, before the deliberation stage itself. The deliberation really occurs at Step 8 and is built around the Satisfaction -Non-regret diagram.

In this step, stakeholders successively present their views to other participants and situate scenarios on the S-R diagram. They explain the weights given to criteria by making their values explicit. They can formulate their points of hesitation. Once everyone has spoken, the facilitator can propose to remove some scenarios that are clearly outperformed and synthesize conflicting positions. At this point, we propose to use the Six Thinking Hats methods developed by De Bono (1999) in the field of creative thinking. Indeed this method can be used to evaluate a concept in group, improve an idea and prevent confusion and non-constructive arguing. Many variants exist and we only present one here. All participants must adopt the same perspective (hat) on a scenario and formulate ideas in this direction. They successively focus on:

• Positive aspects and advantages,

• Negative aspects and risks,

• Ways of improving, optimizing, overcoming risks,

• Emotional reactions (I am convinced that..., That arouses in me a feeling of...),

• Neutral facts (numbers, pointing to lack of information etc.).

The last hat is that of organization which consists in synthesizing what has been expressed. Of course some hats may be left out.

Deliberation can consist in moving from zone to zone, for instance starting by soft consensus and trying to discuss more ambitious outcomes or instead starting from conflicting scenarios and analyze how to decrease regret. If needed, one can come back to the inital performance matrix at any time and criticize it, modify the weights of the criteria or propose new alternatives. The best case scenario for the process is to make positions evolve: a stakeholder accepts a solution that is not optimal in view of agreed efforts of other parties. This case corresponds to Step 9a of the diagram: apparent consensus is reached and one can also trace back initial positions of stakeholders. In many situations however, this may not be reached. Rather than stopping there, we propose a voting procedure before closing the debate, as a way of synthesizing views. Majority judgment11 fulfills many satisfactory criteria; for instance it is claimed to be quite resistant to tactical voting and satisfies the criterion of independence of irrelevant alternatives. Anyway, the choice of the voting procedure could be made by apparent consensus.

Finally in Step 10, the decision-maker makes the final choice in light of deliberation outcomes and justifies it. Feedbacks can then lead to reformulate the issue or to identify another one. If participants were decision-makers, one would stop at Step 9. However, then the questions of stakeholders' selection (and of a potential voting procedure) should be discussed more thoroughly as they would be fundamental for legitimating the process. As we saw in the previous chapter, thinkers of deliberative democracy invented a variety of procedures for this purpose. [START_REF] Van Asselt Marjolein | A look in the mirror: reflection on participation in integrated assessment from a methodological perspective[END_REF] propose to situate participative procedures relatively to 2 attributes: on the one hand, is it aiming at "mapping out diversity"?, or rather at "reaching consensus"? and on the other hand, is the process viewed as a goal ("a way to organize decision-making")? or as a means ("a method to enrich the assessment and decision-making as a part of a decision-support process.")? As we just pointed out, the procedure is designed under the hypothesis of concertation, i.e. participants are not decision-makers (or at least the majority of them isn't), therefore, we would rather situate ourselves in the Process as a means category. Positioning ourselves on the other axis is more problematic. Indeed, the beginning of the process aims at highlighting conflicting positions but the goal of the deliberation phase is to analyze whether or not stakeholders wish to solve this conflict, and in the best case reach apparent consensus. The procedure could therefore be seen in a dynamic way starting from mapping out diversity and then attempting to reach consensus. Moreover, we aim at a certain balance of power throughout the process: each stakeholder has dedicated time to express its views.

Application on Afterres 2050 scenarios

Solagro's Afterres 2050 scenario was already mentioned twice in this thesis. In the conclusion of Chapter 6, we outlined some of its features related to the cereals chain 12 . In Chapter 8, we mentioned a recent evaluation of the scenario's effect on employment 13 .

The main characteristics of the central scenario are described in table F.1 in this chapter's appendix. It is noteworthy that it acts upon modes of production and modes of consumption. Two variants of this scenario are also proposed. The REP version (Résilience et Production, i.e. resilience and production) is more export-oriented and consumes more inputs (mineral nitrogen, pesticides and irrigation). The SAB version (Santé, Alimentation, Biodiversité, i.e. health, food and biodiversity) is rather oriented towards less productivity (especially for nonfood products), less exports but also less inputs and emissions to the environment (nitrogen consumption, ammonia emission, pesticides, irrigation). We show the performance of these scenarios relatively to a set of environmental indicators in table 10.16.

In collaboration with Solagro 14 we planned an experiment of group deliberation, using the Satisfaction-Regret method on these scenarios. Although the set of indicators is incomplete (for instance, no economic indicators are available 15 ), we believe this example corresponds to our scope of study. Indeed, they do not only imply trade-offs between technical criteria but between more fundamental values. Normative questions could for instance be formulated as follows: Should France keep its role of exporter, not to endanger populations of importing countries? Should we rather use this production capacity for energy production and thereby contribute to the objectives of energy transition and climate mitigation? Or, should agriculture focus on local food provision and on preserving soils and the environment?

12 In particular, a reduction of cereals exports, and a reduction of animal proteins in diets leading to less cereals for food purposes (even if direct intake increases).

13 The study lead by Philippe Quirion (CIRED) estimates that, compared to the business as usual scenario,

Afterres would generate about 73,000 additional jobs in agriculture, but 78,000 less in the agro-industry. Additionally, considering change in diets, households would gain purchasing power, leading to increasing final demand in other activities, estimated to 144,000 jobs. The net effect would therefore be positive (noting the limits of such evaluations that we discussed in Chapter 8). Source: http://afterres2050.solagro.org/2016/02/afterres2050-unsolde-net-de-148-000-emplois.

14 Christian Couturier and Sylvain Doublet in particular.

15 Except for the impact on employment which was computed for the central scenario. Beyond the interest of these questions, which are intimately related to the biomass topics we studied in this thesis, the main goal was to test the deliberation procedure previously described to check whether it can easily be implemented, if it effectively facilitates a comprehensive expression of viewpoints and if it can facilitate the reaching of apparent consensus. The workshop was part of a day of scenario presentation organized by Solagro and lasted about one hour. Due the time constraint, it was limited a maximum of 10 participants (volunteers from conference attendees). It was originally planned as follows:

1. Quick presentation of the goal of the workshop and of main steps, 2. Deeper presentation of the scenarios under study and of table 10.16, 3. Going around the table, each participant in turn expresses what criteria matter to him/her in order to make a choice, and why.

4. The group agrees on a limited set of criteria (e.g. no more than 8) and participants evaluate scenarios individually using a qualitative scale (0 to 6 corresponding to the False -Rather False -... -True scale presented before)16 , 5. Each participant defines the importance of each criterion using the same qualitative scale (This criterion really matters for you), We unfortunately only had time to go through the first 7 steps, therefore not engaging in the true debating phase (step 8). Regarding our testing objectives, the experiment however showed that:

• The methodology is simple enough to be quickly understood by everyone,

• Participants are able to express the criteria that matter to them, to evaluate the performance of the scenarios, and to weigh the criteria,

• Unsurprisingly, the procedure is viewed as unusual and a bit puzzling. This feeling would have likely be weaker had we had the time to go through the whole procedure described in figure 10.15 (especially co-construction of scenarios with the same group of participants).

On the use of tools to improve the efficiency of public debates

To conclude this part, it is worth recalling some intrinsic limitations of tools 17 when it comes to public debate or more generally to group animation:

• In order to be efficient, they need to be chosen or at least understood and accepted by participants. For this purpose, they need to be simple and transparent,

• A skilled and trained discussion leader is paramount to be able to make the best of the tools, to change plans to adapt to the form of the debate etc.

• Finally, tools will never replace simple forms of discussion between stakeholders, nor possible trust relationships established over years of working together.

Having these limitations in mind, we also believe animation tools should be more studied and tried out. As emphasized by many authors (e.g. Benasayag and del Rey (2014)), a wellfunctioning democracy is able to expose conflict and deal with it, as much as possible in a nonviolent manner. We can only observe, however, that our education and cultural background most of the time does not favor nonviolent communication (NVC, [START_REF] Rosenberg | Words Are Windows or They're Walls. -Nonviolent Communication[END_REF]). Basic NVC principles are very much like the ones we presented in this part: expression of personal opinions and feelings, listening to others, etc. While these are rather obvious rules, they are much less obvious to put into practice. Because these communication methods and behaviors are not natural for most of us, we believe one has to practice to get familiar with them even though some may sound puzzling at first. Finally, although only participative multicriteria methods were studied in the course of this thesis, many other group animation and deliberation methods (e.g. serious games, creative thinking...) have been developed in the past decades already providing positive results. Learning more about them will be the next step to advance towards improved public deliberation environments.

Part three recap

The third part was designed around the observation that scientific knowledge is insufficiently translated into policy making. Its underlying conviction is that scientists should be more involved in political debates on the sustainability issues that they otherwise analyze, not to act as decision-makers, but rather as honest brokers of policy alternatives helping to structure research questions with a double objective in mind: (i) research questions, although retaining their own justified logic, should not ignore real-world problems and the way to manage them, and (ii) conversely, helping decision-makers to become more aware of the depth of the issues they handle. In the context of this thesis, we therefore reflected on ways the environmental assessment tools presented in the first two parts could be used as supporting information in the context of deliberation and decision-making:

• Sustainability issues being characterized by the inter-connection between environmental, social and economic issues, we first described in Chapter 9 the main steps of multicriteria decision-aiding, with a didactic focus on three multicriteria methods (the weighted average, AHP and Promethee). We then discussed the notion of participation, and presented the normative grounds of deliberative democracy: a decision is legitimate not because it is unanimous, but in so far as the deliberation process that leads to it is. The principle of apparent consensus, a way of reaching decisions alternative to voting procedures, was eventually outlined.

• In Chapter 10, we first clarified the scope of our research question by proposing a typology of decision-making contexts and associated decision-support tools. We made the hypothesis that, contrary to optimization, or technical multicriteria strategies, deliberative multicriteria is adapted to contexts where both uncertainties and value conflicts are high. We defined deliberative multicriteria tools as artefacts aiming at reproducing the principles of multicriteria methods but keeping technicality to a minimum in order to leave more space for other forms of discussion. Keeping this in mind, we adapted an existing method, based on the elicitation of satisfactions and regrets of stakeholders regarding possible futures, with the idea that conflicts emerge for alternatives combining both high satisfaction and high regret (be it internal conflicts or conflicts between stakeholders). We situated this method in a global decision and deliberation-aiding procedure (starting from the identification of a sustainability issue), outlined an experiment of the method on the case of the Afterres 2050 scenarios for a sustainable agriculture, and finally proposed a discussion on the role of tools in public debates.

Conclusion and outlook

Chapter 11

Conclusion and outlook

Arriving at the end of this study, we first would like to step back and take a look at the big picture: What was the original motivation of the research? How did it evolve over time? What are the contributions of the thesis both to research fields and practical management? What are its limits? Secondly, we propose a summary of the perspectives for further quantitative and qualitative developments that were presented over the chapters and try to envision what these joint developments could lead to. Promoting biophysical accounting without questioning its effectiveness and potential pitfalls would be an incomplete endeavor. We therefore attempt in a final section to put together thoughts on the subject and to imagine what could be guidelines to count wisely.

Contributions and limits of the thesis

Original motivation of the research

It is somehow difficult to precisely trace back how we first got interested in sustainable development. Rather than a linear path, it could be described as a mind-map where knowledge on apparently different topics over time becomes connected and ends up forming a consistent view of the world. This being said, with the joint discovery of The limits to growth [START_REF] Meadows | The limits to Growth[END_REF], Jean-Marc Jancovici's analyses of carbon and energy issues [START_REF] Jancovici | Le plein s'il vous plaît, la solution au problème de l'énergie[END_REF] and Aurélien Boutaud's PhD thesis [START_REF] Boutaud | Le développement durable : penser le changement ou changer le pansement ?[END_REF] on the history of the concept of sustainable development and on the Ecological Footprint [START_REF] Boutaud | L'empreinte écologique[END_REF], we clearly engaged in the topic with a biophysical, consumer-oriented accounting perspective. To express it shortly, the concern was: How to measure environmental sustainability in order to complement welfare indicators and prevent collapse? A trifling matter for sure.

Evolution of the research focus

After digging on the National Footprint Accounts thanks to an internship at Global Footprint Network and exchanging with the members of INRIA's STEEP team, it became clear that focusing on regional (subnational scale), would be relevant for numerous reasons, including locks at the international scale, the progressive decentralization of France, and the multiplication of local initiatives building alternatives. The research question therefore became: How to measure the environmental sustainability of a territory from a producer and consumer perspective?

We studied existing approaches, in particular environmentally-extended input-output analysis (EEIOA), life-cycle analysis (LCA), economy-wide material flow analysis (EW-MFA). The choice to focus on supply-chain material flow analysis (SC-MFA) was motivated by the relative lack of literature in France compared to other approaches, but also by the desire to highlight the material basis of the economy. To choose means to renounce: here, we (temporarily) gave up the idea of providing a comprehensive environmental assessment of a territory, in exchange of providing a detailed understanding of the fate of specific materials in all French regions. With an Ecological Footprint background, the focus on biomass supply chains naturally stood out, also in line with the will to be relevant to all (or at least, to the majority of) local territories. The emphasis on environmental stakes was present at the starting point and remained throughout time. As work advanced, it however appeared that providing analysis on economic and social stakes would also be critical in a decision-aiding point of view. Regarding these issues, we relied on existing models and methodologies and did not develop new lines of thought (Chapters 7 and 8). This triple-bottom-line approach [START_REF] Elkington | Cannibals with Forks: The Triple Bottom Line of 21st Century Business[END_REF] is of course intimately related to the decisionaiding part of the thesis developed in parallel of the work on accounting. The initial goal was to reflect on the conditions for our research to best serve decision-making. Because of the specificity of sustainability issues, most of the analysis was targeted towards multi-criteria and multi-stakeholders deliberation, and towards outranking (non-compensatory) methods in particular. We over time became aware that the complexity of these tools was an obstacle to their widespread use. More specifically, sophisticated multicriteria methods are very well adapted to certain decision-making contexts but not for those characterized by high uncertainty and/or value conflicts. Starting from this observation, we asked ourselves how they could be simplified while still retaining their essential strengths.

Contributions to research and management and limits of the thesis

This thesis has made incremental contributions to the fields of Industrial Ecology and Ecological Economics with a proposition of framework for multi-regional SC-MFA (Chapter 3). In addition, coupling MFA with AMC on a practical case hopefully helped clarify the mathematical relationships between MFA, IOA and AMC (Chapters 5 and 6). The uncertainty analysis of the French domestic road freight survey (Chapter 4) will be useful for other research studies, in France and potentially in other European countries. On the practical side, we already had the opportunity to use these results to assess the uncertainties of the EW-MFA of the Lorraine region, and it will probably interest all agents using the SitraM database, first of which are the regional observatories on transport. The work on the forest-wood supply chain (Chapter 7) was presented to different public agencies and could be used to inform the future Regional Scheme on Biomass, Regional Forest-Wood Plans and National Bioeconomy strategy. It seems on the contrary premature to find a direct application to the work on cereals since agri-food issues need a multi-supply-chain perspective. Therefore our case studies on material flows and pressures are rather a proof of feasibility and a step toward this goal. Overall, we can only acknowledge that the tools developed have failed to combine efficiency with sobriety. They still lack transparency and synthesis strength to be really useful to decision-aiding. This is in particular due to the fact that our research was oriented towards broad methodological developments rather than focused on a particular environmental issue. Eventually, as stated at the beginning of the introduction, we experienced that technical developments are partly self-propelled and that acknowledging it is time to stop counting more is not a natural thing. In fact, this observation partly motivated the orientation of this conclusion towards the analysis of the pitfalls of quantification.

