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1

GLOBAL AND LOCAL IDENTIFICATION ON COMPOSITE MATERIAL

E. Péronnet 1 , O. Dalverny 2 , S. Mistou 1,2 and M. Fazzini 2 1 NIMITECH ETUDES, 1 Avenue des victimes du 11 juin 1944, 65200 Bagnères de Bigorre, France 2 PRES Université de Toulouse, INP, ENIT-LGP, 47 av. Azereix, BP 1629, 65016 Tarbes Cedex, France elodie.peronnet@nimitech.fr, olivier.dalverny@enit.fr, sebastien.mistou@enit.fr, marina.fazzini@enit.fr ABSTRACT: This work is about a methodology based on global and local identification on composite material.

One of the main challenges in composite design and development is to be able to compute the damage state at any point of a composite structure during a complex loading. In this context, knowledge of the spatial distribution of the material elastic properties provides a quantitative estimation of the damage level and localization. The work presented here intends to access to such distribution through the association of kinematic fields and finite element model updating method. Such iterative technique has many interesting advantages for structural analysis and industrial requirements, including the numerical framework, the ability to explore complex shapes and loads and a treatment based on surface measurement without any assumption on volume distribution [START_REF] Bonnet | Overview of identification methods of mechanical parameters based on full-field measurements[END_REF][START_REF] Grédiac | The full-field measurement methods in composite material characterization: interest and limitations[END_REF].

In this study, we propose to identify the local elastic properties of orthotropic carbon-epoxy laminates for aeronautics structures by means of kinematic fields obtained under tensile tests. The aim is to be able to predict the spatial variation of such properties and to deduce the damage effects. For this, we consider the case study of a composite structure including a defect that is modeled by an association of two zones with different material properties (Fig. 1); zone number 2 corresponds here to the "damaged" zone compared with the virgin material of zone 1. 2 At first, a global identification of material properties is made to determine the constitutive parameters of the virgin material and then, a local identification is realized in order to obtain the damaged material properties. This procedure is illustrated in figure 3.

Fig.3 Global and local identification procedure

Regarding the first step, an open-hole tensile test is used to identify the in-plane elastic properties of the healthy orthotropic composite structure. Such mechanical solicitation generates an heterogeneous strain field localized near the hole that stimulate the whole strain components [START_REF] Molimard | Identication of the four orthotropic plate stiffnesses using a single open-hole tensile test[END_REF]. The displacement field measurements on the specimen surface are simulated with Abaqus finite element code as by experimental digital image stereo correlation measurements.

The second step in figure 3 corresponds to the evaluation of the gap between the healthy model derived from constitutive parameters identified at the first step and the response of the damaged structure. The representation of the equivalent strain error map (Fig. 4) shows a localized zone with highly different response that corresponds to the part 2 on figure 1. From this, two image processings developed by a specific application in Python language allows to describe precisely the damaged zone outline, which is implemented in the finite element model (step 3 of Fig. 3). Furthermore, this step gives the four coordinates of the zone 2 in the main axes of the material. At the end, a local identification is achieved since step 4 in figure 3 is realized with the same procedure as the healthy material identification to access to the properties of the zone 2 of the material. The capability of the procedure is validated for different configurations of the laminated composite (plies stacking and orientation, components properties).

Fig. 1

 1 Fig.1 Composite structure with two zones of different material properties The methodology is based on global and local identification steps by finite element model updating (FEMU) method.To implement the FEMU technique, a specific algorithm in Python language following the flowchart in figure2has been established. A particular attention has been paid to the matching of the kinematic fields grid and numerical one through the determination of neighboring points and interpolation functions. The cost function minimization is based on the Levenberg-Marquardt algorithm.

Figure 1 :

 1 Figure 1: Identification procedure based on FEMU technique [2].

Fig. 4

 4 Fig.4 Equivalent strain error map


Clémence Thébaut
email: clemence.thebaut@unilim.fr

Paul-Loup Weil-Dubuc

Jérôme Wittwer

The Philosophical Justifications of the "Fair Innings Argument" and Related Controversies

Keywords: health technology assessment, fair innings argument in general (education, income, etc