Regarding the decision-aiding part of the thesis, we believe our attempt to clarify which multicriteria methods should be used depending on the decision-making context was useful.

Perspectives for future work 233

The study of existing multi-criteria methods from a satisfaction-regret perspective as well. We adopted a bias of transitioning from quantitative to qualitative assessments to put the emphasis on the expression of each stakeholder's values. The goal was not to erase conflicting positions but rather to structure the debate in a more efficient way. The suggested deliberation process (Chapter 10) is of course very modest and would benefit from role-plays and real-life applications since theory can only do so much. The study of other deliberation and group animation tools would also be important on that matter.

Perspectives for future work

We detail in this section what we identified as relevant perspectives for future work.

Quantitative developments

A first axis of development concerns the application of the models to other supply chains. This would be especially useful for the other supply chains of the agricultural sector since it will then be possible to have a comprehensive view on the agri-food issues. Typically, the supply chain analysis could be bridged to the regional Afterres 2050 scenarios (or more generally to any scenario). The methods developped are also probably suited for the analysis of construction materials. These materials indeed share with biomass the "local stake" property as the majority of construction minerals used in a region is usually extracted from the region itself1 . A second axis would be modeling domestic supply chains of other countries, using international statistics data (e.g. FAO data, as suggested in the discussion of chapter 6) or more precise local information when available. The model is well suited to encompass different levels of precision among geographic areas. Therefore, having a rough view of the worldwide agri-food supply-chain while providing a more detailed analysis of inter-regional linkage between French and Spanish regions (for instance) would be an achievable goal. As figure 11.1 shows, the supply-chain approach developed in this thesis would however be insufficient to assess all sustainability aspects, or even environmental aspects of a territory. The SC-MFA methodology is better suited in cases where the considered raw material is eventually embodied in a limited number of products. To illustrate this, we saw in Chapter 3 that tracing the fate of starch and glucose was a task in itself and did not study it. Similarly, we did not study second and third transformation lumber products (Chapter 7). Given the scarcity of the data, there is a risk that modeling these flows would have resulted in a false impression of precision. In these cases, we believe providing order of magnitudes 2 to complement the SC-MFA study is a way to handle the issue. While the SC-MFA methodology would probably still be achievable in the case of metals 3 , chemical components would most certainly be impossible to trace after the first transformation. Generally speaking, other tools, probably less detailed but more comprehensive such as IOA) are required to tackle the issue of environmental pressures embodied in consumer goods. In this perspective SC-MFA could for instance be coupled with the territorial LCA methodology proposed by [START_REF] Loiseau | Methodogical proposals for performing an environmental assessment of territories based on the Life Cycle Assessment (LCA) framework[END_REF]. A fourth axis of development is related to the step from environmental pressures to environmental impacts, using the DPSIR terminology (Driver, Pressure, State, Impact, Response) presented in Chapter 9. This will probably necessitate other skills than the one used in the course of our study, the most obvious being knowledge in ecology and biogeochemistry. While pressures are independent of the local environment they arise from, states and impacts are intimately related to it. To take only one example, the state of waterways will not only depend on the quantities of fertilizers used but also on the local water regime (precipitations, flows of surface and underground water), on the type of soil (e.g. rather clay soil or limestone soil) and on local agricultural practices (crop rotation, period of use etc.). This of course complicates the simultaneous study of all territories: it would probably be preferable to be more accurate from an impact assessment point of view and less comprehensive in terms of geographic coverage. Typically, the agri-food and forest-wood supply chain analyses could be linked to the work on ecosystem services networks underway in the Grenoble area4 . The STEEP team of INRIA is as a matter of fact already involved in this project.

Qualitative developments

Although any increment of knowledge is of course worthwhile in absolute, in a decision-aiding perspective, quantitative developments should be guided by a precise enough qualitative objective. Applying this critical lens to our work, the study of the forest-wood supply chain seem 11.3. How to count wisely? Biophysical accounting and democratic challenges235 more relevant than the cereals' one, since it provides new information to stakeholders on management questions such as: Given the current harvest and the local forest resource, could we exploit more wood? Is the local production enough to satisfy today or future needs or are we dependent from imports? Is there a risk of over-fostering the energy wood sector, in particular for the lumber industry? Again, in the case of cereals, a comprehensive view on the food issue would be needed in order to be policy relevant. A first axis of qualitative development would be to apply the different frameworks of stakeholders analysis analysis described in Chapter 8 on a given regional supply chain. Confronting model results with stakeholders would also allow to improve them (in the studied region and in other regions as well since they are all connected). Going one step further, it would be interesting to evaluate in collaboration with stakeholders the possibilities of promotion of more sustainable supply chains. Related to this issue is the sustainable job issue to which we dedicated a few words in Chapter 8. This research would of course involve many disciplines, including geography, sociology and economics. Finally, multiplying opportunities of testing new deliberation tools would help to advance towards more efficient deliberation procedures. Beyond multicriteria methods, this would include analyses developed in group psychology, creative thinking or negotiation theory, to name only a few.

How to count wisely? Biophysical accounting and democratic challenges

Whilst not claiming to provide a comprehensive view on them, we successively investigate the following questions:

• What are the criticisms addressed to quantification?

• What is quantification useful for?

• Taking these issues into account, what could be the guidelines to count wisely and what democratic challenges go along with them?

The criticisms of quantification

We identified two major lines of criticism of quantification: the criticism of indicators and statistics and the criticism of data hyperinflation.

The criticism of indicators and statistics

As Florence Jany-Catrice points out, regarding statistics, the main point raised by critics is well summarized in the three-word title of Marilyn Waring's documentary: who is counting? [START_REF] Waring | Who's counting? Marilyn Waring on sex, lies and global economics[END_REF]. This question indeed conveys a double meaning: on the one hand what institutions are producing the statistics and on the other hand, who, and in wider meaning what, is judged to be worth counting. Another way of expressing these ideas would be that quantification is generally serving dominant forces and is simultaneously a reductive representation of the world. There is no denying that statistics are intimately linked with power, the word itself coming from the German Staat (State). In this perspective, [START_REF] Desrosières | Pour une sociologie historique de la quantification, l'argument statistique[END_REF] interestingly analyzed the various forms of statistics States have chosen to focus on throughout history:

• The engineer State focuses on demography, physical production and inter-industries trade,

• The liberal State focuses on market transparency and market shares (making it possible to identify dominant positions),

• The Welfare State focuses on work statistics (salaries, employment), social inequalities and purchasing power,

• The Keynesian State focuses on national accounting and on analyses of economic situations,

• The neoliberal State designs and uses indicators to evaluate and rank performances (benchmark is promoted in addition to, or in place of, directives and rules).

As [START_REF] Bruno | Statactivism, Comment lutter avec des nombres[END_REF] note, the radical and reformist criticisms of statistics really emerged as a response to the development of benchmark, congruent with this latter form of state. Jany-Catrice (2012) insists on the fact that once an indicator has gained legitimacy and becomes official, there is a risk that it becomes an end in itself rather than a mean of knowledge. In such a case, accounting rules become comparable to rules of law and the indicator "creates its own reality" by progressively shaping the world. As we saw in the introduction, this situation is perfectly illustrated by the Growth Domestic Product (GDP), around which most public policies are built. Finally, while it is widely recognized that indicators always depend on choices and on practical possibilities of measurement, their use is almost always decontextualized and their subjective component forgotten. For instance, OECD commonly compares unemployment rates between countries whereas the different definitions given to unemployment should prevent such a direct comparison.

The criticism of data hyperinflation

The second line of quantification criticism, which we refer to as the criticism of data hyperinflation, is more global and philosophical. [START_REF] Cukier | Mise en données du monde, le déluge numérique[END_REF] define the big data phenomenon and put it in a historical perspective (personal translation): "Hyperinflation of data is a relatively new phenomenon. In 2000, one quarter only of worldwide existing information was available in digital format. Paper, film and other analogical support shared all the rest. Because of the explosive growth of files -whose volume doubles every three years -the situation has undergone a complete reversal. In 2013, digital format represents about 98% of the total. The Anglophone world forged a term to designate this gigantic mass that threatens to escape government and citizen control: big data. [...] Big data constitutes the last manifestation of the irrepressible human desire to understand and quantify the world. [...] Data creation is not digitalization, that designates the process of translating analogical content to a series of machine-readable zeros and ones. It refers to a much wider action, many implications of which still remain unsuspected: digitalizing not only documents, but all aspects of life". After pointing to the uncertainty surrounding future uses of collected data, and to the necessity to protect citizens against their abusive utilization by governments and private actors, the authors raise concerns about losing sight of core components of the human essence through the sole reliance on numbers. In this context, they also question the space left to imagine alternative futures:

11.3. How to count wisely? Biophysical accounting and democratic challenges237

"We can only be glad if data interpretation leads to improve conditions of living, but this should not make us forget basic common sense. [...] Humankind may rediscover the virtues of unpredictability: instinct, risk taking, accident and even mistake. It may then appear necessary to preserve a space where intuition, common sense, challenge to logic, serendipity and all that composes the human substance will stand up to computers. [...] If Henri Ford had asked algorithms to evaluate customers expectations, they would have probably answered: "Faster horses"". A practical example of such threats is analyzed in Grégoire Chamayou's Drone theory [START_REF] Chamayou | Théorie du drône[END_REF], which puts the emphasis on the dehumanization of war (on one side at least), soldiers' bodies being replaced by drones with more and more decision autonomy 5 .

In the same vein, in her book Addiction générale (global addiction), Isabelle Sorente uses the metaphore of addiction to explore our dependence to numbers as well as the deception of numbers [START_REF] Sorente | Addiction générale[END_REF]. Far from being the expression of a superior human rationality, she argues numbers often form a screen between us and reality. Not a single day goes by without us consuming and producing numbers. In this digital era, the body is reduced to a weight, intelligence to an IQ, security to a number of police arrests, a war or natural disaster to a number of casualties. While one could think these information are effective to raise awareness, their accumulation rather produces an anesthetic effect 6 . Sorente goes on arguing that this coldness of numbers in our daily lives explains for a large part the need for intense collective emotions, summoning the examples of Michael Jackson's funerals followed by tens of millions as well as famous sport events. Clearly, the belief that human rationality lies in calculus is a major misunderstanding of our time: if the human mind is no more than a linear sequence of algorithms, then computers are only better versions of us. The author therefore uses the notion of compassion to explain how she thinks our specific rationality can be saved. She defines it as an elementary shift of the human spirit making it possible to imagine oneself in someone else's position. Compassion, thus defined, is the recognition of the multiplicity of points of view on the world and an invitation to leave, at least for a moment, our management/optimization perspective. Numbers are addictive because they provide the illusion of mastering the world and managing uncertainty. They are somehow a reassuring belief. Rather than giving up on numbers, the argument is to acknowledge them for what they are and making space for other perspectives.

Finally, we believe massive quantification, in particular through performance benchmark, is intimately linked to the way people deal with time, and often leads to favor short-term over longer-term issues. In his book Social acceleration, Hartmut Rosa for instance delivers a powerful analysis of the deadline concept [START_REF] Rosa | Social acceleration, a new theory of modernity[END_REF]:

"Activities that are held to be valuable or choiceworthy for their own sake disappear from view. No time is left over for "genuinely" valuable activities. This is at least as true of work as it is of free time. Everywhere it seems like there is no time 5 A recent article by cybersecurity experts [START_REF] Grothoff | The NSA's SKYNET program may be killing thousands of innocent people[END_REF] follows the same ideas and opens up on this: "In 2014, the former director of both CIA and NSA proclaimed that "we kill people based on metadata." Now, a new examination of previously published Snowden documents suggests that many of those people may have been innocent".

6 For instance, learning 22,000 migrants died on their way to Europe since year 2000 [START_REF] Bordenet | Méditerranée : chiffres et carte pour comprendre la tragédie[END_REF] has less impact on public opinion that the publication of a photograph of Aylan, a three-year-old Syrian boy who drowned in Mediterranean sea in September 2015.

available for long-term goals -in the example of the scholar, for instance, writing her new book -because of the constant pressure of small demands in the meantime, things which are very often directly related to keeping open opportunities. [...] Sequencing represents an almost natural means of weighting and ordering activities in accordance with their value. Do the most important or valuable thing first, then the second most important, etc., and the less important things will get done if afterward there are still time resources available. In a functionally differentiated society with widely linked interaction chains, however, this ordering principle is replaced more and more by deadlines and appointments for coordinating and synchronizing action.

[...] The power of the deadline now determines the serial order of activities and, under conditions of scarce time resources, brings it about that goals that are not bound to deadlines or appointments are lost from view because the burden of what "has to get done (before)" smothers them, as it were -they leave behind only a vague feeling that one does not have time to do "anything" anymore. We are constantly "putting out the fires" that flare up again and again in the wake of the many-layered coordination imperatives of our activities and no longer get around to making, let alone pursuing, long-term objectives."

Quantification retains critical contributions

Keeping these arguments in mind, it also seems necessary to remember the contributions of quantification, not to throw out the baby with the bath water.

The most obvious point is that without quantification, we would have to rely entirely on our experiences and perceptions to take decisions and this would of course be an important source of bias. That is all the more true as cognitive psychology showed that we can be deeply convinced by an opinion even when we know we are lacking of crucial elements to decide: what matters is the coherence of the story we can tell. As [START_REF] Kahneman | Thinking fast and slow[END_REF] puts it: " The confidence that individuals have in their beliefs depends mostly on the quality of the story they can tell about what they see, even if they see little. We often fail to allow for the possibility that evidence that should be critical to our judgment is missing: what we see is all there is. Furthermore, our associative system tends to settle on a coherent pattern of activation and suppresses doubt and ambiguity".

Secondly, following [START_REF] Bruno | Statactivism, Comment lutter avec des nombres[END_REF], we believe giving up on numbers would be a tactical mistake in the struggle for sustainability. In this essay, researchers, artists and activists elaborate on the concept of statactivism which can be defined as both subverting mainstream statistics and using quantification for emancipation. Among the numerous examples taken, they explain the major influences of Bourdieu's and more recently Piketty's statistical works on public debate. By analyzing the correlation between simple socio-economic variables, Les Héritiers [START_REF] Bourdieu | Les Héritiers : les étudiants et la culture[END_REF] indeed provided ground to contest the concept of meritocracy, arguing that rather than rectifying cultural inequalities, school was a means of legitimizing them. According to Luc Boltanski, this book, which was "totalizing a series of individual experiences that it objectified statistically" played a significant role in the preparation of 1968. Along with other economists, Thomas Piketty decided to study economic inequalities by zooming on the top 1%, 0.1% and even 0.01% rather than on the top 10%. This work, which 11.3. How to count wisely? Biophysical accounting and democratic challenges239 received worldwide attention, put the issue of inequalities back to the center of concerns and can be related to social movements claiming "we are the 99% ". A last and different example concerns the initiative of building alternatives to GDP. Indeed, showing the paradox between the major shortcomings of GDP and its continuing supremacy in policy-making is necessary but insufficient if no alternative is built. This is precisely the purpose of FAIR (the forum for other welfare indicators) whose efforts lead to concrete results: the ARF (association of French regions) adopted in 2012 a set of 22 technical indicators, half of which are biophysical indicators, and 3 headline indicators, the Human Development Index, the Social Health Index, and the Ecological Footprint. A convention recently signed with Insee, the French national institute of economic statistics, will ensure the availability and update of those indicators at regional levels.

A third aspect worth mentioning is that confronting quantitative models with beliefs initiates a learning process for both stakeholders and scientists. Results can either be in line with people's preconceived ideas, in which case numbers confer objectivity to them and provide orders of magnitude allowing comparison 7 , or on the contrary bring about unexpected knowledge 8 . More generally, quantified modeling is in itself a tool for understanding underlying mechanisms in complex systems, in particular through the use of sensitivity analysis. The World 3 model at the core of The Limits to Growth [START_REF] Meadows | The limits to Growth[END_REF] is still remembered because it helped formalizing the mechanisms of collapse and it was convincing because a large number of scenarios, including optimistic ones, were tested and lead to the same conclusion in the long-run.

A fourth remark concerns the coldness of numbers and their anesthetic effect described by Isabelle Sorente. While we agree with the observation itself, it can simultaneously be argued that cold numbers could sometimes help to take more reasonable decisions. For instance, while decisions should not be made based on the sole comparison of casualties, each situation being complex and set in a different context, the cold comparison of number cannot be simply discarded: it has the power to set into motion reflections on our values. Although numbers must be taken with caution, they can be helpful to distance ourselves from the immediate reality, and therefore, to undertake more reasonable actions based on a clear expression of these values.

Biophysical accounting and democratic challenges

Throughout our study, we exclusively focused on the decision-aiding role of biophysical accounting; it was in particular one of the purposes of the third part to see how it could be incorporated in decision-aiding processes. We now wish to widen this horizon, decision-aiding not being it's only role nor possibly the most important one. In the long-run, the central contribution of biophysical accounting may very well consist in shifting social imagination, which one could argue is a prerequisite for a large-scale radical change. In other words, won't spreading the use 7 For instance, while large exports of raw hardwood was already identified as an issue by stakeholders, our study allowed to quantify it at various scales: in France, about 22% of raw hardwood production is exported whereas in the Grand-Est, this rate increases to about 35%, and even reaches about 50% in Lorraine. 8 The food miles studies performed in the last 20 years showed for instance that large quantities transported on long distances can result in less emissions than small quantities transported on short distances because of higher logistic optimization: regarding climate mitigation issues, modes of production and modes of distribution to customers seem to be the key factors (?). Of course, in both cases, one should also take into account the refrigeration energy consumed by households afterwards.

of biophysical accounting in daily lives, that is progressively thinking more in tonnes and less in euros, bring about a different relationship to the world? Paul Valéry wrote in 1931 that "the time of the finite world [had] come". Ironically, national (monetary) accounting would thrive at about the same period and dominate imaginations for decades. Euros have intrinsically no limits; contrary to the saying, trees can, and do, grow to the sky as the amount of world debt or that of financial derivative products show9 . As money can be printed without limit, people may get the false impression that problems are solved. Quite the contrary, biophysical accounting carries by itself a finite image of the environment, one cannot consume resources that no longer exist, and can therefore set limits to hybris. In a sense, the evolution we are describing here has already started. For instance carbon accounting has now spread beyond the domain of experts to the general public. Whereas it would probably be naive to think that this is sufficient to trigger change, it can certainly contribute to this objective.

We eventually wish to propose the following guidelines for biophysical accounting: sobriety, transparency, integration in decision-chains involving diverse stakeholders, systematic use of complementary qualitative analysis.

Sobriety

We strongly believe quantitative methods, and sometimes relatively heavy ones such as sensitivity analysis, can bring important information to the table and even be a prerequisite to deeper qualitative analysis. We believe at the same time that pros and cons of counting more should be continuously questioned in a cost-benefit perspective: Does the greatest contribution to the research question lies in a more precise quantification? Will the increment of knowledge be worth the additional complexity of the model (and the difficulty to explain it to end-users)?. Clearly, the question of engaging in the big data race is open to industrial ecologists and ecological economists and there is no unique answer to it.

Transparency

This is merely a criterion for any scientific endeavor. Two aspects are worth differentiating here:

• The design of models and indicators should be transparent: what hypotheses are used, what are the data sources, how selection, normalization, aggregation choices have been made and so on,

• One should, as much as possible, evaluate results uncertainties and their sensitivity to hypotheses and input parameters.

Of course transparency goes hand in hand with the possibility of independent control and counter-expertise. Moreover, combining sobriety and transparency is critical if one wants to promote individual autonomy: citizens should be able to read accounts (at least to some extent) in order to fulfill their democratic duty.

Integration in a multi-stakeholders decision-aiding chain When biophysical accounting is used to help decision-making, we argue involvement of re-11.3. How to count wisely? Biophysical accounting and democratic challenges241

searchers should be extended. Upstream, it implies to start by asking citizens, stakeholders and decision-makers what their concerns are, what questions or scenarios they wish to investigate and to build tools accordingly, as much as possible in interaction with them. Downstream, it implies to think of the ways information will be used and of efficient10 forms of deliberation. Didactic open source software tools could potentially play a role in stakeholders workshops.

Use of complementary qualitative analysis

In a time-constrained project, taking the time to conduct qualitative analysis, for instance relying partly on interviews with a large-enough panel of stakeholders, is not always easy if it hasn't been planned from the start. We showed in Chapter 8 that this complementarity was in particular at the essence of territorial ecology. Beyond that, qualitative analysis, for instance under the form of monographs, is paramount if one seeks to reflect the diversity and subtlety of phenomena.

The necessary extension of the domain of democracy

Of course, this situation will remain an ideal as long as locks of the current institutions will stand: in deliberative democracies, people should be able to discuss and re-discuss any subject and to implement a decision once it has been made. They should be able to equally express what subjects matter to them (what economic, social and environmental aspects are worth counting), deliberate on what collective goods should be pursued and on the research priorities to set in consequence. Currently, one can only recognize that decision-makers lack of (or some will say, do not wish to use) key levers of actions to make radical shifts happen. Some critical issues are indeed in practice confiscated from public debate and people are merely left the possibility to adapt to the faits accomplis. If subjects that matter for citizens are left out of the space of possible decisions, then one will fall low in Arnstein's ladder of participation and people may increasingly lose interest in local politics. On the other hand, one should also acknowledge, and take advantage of, the degrees of freedom in existing constraints. As [START_REF] Manin | L'idée de démocratie délibérative dans la science politique contemporaine. introduction, généalogie et éléments critiques[END_REF] emphasizes, participation can be both an instrument for power, to increase the efficiency of decisions and limit conflict, and for citizens and social forces, to redraw the lines of what can be done (personnal translation): "Institutions or practices established with a given purpose, [can quite easily serve] other purposes subsequently or even simultaneously. In fact, generally speaking, robust institutions serve many purposes and satisfy many forces at a time". (2004). A linear interpolation is conducted for weight values inbetween and after.

Maximum daily production without compound feed

Quantity of compound feed per additionnal daily litter of milk % of cereals in the compound 10 L 0.4 kg/L 60%

Table A.6: Hypothesis used to estimate cereals feed of milking cows depending on milk production quantity. It is assumed that additional nutritional feed is needed (60% cereals, 40% soy cakes) for each additional litter of milk above 10 L per day during the lactation period (10 months) [START_REF] Drogoul | Nutrition et alimentation des animaux d'élevage[END_REF]. Table A.7: Impact of the sea exports redistribution operation on the total international exports of regions (all modes of transports included). The regions without a harbor tend to lose some exports to the benefit of the regions with a harbor. The most impacted region is Provence-Alpes-Côte-d'Azur whose exports increase twofold with an additional 600 kt.

Handling the correspondence between production and transport classifications

There exists no trade database at subnational scales that perfectly matches our products classification. Therefore, a few traded categories are more aggregated than our own categories. For instance the wheat category in the transport database includes both our common wheat and durum wheat categories. Table A.9 in this annex shows the full correspondence. Below we use the notation agg k to refer to a group of aggregated goods (e.g. wheat).

After modification, the new objective function which is applied to subnational scales is the following: The drawback here (as indicated by the degen superscript), is that this triggers degeneracy: there is an infinity of possible solutions for each Xi degen although each Xagg k is unique, and the result provided by the algorithm will depend on the solver's implementation and on the initialisation of variables. This is not satisfactory, even if the infinity of solutions is in practice bounded thanks to the constraints. We therefore conduct a second optimization that aims at obtaining a unique solution. A new rule (hypothesis) to make an allocation to each product belonging to an aggregate is needed. We choose to minimize the square values of imports and exports, while respecting the output of the first step, which leads to a balanced allocation inside each aggregated group.

min ✓ X a X i X j ( V a ij V a ij ) 2 ( a V ij ) 2 + X a X i X j ( Û a ij U a ij ) 2 ( a Uij ) 2 + X a X i6 2agg k 8k ( Îa i I a i ) 2 2 Ii a + X a X k ( Îa agg k I a agg k ) 2 2 I a agg k + X a X i6 2agg k 8k ( Êa i E a i ) 2 2 Ei a + X a X k ( Êa agg k E a agg k ) 2 2 E a agg k + X a X b X i6 2agg k 8k ( Îr
of the first order inclusion probabilities is the first step in the algorithmic construction of a sample design. For more details, see section 2.10 of Tillé 2006.

There is an infinite number of sampling designs with given first-order inclusion probabilities, and sampling design algorithms are selected inasmuch as possible to have desirable properties for the second-order inclusion probabilities ⇡ ij . Quite often indeed, the algorithmic evaluation of these quantities turns out to be unpractical for large samples, or to possess undesirable properties making the variance strongly unreliable or even negative. For example, the ordered systematic sampling design [START_REF] Tillé | Sampling Algorithms[END_REF], section 7.1) is a widely used algorithm due to its simplicity (it is used in the TRM survey), but has the undesirable feature to produce a (large) number of vanishing second-order inclusion probabilities. As a result, the usual expression of the Horvits-Thomson variance Eq. (B.5) below gives biased results and cannot be used, and an approximate expression must be found by other means.

Finding practical sampling algorithms with simple-to-evaluate and well-beha-ved ⇡ ij or finding useful approximations of the variance based only on first-order inclusion probabilities for known algorithms is still an active area of research in this field (see, e.g., chapters 3 and 7 of Tillé 2006 for more details).

More complex sampling designs can be adopted besides unequal probability sampling without replacement, e.g. stratified or clustered sampling, but these methods will not be discussed here (see [START_REF] Cochran | Sampling Techniques[END_REF][START_REF] Fuller | Sampling Statistics[END_REF] for more details).

B.1.2 The Horvitz-Thomson estimator and its variance

B.1.2.1 Generic relations

The quantity of interest is the total of any characteristic quantity, Eq. (B.2). The best known and most used estimator is the Horvitz-Thomson one, defined by [START_REF] Tillé | Sampling Algorithms[END_REF], section 2.17 In practice, one needs an estimator of this variance that can be evaluated on the sample at hand. As pointed out above, the main difficulty lies in the evaluation of the second-order inclusion probabilities ⇡ ij . A common strategy to avoid the problem is to approximate the variance estimator with an expression involving only appropriate combinations of the firstorder inclusion probabilities. One of the most simple approximate estimator of the variance b V ( b T ) is given by (Tillé 2006, Eq. 7.20 One can check that E s ( b T c ) = T c ; this follows from the fact that c is not a sampling random variable, but simply a selection or post-selection one. However, the resulting estimator will be precise enough only if the inclusion probabilities are sufficiently correlated with the characteristic quantity in the subpopulation.

Similarly, an estimator of the variance of this quantity is provided by where c i is given in Eq. (B.7). This can be seen by a formal substitution of y i with y i c in Eq. (B.6).

Neglecting the n/(n 1) factor of Eq. (7.20) of [START_REF] Tillé | Sampling Algorithms[END_REF] in Eq. (B.7) is not justified for very small subsample sizes n, but in such cases, the variance is large anyway, and the total estimator unreliable.

B.1.2.3 Rescaling

Weeks vs year The quantities of interest are, e.g., tonnes transported per year, or kilometers travelled per year. On the other hand, our population is made of vehicles-weeks, as the survey selects any vehicle for a single week in the year. As a consequence, Eqs. (B.4) and (B.8) do not give totals per year, but totals per week. On the other hand, the "week" in question is not any particular week of the year, as polls are conducted every single week. It is in effect some year average week total, inasmuch as the the sampling procedure is homogeneous throughout the year. As a consequence, Eqs. Let us define a sample design with replacement that has the same population (size N ), same sample size S, and same first order inclusion probabilities ⇡ i as the sample design without replacement of interest. The simplest such sampling design makes use of the probability p i that element i has to be drawn in the S successive draws that constitute the sample. The probability p i is directly related to the inclusion probability ⇡ i from the probability of non inclusion in S successive draws ⇡ i = (1 ⇡ i ) S : (B.11) This relation can be inverted for future use:

⇡ i = 1 (1 p i ) S = Sp i (Sp i ) 2 2 + O S 3 p 3 i .
Sp i = ⇡ i + ⇡ 2 i 2 + O(⇡ 3 i ). (B.
12)

The totals of interest in the population can be estimated on the sample with the help of the Hansen-Hurwitz estimator [START_REF] Tillé | Sampling Algorithms[END_REF] For large enough samples, hyi ⇡ y and ˜ 2 (y) ⇡ 2 (y) so that the main difference between Eq. (B.26) and (B.27) is the 1 ⌧ factor, known as the finite population correction factor. This denomination has a double justification: first, this coefficient becomes negligible as N ! 1 at constant S, and second, as shown by Eq. (B.25), selecting one element in the population affects the second-order inclusion probability, which is then systematically larger in sampling designs with replacement. These arguments explain why Eq. (B.22) also overestimates the actual variance in generic unequal probability sampling designs without replacement (see, e.g., Tillé 2006, section 2.18 and[START_REF] Berger | Rate of convergence for asymptotic variance of the Horvitz-Thompson estimator[END_REF].

B.1.3.3 Second step: estimating the need for a correction of the replacement sampling design variance estimator

It has just been pointed out above that a potentially important issue of sampling designs with replacement is that they often lead to overestimate the variance of the population totals; corrected variance expressions have been derived in the literature to compensate for this drawback. Before looking into this question, though, it is of some interest to estimate first if such a correction is necessary in the present case; indeed if the number of multiple draws of the same element in a sample is negligible on average, there would be little interest in performing the correction.

To this effect, one must evaluate the average number of multiple draws of any given element i of the population, from which one can in turn quantify the mean number of multiple draws in samples of size S. From our notations and definitions, s i is the number of draws of element i in such a sample; let us further define hs i i s , the sample average of s i , hs i i >1 s the sample average number of multiple draws of i, and hs i i 1 s = hs i i s hs i i >1 s . Let us also define the probability p i (k) that i is drawn k times in a sample of size S (0  k  S). This probability is obtained by direct counting and reads (B.28) where C k S is the usual binomial coefficient. Defining ! i = p i /(1 p i ), one has

p i (k) = C k S p k i (1 p i ) S k ,
hs i i s = S X k=0 C k S kp k i (1 p i ) S k = p i (1 p i ) S+1 d d! i S X k=0 C k S ! k i ! = p i (1 p i ) S+1 d(1 + ! i ) S d! i = Sp i (1 p i ) 2S .
(B.29) One also finds: B.31) where Eq. (B.12) has been used. The quantity of interest here is the population average of hs i i >1 s , E(hs i i >1 s ): (B.32) where ⇡ 3 i is the simple population average of ⇡ 3 i (i.e., not weighted by the probability p i ). Finally, defining by S the mean (population and sample) average number of multiple draws, one has S = SE(hs i i >1 s ) so that E(hs i i >1 s ) is the relative number of multiple draws in a sample of size S. Note also that the same relation applies for a subpopulation N c and a subsample n, mutatis mutandis.

hs i i 1 s = Sp i (1 p i ) S 1 , (B.30) so that hs i i >1 s = 3⇡ 2 i + O(⇡ 3 i ), (
E(hs i i >1 s ) = 3 N X i=1 p i ⇡ 2 i = 3N S ⇡ 3 i ,
A similar logic can be applied to evaluate the relative standard deviation of S:

( S) S =  ⇡ i ⇣ ⇡ 2 i (N ⇡ 3 i /S) 2 ⌘ 2 1/2
N 1/2 ⇡ 3 One also has N/S ' 6.76 (in 2010), ⇡ 3 i = 0.016, E(hs i i >1 s ) ⇡ 1/3 and ( S)/ S ⇡ 10 4 ; i.e., 1/3 of the sample is made of multiple draws in a sampling design with replacement, on average, and with very little variation from sample to sample. This is not a dominant fraction, but it is clearly not negligible either. As a consequence, a correction to Eq. (B.22) is required to tighten the variance estimates.