Financing innovative and costly treatments in various therapeutic fields entails a number of problems in countries where costs are covered by public services. Providing these drugs is forcing actors to define the maximum sums of money society is willing to spend for given health improvements. This raises the question of whether maximum financing should vary according individuals' circumstances, such as the rareness of a disease, lifestyles, social inequalities experienced over a life time, etc. This article examines a particular priority, namely that given to the youngest patients, such prioritising usually refers to the "fair innings argument" (FIA). The challenge is to identify if, and on the basis of what arguments, collective choices should take into account age in the name of a right to live the time required for a complete life, within a context of the scarcity of resources and the pluralism of values. Three arguments are considered. At first we consider that FIA could be justified by the objective of equalizing the opportunities of well-being. Next, we proposed justifying the fair innings argument with the aim of equalizing the time provided to individuals to achieve their plan of life, in accordance with Rawls's theory of justice as fairness. Finally, we proposed considering the FIA as being justified because of the goal of equalizing the time provided to individuals to accept death. These three arguments, of course, have many limitations, some of which we have highlighted.

Introduction

Context

The recent emergence of innovative and costly treatments in various therapeutic fields has raised much hope from a public health perspective, even though financing them entails a number of problems. In oncology, for example, the prices of innovative treatments such as Kadcyla (trastuzumab emtansine, by Roche) or anti-PD1 immunotherapies (Opdivo and Keytruda) can run to €6,000 per month in France: i.e., an additional cost of approximately €100,000 per year yielding an extra, average survival benefit of about 6 months (according to HAS and NICE efficiency evaluations of these treatments) (NICE, HAS). In the United States, a rising number of patients have been forced to give up care due to the high prices set by drug manufacturers [START_REF] Meropol | American Society of Clinical Oncology Guidance Statement: The Cost of Cancer Care[END_REF]ASCO 2016 ;[START_REF] Gaille | Trajectories of Injectable Cancer Drug Costs After Launch in the United States[END_REF]. Such price levels are challenging the sustainability of health insurance systems in countries where costs are covered by public services (OCDE, 2017). Equitable access to such innovative treatments competes with other forms of public investment for which social expectations are strong too: education, the environment, care for dependent persons, combating poverty and exclusion, etc. Providing these drugs is forcing actors to define, more precisely than before, the maximum sums of money public authorities and society are willing to spend for given health improvements. This raises the question of whether maximum financing should vary according individuals' circumstances, such as the rareness of a disease, lifestyles, social inequalities experienced over a life time, etc. Economic health calculations commonly used by health technology assessment agencies are implicitly based on a utilitarian type of principle aimed at maximising the sum of health gains, usually measured in quality-adjusted life years (QALYs), obtained with medical treatments funded. The utilitarian dimension of this calculation is based on the principle for "everybody to count for one, and nobody for more than one", as expressed in the well-known formula "1 QALY = 1 QALY = 1 QALY". Individuals' specific characteristics (age, gender, socioeconomic characteristics, lifestyle, etc.) are not taken into account when assessing the value of a health improvement. Any particular treatment is only assessed according to the quantity of health improvement it procures in terms of life years gained in perfect health or QALYs, whatever the situation of the patient. However, there is much discussion in health economics concerning prioritising health improvements for certain patients. Such prioritisation can be done using weightings applied to health gains. Alternatively, it may be achieved by using variable reference values for interpreting the incremental cost-effectiveness ratio (ICER). This is formally equivalent and similar in normative terms. These weightings or ICER interpretation rules are generally attached to particular pathologies or situations [START_REF] Norheim | Cost Effectiveness and Resource Allocation[END_REF]. Their use may be interpreted as a way of introducing inequality aversion in the distribution of certain outcomes across the population (well-being, health status, lifespan, physical abilities, etc.) [START_REF] Wagland | A fair innings or a complete life: another attempt at an egalitarian justification of ageism[END_REF]. These practices are consistent with recent academic research that proposes considering the principles of egalitarian distribution in economic assessment [START_REF] Sen | Why health equity ?[END_REF][START_REF] Brouwer | Welfarism vs. extra-welfarism[END_REF][START_REF] Grant Cookson | Using cost-effectiveness analysis to address health equity concerns[END_REF][START_REF] Asaria | Distributional cost-effectiveness analysis of health care programmes -a methodological case study of the UK bowel cancer screening programme[END_REF]. Provided that they dispose of accurate data, economists can easily include the priorities of a health system in their calculations. Economics indeed often takes into account distribution considerations in the formulation of social welfare objectives. However, it is absolutely necessary to justify the priorities selected. The translation of social values into the methods and practices of health assessments may lead to (re)directing research and innovation efforts by industry and organisation operating in the health sector. The issue at stake is important.