B.1.3.4 Third step: correcting the variance

A corrected variance estimator can be obtained by generalizing Eq. (B.22) under the form given in Eq. (B.6); a constraint is applied to the parameters c i to specify their expression. In the case at hand, the constraint adopted is that the variance for a uniform probability sampling design should be formally identical to the variance of the equivalent design without replacement, Eq. (B.26).

By construction, c i can only depend on ⇡ i : c i = g(⇡ i ). For a simple random sampling design Comparison with Eq. (B.26) shows that the finite population correction factor will be recovered for c i = 1 ⇡ i , i.e., Eq. (B.7). The form Eq. (B.22) of the generalized variance is theoretically justified when the sampling design without replacement is "close" to an entropy maximizing sampling design (see [START_REF] Tillé | Sampling Algorithms[END_REF], section 7.5, Tillé 2001, section 6.9 and Berger 1998). This is however not the case for the ordered systematic sampling design adopted in the TRM survey. In fact, it is known that Eqs. (B.6) and (B.7) still overestimates the variance [START_REF] Berger | A modified Hájek variance estimator for systematic sampling[END_REF] for this sampling design, because the design makes numerous second-order inclusion probabilities equal to zero, so that a non negligible number of legitimate samples is not incorporated in the sample population. Eq. (B.22), on the contrary, implicitly takes into account all possible samples, because the second-order inclusion probabilities can be expressed in terms of the first-order inclusion probabilities in replacement sampling designs3 , and are never equal to zero.

B.2 Building all combinations of aggregates: an illustrative example

2. 2

 2 Scope of our work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Downscaling material flow analysis: the case of the cereal supply chain in France 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Uncertainties of domestic road freight statistics: insights for regional material flow studies 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Theoretical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3

 3 Figure 3 Knowledge, power, engagement, and action.

Figure 1

 1 Figure 1.6: Knowledge, power, engagement and action. Source: Van Kerkhoff and Lebel (2006).

Figure 2 . 2 :

 22 Figure 2.2: An example of implementation of the Approche filière: the rice commodity chain in Thailand. Source: Tallec and Bockel (2005).

Figure 2

 2 Figure 2.3: Main supply chains of the Belgian economic system. Source: Billen et al. (1983).

Figure 2 . 4 :

 24 Figure 2.4: Flows of iron in Belgium in 1974. Source: Billen et al. (1983).

country

  Animal feed (for cattle, poultry and pigs) Bilans d'approvisionnement (Agreste) country Inputs used by the animal feed industry (Agreste) most of the régions International trade of raw materials and transformed products Bilans d'approvisionnement (Agreste) country SitraM database (based on French customs' data) département of origin/destinationcountry of ori-gin/destination National road freight SitraM database (based on the TRM survey) département of origin/destinationdépartement of ori-gin/destination National railroad freight SitraM database (based on reports from SNCFavailable until 2006) région of origin/destinationrégion of origin/destination National river freight SitraM database (based on reports from VNF) département of origin/destinationdépartement of ori-gin/destination Cereals' consumption patterns Babayou et al. (1996) régions

2

  . statistics based on declarations (and punctual control): e.g. customs, reporting from the supply chains' federations... 3. modeled local data, based on downscaling, 4. extrapolation of statistical surveys on sub-populations

Figure 3

 3 Figure 3.2: The chain of computation and integration between softwares.

Figure 3 . 3 :

 33 Figure 3.3: Steps taken to produce regional MFAs. Automatized parts are shown in white. SUTs: supply-use tables.

Figure 3

 3 Figure3.5 shows the domestic use of each cereal along with imports and exports of transformed products, until final human consumption on the territory. Starch and wheat mill industries clearly stand out as the two main supply chains with respectively 6.2 Mt and 4.4 Mt of grain (wheat and corn) processed. They also produce most of the by-products (3.3 Mt or 81% of the residues). Then comes the malting industry with about 1.6 Mt of barley processed. Other supply chains (bioethanol, pasta and couscous, rice, canned corn, cornmeal) are less significant although together, they add up to 2 Mt 12 . On the imports side, the main flows correspond to flour, starch and glucose, pasta and rice, adding up to 1.1 Mt or 85% of the total imports of transformed products. On the exports side, the main flows correspond to starch and glucose, malt and flour adding up to 2.9 Mt or 78% of the total exports of transformed products. On the consumption side, the main flow corresponds to bread (with 2.6 Mt or 34%), starch and glucose (with 1.8 Mt or 23%), and biscuits (with 1.2 Mt or 16%). Pasta, beer, rice, bioethanol, flour, canned corn add up to 2.2 Mt. 83% of cereals are consumed through food and drink products and 17% through other industrial products 13 . All these figures provide convenient points of comparison for sub-national geographic levels.

Figure 3 . 6 :

 36 Figure 3.6: Flows of cereals > 500 kt/year (average during the 2001-2009 period). The main two countries of destination are shown for each international export flow. AL: Algeria, BE: Belgium, CH: China, EG: Egypt, GE: Germany, IT: Italy, NE: Netherlands, SA: Saudi Arabia, SP: Spain, UK: United Kingdom.

Figure 3

 3 Figure 3.7: Nested territories under study. From left to right: France, Rhône-Alpes région, Isère départment and the territory of the SCoT of Grenoble.

  3 levels of product category: all goods, 10 groups of goods (NSTR between 2002 and 2008) / 20 groups of goods (NST 2007 between 2009 and 2010), 176 detailed goods (NSTR between 2002 and 2008) / 382 detailed goods (NST 2007 between 2009 and 2010).

Figure 4 . 1 :

 41 Figure 4.1: Piecewise models for estimating lower bound, median and upper bound uncertainties based on the size of the subsamples (NB: this is a log-log plot). Extrapolations were classified in size classes as explained in the text: each class is represented by three dots (aligned vertically).Lower dots correspond to 5% percentiles, middle dots to medians and upper dots to 95% percentiles. Explicative models were calibrated in order to properly fit the dots. The piecewise models e (%) = a/n b are drawn in blue lines and the parameters are provided in the two tables. The R 2 of the median model is 0.87. It is interesting to notice that for the three models, the slope increases when the size of the subsample reaches a threshold: upper bounds are the first to decrease, followed by median (for nearly 2000 individuals) and lower bounds.

  Figure 4.2: Analysis of uncertainties of road freight at various spatial and product disaggregation levels. Distribution are shown, with the x axis representing uncertainties computed for the year 2010 and the y axis representing the number of occurrences. Distributions are not drawn for total domestic freight (loading and unloading in France, whatever the region)since there is only one occurrence per product category. Uncertainties above 100% correspond to non-significant extrapolations. Flows between French départements (nuts 3 levels) are not shown but display an even larger level of uncertainty.

  In order to compute flows pc, pe, ic and ie, we use the perfect blend hypothesis: ! pc = p / s . c = c / s . p ! pe = p / s . e = e / s . p ! ic = i / s . c = c / s . i ! ie = i / s . e = e / s . i ), Imports (i), Supply (s), Consumption (c), Exports (e) What happens in the real world: Production (p) is either directed to local consumption (pc) or exports (pe). Imports (i) are either directed to local consumption (ic) or exports (ie). Goods consumed (c) are either produced locally (pc) or imported (ic). Goods exported (e) are either produced locally (pe) or imported (ie).

Figure 5 . 1 :

 51 Figure 5.1: The perfect blend hypothesis made explicit. One formulation is the following: the proportion of production going to local consumption (which is unknown) is the same as the proportion of total supply going to local consumption (which is known).

  2) sun,rain = P (Day n+1 = rain | Day n = sun).P (Day n+2 = rain | Day n+1 = rain) +P (Day n+1 = sun | Day n = sun).P (Day n+2 = rain | Day n+1 = sun) = M sun,rain .M rain,rain + M sun,sun .M sun,rain = M 2 sun,rain

  Figure 5.2 is an illustration of what can be obtained with an MFA. Based on diagram on figure 5.2, we can define the following states in which the material can be found: a. Extracting sector in region A, matrices Q and R :

  's example and basic notations in IOA

Figure 5

 5 Figure 5.4: Diagram of resource flows. r is the resource sector, 1 and 2 are economic sectors, m and n are consumption sectors. The goal is to quantify resources flows (from a to h) that are embodied in trade between sectors. Resources embodied in nodes (sectors) can be quantified as well.

Figure 6 . 1 :

 61 Figure6.1: Fate of corn grown in the Midi-Pyrénées region. Darker color means greater consumption of corn or corn products. With nearly half of the regional production, Spain is by far the main destination. Additional cross-check with FAO statistics shows that Spain only exports about 1% of its corn supply. 10% of the production of corn in Midi-Pyrénées eventually serves local consumption, mostly under the form of meat (7%), seeds and losses and milk products accounting respectively for 2% and 1%.

Figure 7 . 2 :

 72 Figure 7.2: Sankey diagram of the downstream part of the forest-wood MFA. Flows are expressed in 1000m 3 (f) and correspond to a

Figure 8

 8 Figure 8.1: A framework for studying social-ecological systems. Source: (McGinnis and Os-trom, 2014). As the layers show, the main categories can be further detailed with "second-tier variables", e.g. economic trends, equilibrium properties of resource systems, number of resource units, actors' past experiences, government organizations, deliberation processes etc. The full list is proposed in appendix of the chapter (table E.2).

  FIGURE 2 Contrasting Models of the Corporation: The Stakeholder Model

Figure 8 . 4 :

 84 Figure 8.4: Main mechanisms of jobs creations and destructions used to characterize climate policies. Source: translated from Quirion (2013).

Figure 9

 9 Figure 9.1: Driver (D), Pressure (P), State (S), Impact (I) and Response (R) indicators. Source: European Environment Agency.

Figure 9

 9 Figure 9.3: Percentage distribution of MCDA methods by application areas. Source: Huang et al. (2011).

Figure 9 . 4 :

 94 Figure 9.4: Eight rungs on a Ladder of Citizen Participation. Source: Arnstein (1969).

Figure 2 . 1

 21 Figure 2.1 Flow chart illustrating the logic of roles for scientists in policy and politics Figure 10.1: Flowchart illustrating the logic of roles for scientists in policy and politics. Source: Pielke (2007).

  10.1. A typology of decision-making contexts and possible decision-support tools 205 (technocratic model); (2) avoiding policy-prescription (decisionist model); (3) and including stakeholders (pragmatic model).

Figure 10

 10 Figure 10.2: The Pragmatic-Enlightened Model. Source: Edenhofer and Kowarsch (2015).

FinalitiesFigure 10 . 3 :

 103 Figure 10.3: Scale of technicality and scale of values: positions of the concepts of Means, Objectives, Goals, Finalities defined by[START_REF] Maystre | Aide à la négociation multicritère: pratique et conseils[END_REF].

Figure 10 . 4 :

 104 Figure 10.4: Flowchart for choosing decision-aiding tools.

Figure 10

 10 Figure10.5: Decision-aiding tools depending on systems uncertainties and conflict on values: optimization, technical and deliberative multicriteria methods. The x-axis can also be interpreted as the degree of the problem's structuring and the y-axis as the level of stakes. This representation is directly inspired by the one used by[START_REF] Funtowicz | Science for the post-normal age[END_REF] to situate post-normal science relatively to other problem-solving strategies.

  Figure 10.8: The satisfaction-regret matrix with rejection, selection, conflict of soft consensus quadrants. Conflict is characterized by both high satisfaction and high regret.

  Figure 10.9: Flowchart of the ELECTRE I method.

  Performance matrix: each scenario is evaluated relatively to each criterion.

!

  Figure 10.10: Flowchart of the ELECTRE III method.

  Figure10.12: Comparison of Electre (doted line) and Promethee (solid line) concordance indexes. The x-asis is the difference of performance between options a and b and the criterion considered. p and q refer to preference and indifference thresholds. aQb means there is a weak preference for a over b. We can see that in Electre, concordance index c(a,b) (called response on the graph) is equal to 1 as soon as a is indifferent to b, whereas Promethee requires a to be strictly prefered to b. Source: adapted from[START_REF] Schärlig | Pratiquer Electre et Prométhée, un complément à Décider sur plusieurs critères[END_REF].

  Assertion : "scenario a is satisfying and without regret." Satisfaction index s(a) = Maxj( Min( paj, wj ) ) Regret index t being the number of intervals between pai and wj, partial regret raj corresponds to the (t+1) st value of the evaluation scale. Then: r(a) = Maxj( raj ) Non-regret is called r*(a) (if r(a) = Rather True, r*(a) = Rather False) Complete preorder based on global indexes g(a) = Min ( s(a), r*(a) ) Partial preorder based on relations of Preference, Weak preference (e.g. s(a) > s(b) and r(a) = r(b)), Indifference, Incomparability. NB: In Satisfaction-Regret II, the Max operator is replace by a Median operator for the computation of satisfactions and regrets, leading to less situations of incomparability.

Figure 10

 10 Figure10.14: Result of the S-R III method. The graph of preference is bQa, bQc and aRc meaning there is a weak preference for b over a and c, and a and c are incomparable (c provides less regret but also less satisfaction than a). Weak preference (noted Q) refers to the fact that b outperforms a and c on only one criterion (satisfaction or regret) and not on both. Visually, weak preferences are represented by dotted arrows 1 and 2 and incomparability by the broken dotted line 3. For the sake of comprehensiveness, we added two other scenarios, d and e. dIe which means that d and e are indifferent (same satisfaction and same regret). They are therefore situated on the same position on the diagram. Preference relation aPd (or aPe) is visualized with solid arrow 4.

  Figure 10.15: Flowchart of the procedure.

6.

  Loading of performances and weights in an excel sheet to quickly compute Satisfaction and Regret indexes for each participant, 7. Participants successively position their indices on a dashboard and express the values justifying their choices, 8. Analysis of each participant's position and open discussion: Is there a form of consensus? If not, what is the main source of regret and could it be overcome? What information are lacking to make the decision?, 9. Gathering of impressions of participants. What steps were unclear? What could have helped? Suggestions for future implementations.... If enough time, voting procedure based on majority judgment (votes could then be compared the more comprehensive understanding resulting from the deliberation procedure).

Figure 11

 11 Figure 11.1: Schematic representation of complementarity between supply chain analysis and territorial analysis.

=

  i by industry j in region a, I a i , E a i international imports/exports of product i to/from region a, Ir a,b i Er b,a i imports of product i to region a from region b equal exports of product i from region b to region a, Xagg k = X i2agg k Xi degen where X represents matrices Î, Ê or Îr

  unbiased if its expectation value is equal to the desired quantity. Eq. (B.4) shows that the expectation value of the HT estimator over the sample space is unbiased. Indeed, E s ( b T ) = P s b T p(s) = T , from Eq. (B.1), where E s (X) is the expectation of X over the sample probability distribution. The variance V s ( b T ) of the Horvitz-Thomson estimator follows from its definition, and a straightforward calculation gives:

  with S/(S 1) ⇡ 1 due to S this approximate variance estimator is given in section B.1.3.B.1.2.2 Relations for subpopulationsThe preceding considerations are straightforwardly transposed to any subpopulation. In particular, an unbiased estimator of the total in the subpopulation, Eq. (B.3), is given by b

  (B.4) and (B.8) should be multiplied by the number of weeks N w = 52.Because the Horvitz-Thomson is linear, this procedure is obviously equivalent to rescaling the quantities of interest y as y resulting Horvitz-Thomson estimators Eqs. (B.4) and (B.8) have the same formal expression after this substitution, so that the variance will also be the same except for the substitution B.1.3.1 First step: approximating a sample design with replacement by a sample design without replacement

  unbiased. To see this, consider first a single term in the sum: x i = y i /Sp i ; every term of this kind constitutes a realization of the random variable X = Y /Sp(Y ). Its expectation value on the population is T is the sum of S identical random variables identical to X. The expectation value and variance of the estimator are therefore the sum of the expectation value and variance of X, expectation value and variance E and V are computed on the population, and not on the sample space, contrarily to E s and V s . From Eq. (B.17), one obtains an unbiased estimator of the variance:

  Figure B.1: Histogram of the distribution of the first-order inclusion probabilities ⇡ i for the TRM survey.

B. 2 .

 2 Building all combinations of aggregates: an illustrative example 293 discussed in section B.1.3.2, g(⇡ i ) = g(⌧ ) from Eq. (B.23), and Eq. (B.6

Figure

  Figure B.3 shows it is possible to build 19 aggregates based on the three basic extrapolations from figure B.2. Of course, the number of combinations increases when we add new basic flows, levels of products, loading or unloading areas. In the dataset used for the article, about 2.1 million aggregates where built from about 900 thousand basic flows.

Figure B. 2 :

 2 Figure B.2: Example of 3 basic flows extrapolated from a survey on 9 trucks.

  An unsustainable path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Biophysical accounting for strong sustainability . . . . . . . . . . . . . . . . . . 1.3 Knowledge and action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	Introduction
	1 Introduction
	1.1

  . Downloaded from www.annualreviews.org Access provided by University of Ulster at Coleraine on 01/21/15. For personal use only.

  table, which indicates the origin of the goods (either sector-wise or geographically) and a Use table, which indicates the destination of the goods.

		industry 1 .. industry m imports
	product 1
	..	Vij (n,m)	Ii (n,1)
	product n

Table 3 .

 3 1: Supply table and matrices notations. The numbers in brackets indicate the dimensions of the matrices.

		industry 1 .. industry m	exports	consumption
	product 1
	..	Uij (n,m)	Ei (n,1)	Ci (n,1)
	product n

Table 3 .

 3 2: Use table and matrices notations.

Table 3 .

 3 3: Available sources for data in weight unit. All recent years are available when applicable.

	Used for scales...
	R 2 (and p-	value)
	Sample size
	Proxy and source	Recensement Général Agricole 2000 and 2010 (Agreste) a
	Item	Cereals production

Table 3

 3

.4: Chosen proxies. R 2 can be interpreted as the fraction of the sample's variability that is explained by the linear model. The p-values (in brackets) represent the probability of obtaining a similar or better R 2 value if the null hypothesis is true (i.e. if there is no relationship between

Table 3

 3

	.6: Characteristics of each run of the model. One line corresponds to one run. We
	first obtain the national MFA, then downscale it to obtain results in every region, and finally
	downscale the Rhône-Alpes results in every departement of the region. The 741 variables of the
	first run are decomposed as follow: 361 variables for the supply table (19 products * 18 sectors
	+ 19 variables for international imports) and 380 variables for the use table (19 products * 18
	sectors + 19 variables for international exports + 19 variables for consumption). The 25498
	variables of the second (regional) simulation are decomposed as follow: 16302 for the "basic"
	supply and use tables (22 regions * 741 variables), 9196 variables for inter-regional trade. We
	use sparse matrices for the computation as many variables are null (see constraint 5 in section
	3.2.1.3)

.

10

  There is a clear link between SUTs and their representation in Sankey diagrams. Products, and activities (industries, imports, exports and consumption) are the nodes of the diagram. The values in the supply table are represented by links going from activity nodes to product nodes and the values in the use table are represented by links going from product nodes to activity nodes. For the purpose of this study we developped a Sankey

  Table4.2: Fitted slopes versus modeled slopes in a e = slope ⇥ 2V (T )/T model. The R 2 index of the fitted model shows that [V (T )] 1/2 /T is a very good predictor of the error. The suggested model produces slopes very close to that of the fitted model and its R 2 index stays very high.

	Average over ny years Observed slope (fitted	Suggested model 1/ p 1 + (ny 1)/2	R 2 of the fit-ted model	R 2 of the sug-gested model
		model)
	n=2 (2006-2007)	0.82	0.82	0.97	0.97
	n=3 (2005-2007)	0.70	0.71	0.98	0.97
	n=4 (2004-2007)	0.60	0.63	0.98	0.96
	n=5 (2003-2007)	0.55	0.58	0.98	0.96
	n=6 (2002-2007)	0.52	0.53	0.98	0.97

Table 4

 4

	Flow type	Flow	Côte d'Or	Nièvre	Saône et Loire	Yonne
		Balancing inputs	4.5	2.5	6	2.8
	Inputs (Mt)	used) Domestic extraction (un-	7.1	3.1	4.4	5.5
		Domestic extraction (used) 7.8	5.9	7.8	6.3
		Imports	9.4 +/-6%	3.8 +/-17%	12.8 +/-9%	6.5 +/-14%
	System (Mt) Net addition to stock	2.5	1.8	4.0	2.7
		Balancing outputs	3.2	3.1	6.3	2.5
	used) Outputs (Mt) Domestic extraction (un-	7.1	3.1	4.4	5.5
		To nature	5.3	2.6	6.3	3.5
		Exports	10.7 +/-8%	4.6 +/-18%	10.0 +/-7%	7.0 +/-10%
	Indicators	DMI	33 t/cap +/-5%	44 t/cap +/-8%	37 t/cap +/-7%	37 t/cap +/-8%
		DMC	12 t/cap +/-	23 t/cap +/-	19 t/cap +/-	17 t/cap +/-
			15%	21%	12%	20%

.3: Economy-Wide Material Flow Analysis of the Bourgogne region (Alterre Bourgogne, 2013). Uncertainties of trade flows (95% interval of confidence) are computed by the authors.

92

Chapter 4. Uncertainties of domestic road freight statistics: insights for regional material flow studies

Table 4

 4

.4: Economy-Wide Material Flow Analysis of the départements (nuts 3 levels) of Bourgogne (Alterre Bourgogne, 2013). Uncertainties (95% interval of confidence) of trade flows and of the indicators are computed by the authors.

Table 4

 4

.5: Comparison of the 95% uncertainties in the 2010 French and Swedish road freight surveys and the 2013 German survey for the main categories of products

(NST 2007 classification)

. Uncertainties of the French survey are computed by the authors as described in methods section, except for the total which is provided in

[START_REF] Cgdd-Soes | Fiche qualité de l'enquête transport routier de marchandises[END_REF]

. Uncertainties of the Swedish survey are computed based on table 7A of Swedish-Transport-Administration (2011). Uncertainties of the German survey were taken from the table p. 60 of Kraftfahrt-Bundesamt (2014), except for the total which was directly provided to the authors by the statistics office.

  dedicated to Finite Markov Chains, that is Markov chains characterized by a finite, discrete state space 11 . The authors distinguish two equivalence classes of states, transient states and ergodic states: "the former, once left, are never again entered; while the latter, once entered, are never again left". In situations characterized by n states and s ergodic states (i.e. n s transient states), the authors propose to organize matrix P in the following canonical form:

TABLE 1 . -INPUT-OUTPUT TABLE OF A NATIONAL ECONOMY (IN PHYSICAL UNITS)

 1

	Into	Sector 1	Sector 2 Final Demand
	From	Agriculture Manufacture Households Total Output
	Sector 1				100 bushels
	Agriculture	25	20	55	of wheat
	Sector 2				50 yards
	Manufacture	14	6	30	of cloth

The magnitude of the total outputs of the two industries and of the two different kinds of sented in Tokyo, Japan, March l Symposium on Environmental n World held under the auspices l Science Council, Standing Com- Disruption. olff, both members of the research omic Research Project, have pro- t the computations described in aluable assistance I owe my sin-

  Figure 5.3: Example of Input-Output table of a national economy. Source: Leontief (1970).

Table 5 .

 5 1: Production and consumption footprints in IOA and AMC for sectors 1 and 2.Formulas for flows and nodes on figure 5.4 are then provided in tables 5.2 and 5.3.

	Flow	IOA	AMC	Value
	a	F1 = f1X1	Ftot f1	50
	b	F2 = f2X2	Ftot f2	10
	c	m1Y1	Ftot 1	42.62
	d	m2Y2	Ftot 2	17.38
	e	m1A11X1 = m1Z11	Ftot↵1Q11	19.37
	f	m2A22X2 = m2Z22	Ftot↵2Q22	3.48
	g	m1A12X2 = m1Z12	Ftot↵1Q12	15.50
	h	m2A21X1 = m2Z21	Ftot↵2Q21	8.11
	Node	IO	AMC	Value
	r	Ftot	Ftot	60
	1	F1 + m1Z11 + m2Z21 Ftot↵1	77.48
	2	F2 + m2Z22 + m1Z12 Ftot↵2	28.97
	m	m1Y1	Ftot 1	42.62
	n	m2Y2	Ftot 2	17.38

Table 5.2: Embodied resources in flows between sectors: analytical formulas in IOA and AMC frameworks and numeric application. Table 5.3: Resources embodied in each sector (node) in IOA and AMC frameworks and numeric application. The value of a node is equal to the sum of flows entering (or leaving) the node.

  This article was published in the special issue of the Journal of Industrial Ecology Linking local consumption to global impacts.

	Chapter 6
	Environmental pressures embodied
	in the French cereals supply chain

[START_REF] Courtonne | Environmental pressures embodied in the french cereal supply chain[END_REF]

, Environmental Pressures Embodied in the French Cereals Supply Chain. Journal of Industrial Ecology, 20: 423?434.

Table 6 .

 6 1: Sizes of the model's variables.

	6.2.0.3 Coupling material flows with environmental pressures

Table 6 .

 6 2: Datasources for pressure estimation from the producer's viewpoint. The production stage refers to the production of raw materials (called extraction in the MFA terminology). Agribalyse (Ademe, 2015a) an official Life-Cycle-Inventory and Life-Cycle Assessment database for French agricultural products. Base carbone (Ademe, 2015b) is an official database for greenhouse gases emission factors. Agreste is the statistical service of the French Ministry of Agriculture. The IREP database(Ineris, 2015) provides water withdrawals of industrial sites that reach registration thresholds; extrapolations for each sector of the agro-industry were computed on this basis. Chapter 6. Environmental pressures embodied in the French cereals supply chain

	Pressure	Production	Transformation	Transport
	Energy	Agribalyse, national average (ratio	Agreste survey on energy	Base Carbone
		per kg of product)	consumption in the agro-	(ratio	per
			industry (regional data)	t.km)
	Greenhouse gases	Agribalyse, national average (ratio	Energy use times emission	Base Carbone
		per kg of product)	factors	(ratio	per
				t.km)
	Land use	Agreste (French regions), FAO (for-	-	-
		eign countries)
	Pesticides use	Agribalyse, national average (kg of	-	-
		active substance per ha), Agreste
		survey on farming practices (re-
		gional Treatment Frequency In-
		dices)
	Blue water foot-	Mekonnen and Hoekstra (2011),	IREP database	-
	print	Ercin et al. (2012)

Table 6 .

 6 4: Environmental pressures and transport associated with the consumption of 1 kg of meat from France in Italy.

	Topic	Quantities associated to 1 kg of
		meat
	Energy	16 kWh
	GHG	1.6 kg CO2 eq.
	Land use	4.0 m 2
	Pesticides use	0.75 g (of active substance)
	Blue water footprint	130 L
	Sea freight	0.6 t.km
	Road freight	2.0 t.km
	Rail and river freight 0.2 t.km

  Table6.5: Paths from emissions of GHG to final consumption. The column contribution shows the portion of total GHG emissions explained by each path. Picardie, Aquitaine, Haute-Normandie, Bretagne are French regions, Ile-de-France is the Parisian region (with the largest population).

	Rank Path	Contribution
	1	Growing of wheat in Picardie > Consumption of wheat in Belgium	0.56 %
	2	Growing of wheat in Picardie > Consumption of wheat in the Netherlands	0.56 %
	3	Growing of corn in Aquitaine > Consumption of corn in Spain	0.49 %
	4	Road freight from Aquitaine to Spain > Consumption of corn in Spain	0.45 %
	5	Growing of wheat in Haute-Normandie > Consumption of wheat in Algeria	0.42 %
	...	...	...
	31	Growing of wheat in Bretagne > Making of compound feed in Bretagne >	0.18 %
		Animal farming in Bretagne > Consumption of meat in Ile-de-France
	...	...	...
	44	Production of bread in craft bakery in Ile-de-France > Consumption of bread	0.14 %
		in Ile-de-France

Table 7 .

 7 and D.6). 2 shows the impacts of the three policies on production and consumption of wood products in the sector. Three outcomes stem from these results. First, while Sub_C and Sub_T largely modify production and consumption patterns, Exp does not have a major impact on

	7.3.2.1 Variations in quantities
		HRW	SRW	IW (P) fw (C)	hsw	ssw	pw (C) pulps	panels
		(P)	(P)			(C)	(C)		(C)	(C)
	Sub_C +42%	+23%	-20%	+6%	+73%	+33%	+26%	+2%	+1%
	Exp	-5%	-2%	+1%	0%	0%	0%	0%	0%	0%
	Sub_T +42%	+20%	-18%	+4%	+38%	+11%	+45%	+1%	+1%
	Table 7.2: Variations in quantities produced (P) or consumed (C) in 2020 compared to the
	baseline scenario (without policy).
		HRW	SRW	IW (E) fw (I)	hsw (I) ssw (I) pw (I)	pulps	panels
		(E)	(E)						(I)	(I)
	Sub_C -20%	-20%	-3%	-2%	+83%	+42%	+29%	-1%	0%
	Exp	-20%	-20%	0%	0%	0%	0%	0%	0%	0%
	Sub_T -20%	-20%	-3%	-2%	0%	-7%	-24%	-1%	0%
	Table 7.3: Variations in exports of raw products and imports of transformed products regarding
	baseline without policy in 2020.

Table 7

 7

.5: Total welfare variations, budgetary costs and social costs. domestic wood flows. It only slightly reduces HRW and SRW production. This is because

Table 8 .

 8

	Actor	Type	Producer, transformer, distributer, consumer, supporting activity
		Role	Initiator, coordinator, participant, funder
		Interaction mode	Interaction, coordination, coopeation
	Collective action	Membership	Market, redistributive (public), reciprocity spheres
		Size	Number of people or entities, scope of action or
			of influence
		Proximity	Geographical, organizational, institutional
			proximities
		Policy and governance Stakes and objectives of policies
	Environment	Social context	Well-being stakes
		Natural context	Ecological stakes

1: Grid of analysis for studying local supply chains and their relationship to sustainability dynamics. Source: translated from

[START_REF] Debuisson | Les modes d'interaction pour une dynamique territoriale soutenable : un apport à l'écologie territoriale[END_REF]

.