The Fair Innings Argument

This article examines a particular priority, namely that given to the youngest patients. Following the work by John Harris, such prioritising usually refers to the "fair innings argument" (FIA). In his book The Value of Life, Harris stresses that the death of an individual is always terrible. But, it may be considered a tragedy when it takes place before the individual has benefited from a reasonable life, which he calls a "fair innings". Anyone who dies prematurely (i.e., who dies before reaching this age), suffers an injustice which society is justified in preventing. From this perspective, it is legitimate to allocate more resources to individuals who have not reached this age limit and to allocate fewer resources to those who have already reached it. Harris, however, does not specify what this reference age should be, nor the method to define it. According to him, it is not possible to distinguish different degrees of injustice according to the age of death. Anyone who has not had a fair innings is penalised in the same way, be they 20, 30 or 40 years old. Following Harris, Williams however proposes to define the reference age based on average life expectancy at birth for the population as a whole. In contrast to Harris, Williams considers that the injustice experienced by an individual who dies prematurely increases with the difference between the age of death and this average life expectancy. Finally, he recommends taking into account the quality of life over an individual's entire lifetime. This raises important informational difficulties [START_REF] Williams | Intergenerational equity: an exploration of the 'fair innings' argument[END_REF][START_REF] Tsuchiya | Age-related preferences and age weighting health benefits[END_REF][START_REF] Tsuchiya | QALYs and ageism: philosophical theories and age weighting[END_REF]. It should be noted that the fair innings criterion is different to granting priority to the youngest populations because of the longer life expectancy they enjoy. The question that is raised by this criterion is the value given to the same extension of lifetime, at different ages or stages in life. Concretely, the Fair Innings Argument may lead, for example, to favouring the financing of specific health treatments when the life expectancy of a target patient group is lower than the average life expectancy, or restricting access to care depending on a patient's age. From a value point of view, there to be equivalence between providing extra public funding to reduce the mortality of young patients (e.g., children or young adults) and deciding to pay less to extend the life expectancy of older patients. Both situations involve taking into consideration the amount of time an individual has lived and may live. This priority may also be taken into account in calculations using weightings that are applied to the health outcomes of the treatments based on the average age of the patients. In Great Britain, for example, NICE at one point considered to take patients' age into account as a weighting variable in its work on Value Based Pricing. This involved notions of absolute shortfall and proportional shortfall. But this approach was finally given up [START_REF] Towse | Clarifying meanings of absolute and proportional shortfall with examples[END_REF]. Today, no agency gives priority to younger populations in their assessment of health technologies. However, mechanisms do exist to fund expensive treatments, considered inefficient, in certain particular pathological contexts (for example, the Cancer Drug Fund in Great Britain). Most often these are pathological conditions in which patients have a reduced life expectancy compared to the average life expectancy of the general population. The WHO in fact also proposes allocating resources as a priority to health research in therapeutic areas where the burden of disease is the highest, i.e. where the gap between the life expectancy of sick individuals and that of the general population is the largest.

1.3.