874 Academy of Management Review October FIGURE 2 Stakeholder Typology: One, Two, or Three Attributes Present

		POWER
		/			\		~~~~~~LEGITIMACY
		/Dormant\
	Laten StStakeholder		4
					/ Dominant\
					Sa oer		takeholder
	behavior and to manag	l	7	m	Discretionary	l
	trbus	aangerous		Def init ve go	Stakeholder
	s	ttakeholder	Saltakeholder		s
	Depgtaent
					Stakeholder le
			Demanding
		\	Stakeholder		/	8
		only on	ofthestakeholdeattributes-poNwnsetakrholder

The big picture, science, and democracy • 19

			Criteria for determining the roles
			of science in policy and politics
			Is the decision context characterized
			by both values consensus
			and low uncertainty?
		yes			no
		Connected to			Reduce scope
	yes	policy?	no	yes	of choice?	no
	Science Arbiter		Pure Scientist	Issue Advocate		Honest Broker

  T M online Deliberation Support tool), which is usually used as part of a meta-model (called Integraal ) which consists of

	10.2. Deliberative multicriteria tools	209
	Conflict / Stakes	Other
	Deliberative
	multicriteria
	Technical
	multicriteria
	O p t
	i
	m i z
	a t i
	o n
		Uncertainties /
	Problem ill-structured

  As discussed in Chapter 9, in order to answer this question, one can make use of quantitative or qualitative indicators otherwise available (for instance, one can choose to assess the overall social performance of a scenario based on the number of job creations only, or on a composite indicator taking into account other variables). Here, we make the hypothesis that quantitative indicators are available for each scenario and already organized in criteria (x, y, z). This is what is shown in table 10.1, assuming all indicators take values from 0 to 10. Note that table 10.1 corresponds in principle to that of the real case study presented at the end of this chapter (table 10.16) 8

	Choice of an evaluation scale, e.g..
	False, Fairly False, Rather False, As True
	As False, Rather True, Fairly True, True
	Performance matrix: each scenario is evaluated relatively to each criterion with the above scale, by responding to the assertion: "Scenario a is satisfying regarding criterion j." Notation : paj	Weighting of each criterion with the above scale by responding to the assertion: "Criterion j is important." NB: these weights in fact correspond to the performance of an ideal scenario (for which, increasing performance does not increase satisfaction significantly). Notation: wj

Table 10 .

 10 1: Quantitative indicators available for the evaluation of each scenario.

	One can then translate those quantitative information into qualitative judgments by an-
	swering the assertion, which results in table 10.2:
		x	y	z
	a	T	T	F
	b RT	RT	ATF
	c	T	ATF	RF

Table 10 .

 10 2: Performance matrix expressed in qualitative terms.Then, qualitative weights need to be chosen by responding to the assertion: Criteria i is important. One has to use the same qualitative set as in table 10.2, which gives:

	x	y	z
	T RT ATF
	Table 10.3: Criteria weights.

  Table A.1: Conversion factors (kg of cereal output per kg of cereal input) deducted from the cereals inter-profession yearly report. Table A.2: Contribution of production, trade and stock variation to apparent consumption. Net imports includes primary and transformed products, expressed in weight of grain equivalent. When all terms are positive, production and net imports contribute positively to apparent consumption contrary to stock variation (final stock -initial stock). Table A.5: Chicken lifetime cereals intakes depending on carcass weight. After Drogoul et al.

	Conversion carcass weight (kg)		cereals feed (kg)	Factor
	0.75	From common wheat to flour	1.5	0.77
	1.1	From durum wheat to semolina 2.4	0.86
	1.4	From maïze to cornmeal		3.2	0.53
	1.7	From common wheat to starch	4.5	0.53
		From maïze to starch			0.63
		From barley to malt			0.88
		From wheat or maïze to bioethanol	0.68
	Year	Production	Net imports	Stock variation	Apparent consumption
	2001	182%	-83%	1%	100%
	2002	202%	-97%	-5%	100%
	2003	182%	-94%	12%	100%
	2004	212%	-102%	-10%	100%
	2005	190%	-96%	6%	100%
	2006	186%	-89%	3%	100%
	2007	173%	-72%	-1%	100%
	2008	192%	-87%	-5%	100%
	2009	204%	-99%	-5%	100%
		191.5%	-90.9%	-0.6%	100%
	Period average
		64 453 kt	-30 592 kt	202 kt	33 659 kt

  TableD.1: Conversion factors (to wood fiber equivalent (m3 (f))) used in the study. Products marked with a ⇤ are taken fromWeimar (2011), the others are provided by the authors.

	Product	Original unit	Conversion factor (m 3 (f) / original
			unit)
	Standing timber	m 3	1
	Lumber	m 3	1
	Roundwood (imported	Tonnes	softwood: 1.05, hardwood: 1.12,
	or exported)		hypothesis: greenwood density
	Pulpwood	m 3	1
	Fire wood	m 3	1
	Forest wood chips	m 3	1
	Ties	m 3	1
	Staves	m 3	1
	Sawnwood	m 3	1
	Sawnwood (imported or	Tonnes	softwood: 1.36, hardwood: 1.75,
	exported)		hypothesis: 15% moisture
	Sawmill residues	Tonnes	1.1
	Sawmill woodchips	Tonnes	1.1
	Veneer	m 3	1
	Particle board⇤	m 3	1.25
	Fibreboard⇤	m 3	1.47
	MDF board⇤	m 3	1.39
	Plywood⇤	m 3	0.96
	Wood floor	m 2	0.015
	Pallets and wood pack-	Tonnes	1.1
	aging
	Mechanical paper pulp⇤	Tonnes	2.22
	Chemical paper pulp⇤	Tonnes	2.13
	Old papers⇤	Tonnes	1.54
	Paper, cardboards⇤	Tonnes	1.54
	Wood wastes	Tonnes	1.1

We chose these terms because they are commonly used in the field on economics and by the environmental assessment community, however, the terms biogeochemical accounting express what we do more accurately.

"I will go and find growth with my teeth! ", Nicolas Sarkozy during the 2007 presidential campaign (personal translation).

Standardized IOT in monetary units do not take into account all production factors, especially not those relevant to environmental issues, and are treating investments as exogenous.

When conducting LCA, one traces back production step upstream, that is from the final product to the (first-level) inputs required to make it, then to the (second-level) inputs required for these (first-level) inputs etc. Without a threshold, this can of course go on forever.

The ecosystem Belgium -Essay of industrial ecology.

Two kind of materials are distinguished: substances, that is any chemical element or compound composed of uniform units, and goods, that is economic entities of matter with a positive or negative economic value [...] made up of one or several substances(Brunner and Rechberger,

2003).2 Many investigations dedicated to metals life-cycle flows are linked to the Stocks and Flows (STAF) project at Yale university.

Schéma de cohérence territoriale: the SCoT is an urban-planning document dedicated to a group of towns or urban areas.

French IO tables indeed come into a too aggregated form to reach the level of detail we are interested in here.

The study of specific material/environmental flows associated with it will be tackled in a next step as described in the introduction.

For instance, Binder et al. (2004) and[START_REF] Cheng | Spatial and temporal flows of China's forest resources: Development of a framework for evaluating resource efficiency[END_REF] convert all flows of wood-related products into their equivalent in cubic meters of round-wood.

The fact that the sample size is small (96 individuals at best) has to be balanced by the fact that it is exhaustive.

For instance, French wheat loaded in the Centre région, transported by road to the Rouen harbor and then exported by sea to Algeria will be counted in the customs statistics as from the Centre région to Algeria and in the national transport statistics as from the Centre région to Rouen, leading to a double-counting of exports of the Centre région.

This survey is mandatory for all European Union members.

A few elements also come from the detailed results that are not shown here.

After only 100 simulations, 96% of the standard deviations are within +/-20% of their final value.

Note that the uncertainties reported in their article correspond to one standard deviation (68% confidence interval), whereas here we chose to express them as two standard deviations (95% confidence interval).

Enquête permanente sur le Transport Routier de Marchandises: permanent survey on road freight.

Note that since January 1st 2016, metropolitan France is divided into 14 regions.

This excludes for instance mistakes in the answers from truck drivers, possible errors during the treatment of the forms or bias due to the handling of nonresponse. These sources of error are quite difficult to quantify. Nonresponse is handled by a simple correction factor.

The combinatorial effect implies that the vast majority of the studied extrapolations have small subsample sizes. Therefore data has to be organized into subsample size classes to prevent a ponderation bias during the analysis. More details are available in the Supplementary Material file.

All the R 2 indexes are computed with the formula R 2 = 1 SS residuals /SS total .

This hypothesis states that the proportion of production going to local consumption (which is unknown) is the same as the proportion of total supply going to local consumption (which is known). The same applies to the proportion of production directed to exports. This assumes constant stocks on the long run.

This means that uncertainties of production, international trade and domestic trade by other modes of transport are not considered. It is however very likely that domestic road freight data are the less precise.

A similar formula was also derived by[START_REF] Kastner | Tracing distant environmental impacts of agricultural products from a consumer perspective[END_REF].

Still using the perfect blend hypothesis and assuming that stock variations are null. This stock hypothesis is a common assumption that is justified on average over a few years, especially in a just-in-time production economy.

François Quesnay's Tableau Economique (1758), is recognized as an earlier, cruder form of IOT; the former laid the foundation of Physiocratic economics, i.e. a French school of thoughts putting land and agriculture at the center of wealth creation.

Final consumption of households and administrations and most often investments (considered a final demand category for the sake of simplification).

Note that we use the terms production and output indifferently.

In fact, confusion between the quantity and price models may occur when the quantity model is only expressed in monetary units, as it is the case in most national accounts.

Note that in macro-economics there are three equivalent ways of computing the growth domestic product: providing some adjustments (e.g., taking depreciation, taxes on added-value and subsidies into account), GDP is (i) the sum of sectoral growth value-added (value of output minus intermediate consumption expenditures), (ii) the sum of final expenditures, and (iii) the sum of salaries and corporate profits.

In other words, T (f ) is a 3-dimensional tensor and its ith element corresponds to the diagonal matrix of size (n,n) formed with the ith row of matrix f .

If that wasn't the case, once entered, transient states would never be left, which would imply they are not transient but ergodic states.

Note that vector F used in section 2 corresponds to Ftot in this section.

When several pressures are studied, one simply needs to add rows to f and f : one row then correspond to one pressure.

These production layers can be viewed as the Taylor decomposition of the Leontief matrix: L = (I A) 1 = I + A + A 2 + A 3 + ....

Supplementary material for Chapter 6 describes an algorithm to compute these path in the case of AMC.

Chapter 5. Formal links between methods aiming at tracing flows downstream, which is the case for an export-oriented supply chain as the French cereal chain.

IO tables are not compiled at the level of French regions and the national table only distinguishes between

This number includes livestock and crop farming (most of the emissions acounted for occur under the form of methane and nitrogen protoxide).

In addition to the example provided in the previous chapter (figure D.3 in supplementary material), we illustrate this in the case of Argentinean soy (figure E.1 in appendix).[START_REF] Barles | Urban metabolism and river systems: an historical perspective -paris and the seine, 1790-1970[END_REF] already used this representation to show how the quantity and valuation of urban waste, and human excreta in particular, changed over the last two centuries, how the roles of actors (households, cities, farmers, waste collectors or fertilizer companies) were consequently redistributed and how these evolutions affected the environment

.2 This summer school, entitled "Territorial ecology, an emerging disciplinary field ", took place in the town of Aussois, in June 2013 and was organized by Nicolas Buclet (CNRS, Université Grenoble Alpes) and SabineBarles (CNRS, Université Paris

1).3 This field was presented in the introduction (Chapter 1), with the attempt to show in what aspects territorial ecology differs from industrial ecology.

Although the original design of the framework was dedicated to common-pool resources,[START_REF] Mcginnis | Social-ecological system framework: initial changes and continuing challenges[END_REF] argue it is also relevant for public goods, and supporting ecosystem services in particular. In economics, both common-pool resources (also called commons) and public goods are non-excludable, however, contrary to public goods (e.g. air), common-pool resources are rival (e.g. fisheries).

This typology is based on two attributes: "supply chain density" (defined as the number of links between actors divided by the number of possible links), and "centrality of the focal organization" (a star-shaped network will have a centrality index of 100% and a linear network a centrality of 0%).

Four attributes are assessed based on the network's structure: robustness, reactivity, flexibility and adaptability

.7 The authors for instance wonder: "Below what density or centrality level is a network's survival threatened? " (personal translation from[START_REF] Bassene | Organisation en réseau et durabilité systémique de deux filières alimentaires (riz biologique et petit épeautre en France)[END_REF]).

"The plain truth is that the most prominent alternative to the stakeholder theory (i.e., the "management serving the shareowners" theory) is morally untenable"[START_REF] Donaldson | The stakeholder theory of the corporation: Concepts, evidence, and implications[END_REF].

[START_REF] Etzioni | Economy-wide material flow accounts and derives indicators: a methodological guide[END_REF] distinguish coercive power, based on physical force, utilitarian power, based on financial and material resources and normative power, based on symbolic representations.

Note that the contribution of stakeholder theory to the field of supply chain management has been studied[START_REF] Wittke | The contribution of stakeholder theory to supply chain management: A theory evaluation[END_REF]. However, supply chain management is not of direct interest to our work since it mainly studies firms' sourcing strategies (make-or-buy choices), supplier strategies, and contracting decisions.

In economic geography, the economic base theory introduces a typology of local sources of revenues: the productive (or export) base for instance includes salaries of exporting activities (industry, agriculture, business to business services etc.), the residential base includes retirement pensions and revenues from touristic activities, the public base includes wages of civil servants and the sanitary and social base accounts for health care and other social transfers[START_REF] Davezies | La République et ses territoires: la circulation invisible des richesses[END_REF].

This scenario, built by the négaWatt association, is based on a massive development of energy savings (through sobriety and energy efficiency) and renewable energies. By 2050, it aims at a division by 16 of 2010

This scenario is in fact the biomass part of the négaWatt scenario.

[START_REF] Wahnich | L'intelligence politique de la révolution française[END_REF] shows the permanent tension between the legitimacy of the National Assembly and that of the people during the French Revolution. In particular, she analyzes the right to resist oppression, enshrined in the Declaration of the Rights of Man and of the Citizen, and its implementation in the popular uprisings that punctuated the period 1789-1792.

See Chapter 8 for a description of these attributes.

This paragraph is for a large extent derived from the courses given by Olivier Mora (INRA) and Thomas Houet (Université Toulouse 2) during the SCEMSITE "winter school" on territorial participatory scenario building and modelisation.

The latter designed in particular the Delphi method to forecast the impact of technology on warfare[START_REF] Linstone | The Delphi method: Techniques and applications[END_REF].

Of course one can argue an indicator is never completely neutral, on the other hand limiting bias is possible.

This point however needs to be qualified as the theorem is demonstrated for ordinal preferences only (in opposition to cardinal preferences): one can rank candidates but cannot express its preference intensities. Taking into account cardinal preferences is proposed by some voting procedures, which can then respect reformulated versions of Arrow's conditions[START_REF] Sen | Collective choice and social welfare[END_REF].

Outranking methods are used worldwide, but have been mostly developed by the French school. Hence the French spelling of Prometheus.

This article was published in English under the title On legitimacy and deliberation[START_REF] Manin | On legitimacy and political deliberation[END_REF], however the citations provided here are personal translations since we couldn't access the English version when writing this synthesis.

STEEP team, Inria Grenoble, France.

In his book about the Lyon-Turin railroad project,[START_REF] Ibanez | Trafics en tous genres[END_REF] insists on the fact that the opposition to useless imposed mega-projects relies a lot more on the questioning of their public utility that on the NIMBY (not in my backyard ) effect.

The term deliberative multicriteria is used in some articles as a synonym of participatory multicriteria, that is involving several stakeholders (e.g. in[START_REF] Proctor | Deliberative multicriteria evaluation[END_REF]).

Université Versailles Saint-Quentin, France.

Except lines and columns are transposed.

E.g., if criterion weight is Rather True and scenario performance is Rather False, the distance is of two steps and partial regret is As True as False.

[START_REF] Rousseau | La décision participative : une démarche pour gérer efficacement les conflits environnementaux -document de travail 96-24[END_REF] insist on the fact that the agreement on the decision-making procedure is: "the foundation that will confer legitimacy to the decision". One can extend this notion and apply it to any rule used during the deliberation preparation workshops: speaking time, respect of others etc. For instance, the PAT Miroir c method can be used where participants are first asked to express their concerns about the process, their incentives for participating and the temptations they know will happen. Proposals are then formulated in the form of precautions, strategies and instruments and code of behavior. Initial formal discussions of this type usually help achieving more confidence in the group.