Objective The aim of this article is to consider the normative stands biases which underlie these practices, and to test them using theories of social justice. It is not enough to consider that premature death is a tragedy or a misfortune to judge that it is an injustice, as it is proposed by Harris and Williams. If all misfortunes were injustices, then satisfying our demands for justice would be impossible. We would then risk, in the words of Pogge, of falling into a "bottomless pit" [START_REF] Pogge | Realizing Rawls[END_REF][START_REF] Pogge | Relational Conceptions of Justice : Responsabilities for Health Outcomes[END_REF]. To establish that a misfortune is also an injustice can only be done by referring to a theory of justice whose purpose is to establish a boundary between, on the one hand, what is just and unjust and the other hand, what does not belong to such an evaluation. The question then is whether and on with what arguments, in the context of pluralistic societies which respect different conceptions of a good life, the community is justified in offering everyone a minimum life lifespan, ahead of other objectives. More specifically, it may be asked why it is justified to try to equalise lifespans rather than achieving something else. This article follows recent publications on this subject [START_REF] Wagland | A fair innings or a complete life: another attempt at an egalitarian justification of ageism[END_REF]Brognar 2014;[START_REF] Menzel | Age-Related Prioritizing: Assessing the Sufficiency, Prudential Lifespan, and Fair Innings Accounts, Workshop -"What We Owe Older People" Centre for Bioethics[END_REF]Sodberg 2016;[START_REF] Nagel | Death, in Mortal Questions[END_REF]Lauerer 2016, andalso MacMahan 2002) and it seeks to contribute to this debate, which has recently been reopened. As with Sodberg, Bognar and Macmahan, we propose mobilising Nagel's concept of a deprivation account (Section 2) and the argument for a prudential lifespan account by Daniels (Section 3) to justify the fair innings criterion. However, we will discuss these concepts differently. On the one hand, we propose linking Nagel's concept of a deprivation account to the goal of equalising well-being opportunities. On the other hand, we provide an additional critique of the concept of a prudential lifespan account by considering the possibility of an evolution of life plans defined a priori at the approach of death. Finally, we propose a third justification, unprecedented, for the fair innings criterion, based on the goal of equalising the time available to everyone in order to accept dying (Section 4). It should be noted that there are different ways of implementing the fair innings criterion. In a moderate form, the fair innings criterion leads to giving the youngest a relative priority, while in an extreme form it could lead to the end of collectively funding health care for patients beyond of a certain age, and even to considering forms of euthanasia. These various forms of fair innings depend on the degree of aversion to inequalities of the lifetimes retained: the extreme form of fair innings implies an absolute degree of aversion to inequalities in lifetimes, while the moderate form implies a lower degree of aversion. In the context of this article, we are not considering this extreme form of fair innings because its social acceptability is unthinkable, as evidenced by the intensity of the debate that even moderate forms of fair innings generate [START_REF] Rivlin | Why the fair innings argument is not persuasive[END_REF][START_REF] Fisher | Healthcare rationing in Australia: Should the young be favoured over the elderly? Bioethics Outlook Plunkett Centre for Ethics, A joint centre of Australian Catholic University and St Vincent[END_REF]).

Equalizing life years in the name of an equal opportunity of well-being

Following [START_REF] Macmahan | The ethics of killing: problems at the margins of life[END_REF] and [START_REF] Solberg | The badness of death and priorities in health[END_REF], it is indeed interesting to begin by justifying the fair innings criteria by drawing on the concept of the deprivation account put forward by [START_REF] Nagel | Death, in Mortal Questions[END_REF], in an article entitled "Death". In this article, Nagel aimed to challenge the hedonistic argument that death has no value in itself, neither good nor bad, since it cannot be experienced by a subject: the subject disappears at the instant of experiencing death. "Death is nothing for us, because as long as we exist death is not here, and when death comes, we are no more." (Epicurus, Letter to Meneceus). In contrast, Nagel suggests considering that the value of an individual's death depends on what it takes away from the person, that is to say activities which the subject can no longer do and which are sources of pleasure or displeasure. "Death is an evil because it brings to an end all the goods that life contains. It is bad not because of any positive features but because of the desirability of what it removes" [START_REF] Nagel | Death, in Mortal Questions[END_REF]) (for a more precise presentation of the notion of "deprivation account", see [START_REF] Bradley | When Is Death Bad for the One Who Dies?[END_REF][START_REF] Johansson | The time of death's badness[END_REF]2014). Nagel admits that depending on their age, individuals have a certain number of years of life remaining, which are rich in future possibilities (personal relationships, aesthetic experiences, pleasures): and so they are more or less harmed when they are deprived of these early: "The death of Keats at 24 is generally regarded as tragic; that of Tolstoy at 82 is not. Although they will both be dead forever, Keats's death deprived him of many years of life which were allowed to Tolstoy; so in a clear sense Keats's loss was greater, (though not in the sense standardly employed in mathematical comparison between infinite quantities.)" (Nagel, 1970). Premature death not only deprives an individual of satisfactions related to the activities they could actually have fulfilled, but also the satisfaction of simply being able to project oneself into the future, as Singer states clearly: "For preference utilitarians, taking the life of a person will normally be worse than taking the life of some other being, since persons are highly future-oriented in their preferences. To kill a person is therefore, normally, to violate not just one, but a wide range of the most central and significant preferences a being can have." (Singer, 1993, p. 95). However, it is necessary to specify that Nagel himself does not mobilise this notion of a deprivation account to justify taking age into consideration in the allocation of health resources. Unlike Sodberg, it does not seem possible to us to base the fair innings criterion directly on the concept of a deprivation account alone. To do so, it would be necessary to go further than Nagel, considering on the one hand that it is justified to distribute these deprivation accounts equitably. On the other hand, it requires using the number of years of life to estimate these deprivation accounts, which amounts to admitting that the deprivation account is identical for all individuals of the same age, whatever their preferences and circumstances. This choice could be justified by the technical impossibility of measuring ex post and individually the amount of well-being they would have received had they lived longer. It would then be considered acceptable to measure well-being opportunities, rather than actual well-being, and to take lifetime as an indicator of these well-being opportunities. Being alive is the first condition for an individual to feel satisfaction. According to Arneson (1988), liberal egalitarian theories centred on an objective of equalising opportunities, based on an equitable distribution of primary goods or objective resources, use the latter, in the same way, to approximate the quantity of well-being that would benefit each individual.