This voting procedure is suggested by[START_REF] Balinski | Majority judgment: measuring, ranking, and electing[END_REF]: voters freely grade each candidate in one of several named ranks, for instance from "excellent" to "bad", and the candidate with the highest median grade is the winner.

The method does not require that every participant has the same criteria or even the same number of criteria. It may however facilitate the comparison process afterwards.

This is in particular showed by the regional EW-MFA conducted in France in Ile-de-France(Barles,

2009),Bourgogne (?), Midi-Pyrénées, Alsace (?) and Lorraine.2 For instance, in the case of wood, an order of magnitude of the territorial trade balance for furnitures.3 See for instance the work of[START_REF] Bonnin | Development of a dynamic material flow analysis model for French copper cycle[END_REF] for the analysis of the French copper cycle.

See the ESNET project (http://www.projet-esnet.org): future of ecosystem services networks in the Grenoble urban region.

In a blog post, Jean Gadrey tries to summarize different approaches to measure the disproportion between finance and real economy[START_REF] Gadrey | La finance pèse-t-elle 100 fois plus que l'économie réelle ? 10 fois plus ? bien moins ?[END_REF].

Efficient meaning in this context achieving the goals of making everyone's positions clear, including conflicting ones, and understanding what is and what is not negotiable.

Second-order inclusion probabilities are necessarily different.

This expression is not derived here, as it does not provide useful information to further reduce the variance.

Note that sample weights have to be re-calibrated in order to leave the total unchanged: for instance if we remove half of the population surveyed in a given year, we have to double the weights of the remaining half population.

This procedure can then be easily adapted in order to decompose an entire row or column of matrices B, ẐB, L.

This simply means that in order for a product to be consumed in a region, it must be first available in this region.

Acknowledgments

This PhD thesis is for many reasons a joint achievement and I would like to thank all those who contributed to it in one way or another.

First, I was lucky enough to benefit from exceptional guidance with my two PhD directors Denis Dupré and Pierre-Yves Longaretti. Thank you both for your good spirit and cheerfulness, for your availability, for your scientific rigor, for helping me to tackle obstacles one by one, and of course for proofreading this manuscript, sometimes late into the night... I also wish to thank the members of the jury committee, Nicolas Buclet, Gilles Billen, Natacha Gondran and Emmanuel Raufflet for accepting to review this thesis, and for their insightful comments.

I'm especially grateful to Julien Alapetite, without whom I might not have been able to eventually start this thesis, and who contributed greatly to many results presented here. Thank you for this rich and pleasant collaboration as well as for your training in programming! I am grateful to Artelia for co-funding this PhD and for offering me many opportunities to confront academic knowledge and on-field studies. I especially thank Catherine Freissinet and Jérémy Gasc for their precious advice and enthusiasm all along the PhD. I also want to thank everyone from the Paris and Grenoble teams for their friendliness during my short-butproductive stays! I consider myself extremely lucky to have spent all this time in the STEEP team of IN-Acknowledgments: This research has been funded by grants from Inria and Artelia Eau & Environnement.

Acknowledgments

This research was funded by grants from Inria and Artelia Eau & Environnement. The authors would like to thank the freight statistics team from the French Ministry of Ecology, and especially Mr Mahmoud Jlassi, for their kind collaboration, which was essential to the study.

Acknowledgments

This research was funded by grants from Inria and Artelia Eau & Environnement.

List of Figures

1.1 Modeling collapse: a scenario from the limits to growth . . . . . . . . . . . . .

Transition to part three

The first research objective of this thesis was to complement existing biophysical accounting tools, at subnational scales, with a special attention on assessing both producer's and consumer's responsibilities for environmental pressures. The first two parts were mostly dedicated to this effort: we presented the SC-MFA model, which assesses material flows of a given supply chain at the national and regional levels and an extension to environmental pressures associated with these material flows. Furthermore, we introduced, although in less details, possible ways of coupling this model with socio-economic stakes, for establishing a diagnosis and for exploring scenarios. The basic material for designing qualitative and quantitative environmental, social and economic indicators is therefore identified and could be used to assess supply chains' evolution scenarios.

Our work was oriented towards advancing methodologies rather than towards studying specific issues, although we have discussed some throughout the articles. For this reason, we do not build nor evaluate by ourselves such supply chains' scenarios, but instead examine the second research question of this thesis. Lots of information are (potentially) available with these tools, however, under what conditions could they best serve decisionmaking? As we saw in the introduction, (i) sustainability calls for multicriteria assessments of alternatives (beyond economic optimization strategies) and (ii) uncertainty surrounding scientific knowledge is an additional argument to legitimate various perspectives on an issue, and therefore to involve stakeholders in decision-making processes. Two difficulties then arise:

• How can one make a decision when there is no first best option, that is, how to arbitrate between conflicting criteria?

• How can different stakeholders reach a decision? Or at least, how can the deliberation process illuminate the final decision-maker and legitimate a choice?

Part 3 will attempt to address them. Chapter 9 is mainly dedicated to a presentation of decision-aiding processes, deliberation and multicriteria analysis. In Chapter 10, we start by clarifying the scope of decision-making contexts we wish to focus on, then propose a deliberative multicriteria procedure, and finally outline a future experiment of the method.

AHP (Analytical Hierarchy Process)

AHP is well adapted to human thinking. Therefore its results are more likely to reflect the judgments of the decision-makers. Indeed, it uses pairwise comparisons to assess:

• How well each alternative performs against each criterion. In this step, the available information on alternatives (qualitative or quantitative, in our case, the grades in French and Maths) are used to produce a relative scoring of alternatives for each criteria. The score is relative to the other alternatives it is compared with.

• How important is each criteria; this step leads to the choice of the relative weight of each criteria.

3

The weighted average penalizes balanced profiles because it allows full compensation between criteria: poor Math skills can be compensated by excellent French skills. In many cases, this is not a desired property, so decision-makers should be aware of it. For instance, here, the school may want to select someone that has (at least) an average level in French and Math.

Remark: the weighted average does not always eliminate balanced profile; for example, if Juan has 7 in both Math and French, it dominates both Lara and Pablo for equal weights.

However, it has a strong tendency to do so as can be seen from the fact that 7 is already a high grade.

2.2.2. AHP!(Analytical!Hierarchy!Process)! AHP is well adapted to human thinking. Therefore its results are more likely to reflect the judgments of the decision-makers. Indeed, it uses pairwise comparisons to assess:

-how well each alternative performs against each criteria ; in this step, the available information on alternatives (qualitative or quantitative, in our case, the grades in French and Math) are used to produce a relative scoring of alternatives for each criteria ; the score is relative to the other alternatives it is compared with, -How important is each criteria; this step leads to the choice of the relative weight of each criteria.

The scale used for pairwise comparisons is the one below: The scale used for pairwise comparisons is the one below: The last step consists in attributing weights to each criteria. As discussed in the AHP section, this is rather simple to do with only 2 criteria but can become more subtle in the presence of 3 or more criteria. In the latter case, AHP could be used to define weights that correctly reflect the decision-maker's opinion. Below we use two different sets of weights to illustrate the type of output provided by Prométhée.

CASE ONE. Weights of 0.5 for French and Maths. We compute a weighted average of preference and rejection intensities of each alternative and then display them on the following graph: 7 For instance, Juan has an average preference intensity of 0.4 in French because he scores 0.8 against Lara and 0 against Pablo.

We repeat this for each criteria, in our case for Math:

The last step consists in attributing weights to each criteria. As discussed in the AHP section, this is rather simple to do with only 2 criteria but can become more subtle in the presence of 3 or more criteria. In the latter case, AHP could be used to define weights that correctly reflect the decision-maker's opinion. Below we use two different sets of weights to illustrate the type of output provided by Prométhée.

Weights of 0.5 for French and Math.

We compute a weighted average of preference and rejection intensities of each alternative and then display them on the following graph:

The higher the alternative is located, the best it is (it is more strongly preferred and less strongly rejected). In this case, we can conclude that Juan is preferred over Pablo and Lara and the decision is easy to take for the decision-maker.

It is interesting to see that Juan is not strongly preferred but rather substantially less rejected than the other two options.

CASE TWO. Weights of 0.8 in French and 0.2 in Maths. The choice of this coefficients means that the school attaches more importance to French than to Maths. This question is independent from defining a scale of values for each criteria (e.g. saying that the difference between grades 10 and 6 is less important than the difference between 6 and 2). In this case, the output will look like this:

PROMETHEE

Performance matrix: each scenario is evaluated relatively to each criterion. n : number of scenarios.

Weighting of criteria: q: number of criteria

Choice of preference function for each criterion (to what extent does a performance difference matter for this criterion?)

For each criterion k, and ranked couple of scenarios (a,b), computation of:

For each ranked couple of scenarios (a,b), computation of the multicriteria degree of preference:

For each scenario a, computation of preference and rejection intensities:

For each criterion k, for each scenario a, computation of criterion-specific preference and rejection intensities:

For each scenario a, computation of preference and rejection intensities:

Figure 10.11: Flowchart of the Promethee method. The two branches at the bottom correspond are two equivalent ways of expressing the positive and negative flows ( + and ). Note that the Promethee method was informally used (without explicit preference functions) in Chapter 9 on a minimal example.

Appendix

Appendix A

Supplementary material to Chapter 3

Additional tables Figure A.1: Supply (above) and Use (below) tables of the study. White cells have to be filled, grey cells mean the corresponding quantity is null. At subnational scales, additional columns for inter-regional trade are added. The starch and glucose category encompass both mid-products and finished products containing those substances. Indeed, the number of products containing starch derivatives is huge, both in food and in non-food industries (chemistry, textile etc.) and tracking them is beyond the scope of this study. [START_REF] Drogoul | Nutrition et alimentation des animaux d'élevage[END_REF]. Production refers to the number of animals slaughtered a given year. Livestock refers to the number of living animals at the end of the year. Care was taken in order to avoid double-counting. For instance intakes of poultry does not include the cereals fed to the laying hen (which are considered separately under the category "egg to be hatched"). Moreover for each category of animal, either the lifetime approach or the annual approach is used. The underlying hypothesis that we make by summing up the two approaches is that stock variation is negligible. et al., 1996), results partially reconstructed by the authors. Bread is by far the main form under which cereals are consumed in France, which means that a 20% difference with the national average, as in the case of the parisian region, can impact the cereals' MFA significantly.

The second optimization under constraint is therefore:

◆ subject to the following constraints:

All terms are positive:

X 0 where X represents matrices I, E or Ir,

For each region, international imports of all products belonging to an aggregate equal the aggregated imports found in the first step of the optimization:

Same for international exports:

Same for inter-regional trade:

Resource equals use constraint:

Geographical aggregation constraint for international trade:

where X represents vectors I or E.

We point out that this process is transparent when results are presented in aggregated forms, such as in figures 3.8, 3.9 and 3.10: everything appears as if only the first optimization had been done. Table A.9: Correspondence between the NST transport statistics classification (used in the SitraM database) and the product classification used the MFA study (left column). NA stands for Not Applicable and indicates that no suitable correspondence was found: for those products, the trade data was initially set to zero, before being modified during the data reconciliation process. This hypothesis is conservative in the sense that in minimizes the inter-regional trade of those flows (canned corn and bioethanol).

Regional MFA diagrams

We show below the diagrams corresponding to 5 of the 22 regional MFAs computed. They were chosen because they were representative of the variety of regional profiles.

Supplementary material to Chapter 4

The document is structured as follows:

• Section B.1 presents and explains the relevant material and results from survey sampling theory that are used in the main text. NB: these ten pages have been written by Pierre-Yves Longaretti (co-author of the article and co-director of this thesis).

• Section 2 is an illustration of data treatment that shows how combinations of aggregates are generated based on basic extrapolations,

• Sections 3 is an annex to the theoretical results section of the article, dedicated to model uncertainties for a single year based two other explanatory variables (the number of observations and the tonnes transported),

• Section 4 is also an annex to the theoretical results section of the article, but dedicated to the study of uncertainty reduction when averaging over several years: it explains how independent multi-year samples are built and illustrates the results on a dedicated plot.

B.1 Unequal probability survey sampling in a nutshell

The French road freight survey (TRM survey) is statistical in nature, and makes use of a specific unequal probability sampling method without replacement to estimate totals of interest, such as the total number of tonnes, kilometers travelled or tonnes-kilometers transported by road from any given origin to any given destinations and category of goods.

The TRM survey also makes use of constraints from auxiliary quantities of known totals to improve the desired total estimate, but this form of constraint is ignored here, as it provides only a modest correction to the variance in most cases and as its implementation requires information we do not have. However a simple correction for non-response is included.

The TRM survey only provides the error on the aggregated total (for all origins, destinations and categories) while we are interested in the error on the various disaggregated totals. The object of the present discussion is therefore to provide the reader with relevant results and explanations from survey sampling theory in order to perform an estimation of the errors of these various disaggregated totals. It is also intended to provide a minimal guideline to the relevant literature; as a consequence, literature citations are focused on the few books and articles most directly related to the problem at hand.

The following subsection is devoted to introducing important definitions and notations; some of these are already given in the main text, but reproduced here, sometimes in more detail, for the reader's convenience. The next one will give relevant results for totals and their variances for samplings without replacement. The last one will provide a heuristic justification for the approximation we use in this work. All relations are demonstrated (unless otherwise stated) for the interested reader to get a feel of what these relations are about, and as the technical literature has a mathematical flavor that can be daunting for the non-mathematician.

B.1.1 Definitions and notations

One considers a population of N elements (here vehicles-weeks) denoted i (1  i  N ). Samples of fixed size S are drawn from this distribution. Typically in the problem at hand, N ' 5 ⇥ 10 5 and S ' 8 ⇥ 10 4 , while the number of usable answers is ' 5 ⇥ 10 4 (this last figure makes non-response -which includes all unusable answers -non negligible and a correction for this is generally applied).

Several quantities need to be defined to specify what is meant by unequal probability sampling without replacement.

Samples. Samples are designated by s = (s 1 , s 2 , . . . , s N ) where s i is the number of times a given element i is present in the sample. The set of all such samples is denoted F . A sample without replacement has s i = 0 or 1, by definition (an element cannot be selected more than once). A sample with replacement has 0  s i  S where S is the size of the sample. Samples of fixed, predetermined size are the only ones of interest here; then, by construction,

Sample design. The sample design is the probability distribution p(s) defined on the set of samples F . As a consequence, both s i and the inclusion indicators i defined right below are probabilistic quantities 1 . Note that in this form of probabilistic description, the elements of the populations are not random variables, as the elementary probabilistic event of interest is the selection of a whole sample, not the successive selections of elements of the population.

Inclusion indicator and inclusion probabilities. The inclusion indicators (or inclusion variables or Cornfield variables)

i are defined by i = 0 if s i = 0 and i = 1 otherwise (s i 1), i.e., an inclusion indicator measures the presence of its associated element in the sample and ignores its possible repetitions.

The first-order inclusion probability ⇡ i relates to element i and defines its probability of being present in the sample. By construction the probability of absence is ⇡ i = 1 ⇡ i . By definition of the sampling design and inclusion indicator:

Similarly, the probability that both i and j are present in the sample is the second-order probability ⇡ ij = P s p(s) i j . By definition, ⇡ ii = ⇡ i . For fixed-size and non-replacement sampling designs,

Unequal probability sample designs. Unequal probability sampling designs are characterized by the fact ⇡ i is not constant (not independent of i).

1 No distinction of notation is made here between a random variable and its associated realizations.

B.1. Unequal probability survey sampling in a nutshell 285

Characteristic quantity. This refers to any quantity of interest on the whole population, for example the quantity transported per year (tonnes) corresponding to specific criteria (loading and unloading locations, category of product transported). Quantities of interest are denoted y in a generic way. The most important quantity one tries to estimate through survey sampling is the sum total of y on the whole population

In the probabilistic description adopted here, y i is a parameter, not a random variable.