("We may insist that governments have regard to primary good share equality or resource equality as rough proxies for the welfarist equality that we are unable to calculate." (Arneson, 1988: 87)). But it would also be possible to justify this objective of equalising welfare opportunities in itself, and not by default, as Dworkin and Sen have done [START_REF] Dworkin | Sovereign Virtue: The Theory and Practice of Equality[END_REF][START_REF] Sen | Development as Freedom[END_REF]. For these authors, it is preferable to distribute resources equitably in order to equalise well-being opportunities, rather than actual levels of well-being, as the latter vary as a function of tastes and circumstances, as well as individuals' success which depend on their original circumstances, and on parameters dependent on individual responsibility (such as effort and motivation). It is therefore preferable to distribute resources equitably to allow everyone reach a certain level of well-being fairly, while at the same time leaving them with the responsibility of actually attaining this level of well-being. From this point of view, it is possible to consider that lifetime is one resource among others.

Equalizing life years in the name of equal opportunity for everyone to develop their own life plans

Secondly, it seems possible to justify the FIA in the name of equal opportunity for everyone to develop their own life plans, on the grounds of the Rawlsian conception of justice as equity, as it is proposed by Norman Daniels, in an essay titled Am I my parent's keeper?. For Rawls, every individual is capable of rationally ordering his/her desires and organizing them according to a system of ends in which short term projects are integrated into long term projects (Rawls, 1971, pp. 479-480). Accordingly to Daniels, restricting access to health technologies according to age is not a source of inequality as, unlike other individual characteristics such as gender or skin colour, all individuals end up aging (a similar argument can be found in McKerlie ( 2001)). The question raised by the FIA concerns the fair distribution of resources according to the ages of life. Daniels states it is likely that rational and cautious individuals, when placed behind Rawls's veil of ignorance, choose to allocate resources in such a way as to maximize the chances of benefiting from a normal life expectancy, even if this means not prolonging their own lives if they were to be lucky enough to reach old age. "Therefore it seems prudent for me to reserve certain life-extending technologies for my younger years. I would thus maximize the chances of my living a normal lifespan" (Daniels 1988, p. 496). The majority of people are aware that they are mortal and conceive of their life project given the representation they have of their life expectancy. It is essential that they are able live to an average age because it is during these years that they realise their life project. In addition, it seems prudent to them to keep some of their resources to finance medical-social care in order to guarantee a satisfactory level of life quality in old age, even if this once again means giving up on prolonging their lives. Daniels indicates that such trade-offs are quite close to the choices made in the UK's NHS, which limits certain technologies depending on patients' age (e.g., dialysis) and which invests in care favouring the autonomy of older persons so they may stay at home. Moreover, the fair innings argument could be justified in the name of the maximin principle which aims at distributing resources so as to improve as much as possible the situation of the most disadvantaged persons. There is no doubt, according to Daniels, that dying young is one of the worst situations possible. Yet Daniels went on to question this argument in a more recent book (2008), questioning whether the FIA could indeed be justified using the concept of equity as the basis of justice. In his more recent opinion, the idea of a fair innings is a particular stance, as it refers to one conception of a good life which is valid among other conceptions. To consider that a good life involves living sufficiently long is just one position among an irreducible plurality of other positions. Daniels confines himself therefore to considering that the fair innings argument is not unfair in itself. It is still possible morally to adopt this stance collectively, provided that the decision to do so is based on a deliberative process which meets conditions Daniels goes on to define. These are based on what he calls accountability for reasonableness (on the evolution of Daniels' thinking on the FAI see [START_REF] Brauer | Age rationing and prudential lifespan account in Norman Daniels' Just health[END_REF]. It seems to us that another criticism can be levelled at this justification of the fair innings criterion, based on the objective of equalising time given to individuals to achieve their life plan. In particular, the evolution of life plans throughout a lifetime needs to be examined, especially with the approach of death. The adaptation of preferences is a phenomenon that is well-known in behavioural economics (Tversky and Kanneman 1992). Following Heyd et Miller, it raises questions not only about the validity of ex ante preferences, but also about the relevance of life plans defined a priori. "The phenomenon of 'adaptive preferences' usually considered as limiting the rationality of more 'local' choices, seems to be essential and inevitable in the context of life planning, of the formation of human personality as whole" (Heyd and Miller 2010, p. 27). It is possible that the imminence or prospect of death reveals the strength of an individual's opinions. At this moment, an individual's most authentic preferences could be revealed and that a person's life project is defined retrospectively. From this perspective, it is therefore not possible to consider that beyond a certain age, reasonable and prudent individuals are meant to have achieved the objectives of their lives. This is because these objectives can only become clear when people face death, whatever their age. The weeks, months or even years that can be gained through medical care would then be an opportunity for individuals to examine their lives in the light of their "true" preferences and goals, which can be clearly viewed at this moment. Such a reprieve from imminent death could thus provide them with the opportunity of attaining a sense of accomplishment through reviewing their lives and through any actions they may decide to undertake accordingly (words, acts or various experiences). Yallom (1980) recalls that this idea of death as a revelatory experience is often mentioned both in classical literature (e.g. In The Death of Ivan Illich or in Dickens' tale A Christmas Carol) as well as in philosophy (according to Heidegger, consciousness of death allows individuals to move from an inauthentic mode of being towards an authentic mode of being, called the ontological mode) (Heidegger, 1927).

Equalizing life years in the name of an equal chance to accept death

Lastly, it seems to us that a particular priority could be given in contexts where the end of life occurs early and suddenly, and that it is possible to delay death for some time, in the name of equalising the time given to individuals to accept death. This is especially the case of pathologies such as certain cancers, which are diagnosed in very late stages, thus limiting the life expectancy of patients to less than one or two years, sometimes less. In this case, costly therapies may be proposed to provide these patients with a few additional months of survival. The value given to this reprieve of time today raises concrete questions concerning public policy. The utilitarian framework underlying the calculations of health economics, which are based on estimating differential cost/QALY ratios, yields low valuations in terms of the social value obtained by these therapies, compared to their costs: the extra lifetime is short and the quality of life is often very poor. It is possible, however, that such estimations fail to take into account some benefits these therapies may bring to patients, namely more time to prepare themselves and their relatives for their death. This reasoning is in line with doctors' thoughts about the notion of "compassionate resuscitation" (Deciron-Debieuvre, 2016). Giving a variable priority to patients' age is justified not so much by the lifespan of which an individual benefited as the unpredictable and sudden nature of death compared to statistical and social norms. This deprives a person of the possibility of implementing a process which classical philosophers, from Plato (with the death of Socrates, as it is described for instance in the well-known prosopopoeia of the Laws in Crito (Plato, Crito, 50 a-c)) and Montaigne (Rohrbasser, 2004), as well as some psychoanalysts, have endeavoured to describe, and at the end of which an individual may be ready to die [START_REF] Has | anticorps ciblant le récepteur HER 2 couplé à un cytotoxique[END_REF]. For these classical writers, for example, the acceptance of death involves the recognition of a form of transcendence, via the idea of Good and Truth in Socrates (Guardini, 1948), or Destiny and World Order for the Epicureans as well as for classical or modern Stoics (Cicero, On the Good Life, chap. 3 ; Montaigne, Essays, Book 1, chap.19). Other forces and strengths are of course possible. Giving more priority to patients at risk of premature mortality could in this case be justified by the idea that this psychic work is undertaken from the moment when an individual becomes aware of his/her finiteness. This is something which the younger people tend to ignore, as they are taken up by their daily activities (Hetherington, 2013, p. 96). "This 'finiteness', which we share with all living things, however, is not self-evident, because we live most of the time in the forgetfulness of our own mortality. This is what led Freud to assert that 'no one, deep down, believes in their own death or, what amounts to the same thing: in the unconscious, each of us is convinced of our immortality '." (Dastur, 2009, p.7) Advancing age, along with other events in life may then remind individuals of this finiteness, and lead them to start accepting it. It is more likely that individuals are "ready" to die when they are older than when they are younger. It should be emphasised that in present health systems, the priority given to extending the lives of the youngest individuals results in the provision of therapeutic means being left to the discretion of patients, with the advice from their doctors. There is no question of imposing on anyone extending their survival against their own preferences. The limitation of this third justification is that it implies verifying that the degree of acceptance of death does actually progress with age, without imposing a duty on individuals to be wise, as part of a perfectionist approach of the good life. The question then arises of whether it is really possible to prepare for death, above and beyond basic discourses held throughout one's life. Fiat thus describes how the proximity of one's own death, or that of others, leads to a particular rationality which is distinct from the daily rationality: "Even if one has prepared oneself for death, and for love, their occurrence always overflows the container designed to accommodate them. Their manifestation immediately saturates the receptive capacities of the person experiencing them. It seems to me that to describe the occurrence of death or love requires constructing another phenomenology than the phenomenology which describes the ordinary phenomena of life; unless in fact it is necessary to break with phenomenology itself and instead invent something like an epiphanollogy that is up to the task" (Fiat 2001, p. 127). Menzel's analyses of the value of hope in end-of-life situations, even when futile, illustrates this particular form of rationality (2011).