Subpopulation index and total. We are mostly interested in evaluating totals on welldefined subpopulations, identified by a given origin (o), destination (d) and category of goods (c) transported. These subpopulations are symbolically represented by an index c i , taking two values: c i = 1 if i belongs to the desired c =(o, d, c) subpopulation, and c i = 0 otherwise. It must be noted that the index c i is not a random variable. It is a fixed parameter allowing us to sort out the relevant elements in the total population or in a sample. In particular, we do not redraw a subsample of the considered sample within this category, we just post-select the relevant elements within the drawn sample.

The associated total is

Subsamples. The members of a subpopulation belonging to a given sample are called a subsample here, although they result from a post-selection process and not a second sampling stage. A subsample size is denoted n.

Sampling algorithms. A sample design is specified by its probability distribution p(s) over the sample set F , and is constructed algorithmically. For the simple equal probability or replacement cases, the first and second order inclusion probabilities can be specified analytically.

In sampling designs without replacement, elements are not reinserted in the original population if selected in one of the successive steps of the sampling algorithm; on the contrary, a given element can be selected any number of times in a sampling design with replacement. Sampling designs without replacement are more complex to implement but their interest comes from the following theorem (see [START_REF] Tillé | Sampling Algorithms[END_REF], section 2.18): sampling designs with replacement are suboptimal in the sense that designs with smaller variance (i.e., more precise, an essential property) and identical first-order inclusion probabilities 2 can always be found.

Unequal probabilities are useful when the quantity of interest is not evenly distributed in the population. In particular, if one can find an auxiliary quantity X i that is known to be (at least approximately) correlated to y i , one can substantially improve the quality of the estimate of the total T at constant sample size S by designing the probability to be proportional to X. For the TRM survey, the first-order inclusion probabilities are proportional to the vehicle's age and payload, with a correction factor for some specific categories of vehicles. The specification of y 0 to y in Eqs. (B.5), (B.6) and (B.9). Note however that this substitution does not imply that for any given truck, the total load transported in the year is N

w times what is transported in the poll week, due to seasonal variations; it just means that this is a reasonable extrapolation on average over all vehicles-weeks.

Nonresponse A similar correction is performed to account for nonresponse. Denoting S nr the number of usable forms, nonresponse is taken into account by substituting a scaled first order inclusion probability to ⇡ i :

A better correction is obtained by performing the same correction by category (origin, destination, product transported) except maybe for the categories with very small number of elements. The inclusion probabilities provided by the public organization (SOeS) in charge of the TRM database are already corrected for nonresponse in this way and the inclusion probabilities used in all formulae are in fact the primed ones, not the original ones, but we have not made the distinction in notation, for simplicity.

B.1.3 Elements of justification of the adopted estimator of the variance

It is possible to provide some justification of Eqs. (B.6), (B.7) and (B.9). This will be done in this section with the help of the following reasoning:

• First, an unequal probability sampling design without replacement is approximated by an unequal probability sampling design with replacement characterized by the same firstorder inclusion probabilities. The usefulness of this approximation comes from the existence of analytic expressions for the total estimator and its variance in sampling designs with replacement.

• However, it is known that the resulting variance is not optimal (it is generically overestimated). This will be explicitly shown by taking the limit of a simple random sampling design (equal probability) where the sampling with and without replacement can be analytically compared.

• On can estimate the error introduced by the sampling design substitution procedure by computing the average number of occurrences of any element in a sample. This will allow us to estimate that on average, the number of elements that are multiply present in the equivalent design with replacement is about 1/3 the total size of the sample in the case of the TRM survey. This indicates that the overestimation of the variance is most probably not negligible, so that a tighter estimator would be a welcome improvement.

• A correction is applied through a generalization of the expression of the variance estimator, subject to the constraint that the correct variance must be formally recovered for a simple random sampling design without replacement. The corrected estimator is known to still overestimate the variance for the ordered systematic sampling design, though, so that we still err on the side of safety.

One can check that this estimator is unbiased from the following intermediate identity, which can be verified by direct calculus:

from which one obtains:

Note that as ⇡ i ' Sp i , the Hansen-Hurwitz estimator is closely related to the Horvitz-

where h•i s is the mean observed on the sample. Note that this relation is of the generic form Eq. (B.6) with c i = 1.

B.1.3.2 Interlude: simple random samplings with and without replacement

It is useful to see why Eq. (B.22) overestimates the variance of a sampling design without replacement. This is most easily seen by considering sampling designs with uniform probability (aka simple random sampling designs), for which all relevant relations can be derived analytically.

Let us examine first a uniform probability sampling design without replacement. In this case, and denoting C q p = p!/q!(p q)! the binomial coefficient,

where the superscript wor refers to "without replacement". Defining

B.3.2 Estimating uncertainties based on the number of observations

By default, the French statistical office does not provide the size of the subsample on which each extrapolation is based. It provides instead the number of observations on which they are based (see glossary in the article). We use the same method as the one described in the article to propose an explicative model based on this variable:

• the sample is divided into 29 classes defined by an interval of number of observations,

• for each class, we compute the 5%, 50% (median) and 95% percentiles of uncertainty,

• we propose a model depicting the low, median, high uncertainty estimations depending on the number of observations. Looking at the median model, it is striking that part of the slope is almost flat between about 1200 and 3400 observations. This does not occur when the explicative variable is the size of the subsample, which is one reason why the latter is a better predictor. Table B.1: Lower, median an upper uncertainties estimations for different number of observations, based on the models depicted in figure B.5. We see that below 50 observations, there is risk for the statistic not to be significant (above 100% of uncertainties), although it can be significant in some cases. Above 500 observations, there is a 95% chance that the uncertainty is lower than 50%, the median estimation being 29%.

B.3. Estimating uncertainties for a single year based on explanatory variables297

The number of observation is a predictor of lower quality than the size of the subsample, generally resulting in a wider interval between lower and upper bounds for a given class. The R 2 of this model is 0.77 compared to 0.87 for the subsample size model. This should encourage the statistical office to publish the information on the sample size by default.

B.3.3 Estimating uncertainties based on the quantities (tonnes) estimated

The number of tonnes is in turn tested as explanatory variable for the uncertainty. Results are shown in figure B.6. the R 2 index of the median model is 0.63. We can conclude that the hypothesis "the higher the quantity transported the smaller the uncertainty" is only partially true. Other explanatory variables, such as the subsample size, should be preferred when it is possible.

B.4 Uncertainty reduction when averaging over several years

B.4.1 Building independent multi-year samples

In the survey, every year, half of the sample is renewed (half the trucks surveyed year i will also be surveyed year i + 1) as shown in table B.2. When averaging over n y years, there are 2 ny 1 independent samples possible. Table B.3 shows 1 among the 16 possibilities for an average over 5 years 4 . Among the independent samples generated, we chose the ones of the largest size. Appendix C

B.4.2 Results

Results

Supplementary material to Chapter 6

Excel spreadsheets with additional information are available on the journal's website (look for Supporting Information on this page: http://onlinelibrary.wiley.com/doi/10.1111/jiec.12431/abstract).

Classifications used

Pressure ratios used

Algorithm for Structural Path Analysis

Here, we show an algorithm for the structural decomposition of the term B ij , i th row and j th column of matrix B 1 .

Given the structure of matrix R, in each column of R, only one term can be non-zero. Indeed, a column represents the final consumption of specific product in a specific region so the potentially non-zero row corresponds to the same product-region, but expressed in the index numbering of matrix Q 2 . Let index() be the function that takes a column index of matrix R and returns the corresponding row index of matrix Q 3 . Then:

Hence:

Following the Taylor decomposition of matrix N = (I Q) 1 :

The following table shows the different types of paths and the count of each type (we note n the number of rows (or columns) of matrix Q).

Depth of the paths Form of the paths Count

In order to decompose the term B ij , using the notation index(j) = j 0 as defined above, we can use the following algorithm: a. We define the followings variables:

• "threshold" as a cut-off value entered by the user

• "paths" as the list of paths that have a value greater than the threshold

• "path" as the list of visited nodes in the path being explored

• "row" as the last node visited in the path being explored

• "value" as the current value of the path being explored f. We order the paths found by decreasing value.

Appendix D

Supplementary material to Chapter 7

The Wood fiber unit

Definitions and abbreviations

M : mass, V : volume, p : product, w : water, o : other components, ⌧ : moisture rate,

Water can be present in wood in two forms: water in wood fibers and free water. Free water appears above the saturation point and has no impact on the volume. Below the saturation point, wood fibers start to lose water and the volume decreases.

wf : wood f iber at the saturation point

The product is made of a single wood specie and no other components

saturation (which is the default assumption when no other information is available), then V wf = V p . In the model, this is for instance the case for the production of sawnwood. Furthermore, given a coefficient of retraction f (⌧ p ), defined by V p = f (⌧ p )V wf , we have:

The product is made of a single wood specie and other components

Then:

The product is made of different wood species and other components Let ↵ i be the fraction of wood specie i in the product mix. We have: . These coefficients represent the quantity of raw products (HRW, SRW, IW) required to produce one unit of transformed product (fw, hsw, ssw, pw, panels, pulp). Some industries are assumed to produce no waste residues (fw, panels) according to MFA. Plywood is assumed to be made of either HRW or SRW.

FFSM Calibration coefficients

Equations of the Material flow analysis

This formalism was already presented in Courtonne et al. (2015). The optimization function has however been adapted for the present study as we explain below. As shown above, the supply table comprises the supply matrix V and the imports vector I whereas the use table comprises the use matrix U , the exports vector E and the (final) consumption vector C. For instance U ij refers to the quantity of product i that is used by sector j and C

i refers to the quantity of product i that is consumed by end-users on the territory. These tables are subject to constraints (we use hats above letters to refer to data resulting from the reconciliation process, original data are represented without a hat):

• Constraint 1 : mass conservation of each product (note that stocks are neglected because we are working on a three-years average):

• Constraint 2 : mass conservation in every transforming industry:

.m and j is a transforming sector (D.2)

• Constraint 3 : Technical conversion factors between products (e.g. rate of sawmill residues),

• Constraint 4 : All flows have positive values,

• Constraint 5 : Matrices V and Û are sparse (mostly empty), for instance the wood panel industry cannot produce nor consume sawnwood.

Our goal is to minimize the discrepancy between original data and estimated/output data while respecting the constraints. This problem can be expressed in many ways depending on the expression of the distance between original and final data. We first used a classic weighted least square optimization:

subject to the set of constraints 1 to 5 (D.3)

In equation D.3, refers to the standard deviation of the data. They make it possible to treat data sources differently depending on the assumed (or possibly measured, or constrained) uncertainties. We however changed the distance used for minimization we because we found weighted least squares could lead to extreme allocations in specific cases. The minimization implemented is the following:

subject to the set of constraints 1 to 5 (D.4)

We divide each term by instead of dividing it by 2 . We consider this distance a good balance between penalizing absolute and relative differences. Testing the impact of different plausible distances on results is part of our next research leads.

Supply and Use Tables before and after the data reconciliation process

Comparing material and monetary flows in the lumber chain Monetary flows are estimated based on average unit prices for each product category. We can see niche products as wood stave and plywood mobilize little material flows but generate significant added value. Conversely, products of lesser quality such as pulpwood and sawmill residues appear a lot less significant in monetary terms.

Consequences of logs leaks reduction policies on material flows

Downscaling of the MFA: results for Lorraine

During our PhD, we participated in the elaboration of the economy-wide MFA of the Lorraine region, supervised by Richard Marcelet of the DREAL Lorraine (Regional direction of environment, planning and housing). After the presentation of overall results, it was chosen to focus more particularly on wood, among four other materials. We therefore provided the following results, based on the Grand-Est study presented at the beginning of Chapter 7. Only Exp value is presented on the X-basis, the level of the Sub_T is then chosen by a trial and error process. Results shows a U-shaped curve with a minimum for Exp= 5 e/m3 and Sub_T =80%. The net social cost is then 7 Me, which is smaller than the Exp policy alone and which makes this combination potentially interesting from a cost-efficiency perspective. ). We can see that the forest stock is increasing (which as outlined in Chapter 7 doesn't necessarily mean that this stock can be harvested from technical-economic viewpoints). A second observation is that about 50% of the production of hard roundwood is exported abroad (mainly to Belgium and Germany). This issue, already highlighted at the level of France and studied in the course of Chapter 7, is therefore even more striking in Lorraine.

Appendix to

Appendix to Chapter 10

EssentiaUy pragmatic, the concept of "govemance" is, thus, part of a "toolkit" -a very impressive and extensive list of managerial recipes or instruments supposed to bring about appropriate responses to the crisis of traditional political democracies, centred around state authority (see Table 10.1). The success story of the word "govemance" -that, as has been said, cannot be understood except in reference to the present context -can be undoubtedly explained by the feeling -one could almost speak of a mythical beliefthat we now have at our disposal a "cookbook of modern politics" containing aU the recipes needed (the sine qua non) for overcoming the contradictions of coUective action. A catalogue of "universal" tools, capable of responding to an situations, even the most complex, without any ideologic al vision of "good governments" -in that it is a rather abstract vis ion of democracy, conceived of as an open and pluralistic interaction between actors. Unambiguity with regard to the attribution of responsibilities • The risks are reversible: The "substantial rationality" model can be applied (cost -benefit analysis). • Stable scientific knowledge can be considered as a "common world for aU the actions" (as a basis for actions). • What is at stake: economic effectiveness and! or the basis of weU founded interests.

Source: Olivier Godard

It is this neutral, optimistic and managerial view of coUective action that is put strongly into doubt by two other terms: "govemability" and "governmentality." sion). In some situations, contradictions may be generated by negotiation or pragmatism; in others a chaotic process, essentially regulated by crises may be unavoidable (see Table 10.2).

Table 10.2: Decision making in a controversial world

• Prevailing of the scientific and social construction of the problems over the direct perceptions of involved groups or decision makers. • The appropriate representation of non involved parties is at stake: future generations, other countries, natural species, the biosphere, etc. • Those missing "third parties" have contradictory spokesmen.

• The scientific knowledge is stiH controversial with regard to the aspects of the problem the most relevant to the action. • Due to potential irreversibilities and! or to the magnitude of potential risks, some stakeholders or involved parties feeI that action must be taken immediately, without waiting for a more consolidated knowledge base. • The scientific assumption, the "visions of the world", become strategic varaibles which give rise to new forms of competition. • What is at stake: the building of "epistemic communities" and of "environmental conventions".

Source: Olivier Godard

All of this is of course well known to specialists in political science. However, the immense advantage of the concept of govemability is to constantly remind us that the processes of government cannot be dissociated from the structural contexts in which they take place -the idea of a "universal toolkit" leading to this at times being forgotten.

"Governmentality": A critique of the ideological neutrality of "good government "

Despite their differences, the two previous concepts of "govemance" and Evaluation environnementale de territoires à travers l'analyse de filières

La comptabilité biophysique pour l'aide à la décision délibérative

Résumé : Les conséquences de nos modes de production et de consommation sur l'environnement mondial sont reconnues et analysées depuis plusieurs décennies : changement climatique, effondrement de la biodiversité, tensions sur de nombreuses ressources stratégiques etc. Dans ce contexte, notre travail vise à fournir un outil comptable d'aide à la décision, en unités physiques, par opposition à une comptabilité monétaire, pour l'évaluation environnementale de collectivités territoriales et en premier lieu de régions françaises. Pour cela, nous nous intéressons aux filières de production que nous analysons à partir des quantités de matières qu'elles mobilisent au cours des étapes de production, transformation, transport et consommation. Nous analysons ensuite les enjeux environnementaux mais aussi socio-économiques liés à ces flux de matières, en distinguant ce qui relève de la responsabilité des producteurs et de celle des consommateurs.

Ces informations ayant une visée opérationnelle, nous proposons pour finir une méthode d'aide à la délibération entre plusieurs parties prenantes, inspirée de méthodes multicritères.