Conclusion

The still-inescapable character of death, which until recently has marked the philosophies of death, beginning with Stoic philosophers (see Cicero, On the Good Life) presents itself today differently. Hardwig discusses more precisely the evolution of the relationship to death, induced by technological development. He stresses in particular that from now on individuals know a few years in advance that their end is near: "Dr. Joanne Lynn once observed that the average American now knows three years in advance what she will die of.(…) Earlier diagnoses will be possible, giving us a more advanced warning of our terminal illnesses. Better treatments will also be available, allowing us to fight our terminal illnesses for a longer period. Unlike most people in previous generations, we now live facing death for a very long time" (Hardwig 2006, p. 4). The joint development of scientific progress and health insurance systems raises the question of collective (or social) responsibility for access to technologies which can delay death. The question of the acceptance of death, which used only to be an intimate question, is now also the subject of joint decisions. This situation raises new ethical questions about the value of death from the point of view of the theories of justice. In this paper, we have examined three arguments justifying the fact that the value of death decreases as an individual grows older due to the aim of equalizing lifetimes, commonly called the fair innings argument. At first we consider that FIA could be justified by the objective of equalizing the opportunities of well-being. Next, we proposed justifying the fair innings argument with the aim of equalizing the time provided to individuals to achieve their plan of life, in accordance with Rawls's theory of justice as fairness. Finally, we proposed considering the FIA as being justified because of the goal of equalizing the time provided to individuals to accept death. These three arguments, of course, have many limitations, some of which we have highlighted. The purpose of this work is to contribute to public debates on priority criteria used in the allocation of health resources. The ethical controversies raised by the fair innings argument are particularly strong. To some, like Harris and Williams, it seems intuitive. But for others, the notion of a fair innings seems to be radically opposed to deeply-rooted moral conceptions held in our societies (respect for elders and filial sentiment, the sacredness of all human life, or support for the most vulnerable). Death as such is the subject of psychological and social taboos which make it difficult to organise reasoned discussions (Déchaux, 2001). The controversies surrounding the FIA may also be sharpened by the personal and professional experiences which determine any individual's views on the issue. The value of death is ultimately little-discussed by contemporary social justice theorists. We believe it is necessary to further discussions on the possibilities of applying the principles of equity used in the distribution of resources

Université de Limoges, Unité Inserm UMR 1094 (NET), 3 rue François Mitterrand, 87000 Limoges France ; Chercheure associée au LEDA-Legos Paris Dauphine-PSL

Espace Éthique de la région Ile-De-France, CESP U1018 (Inserm/Paris-Saclay)

Université de Bordeaux, Bordeaux Population Health, Inserm U1219


Alberto Grillo

Eva Raiber

Exit polls and voter turnout in the 2017 French elections *

Keywords: Exit polls, voter turnout, underdog effect, bandwagon effect JEL codes: D72

Belgian and Swiss media regularly interfere during French elections by releasing exit polls before polling stations close. These foreign media profit from a law forbidding the same behavior by their French counterparts to receive large inflows of web visits from France. We exploit the unusual timing and degree of confidence with which exit polls were released in the second round of the 2017 presidential elections to investigate their effect on voter turnout. Our analysis is based on comparing turnout rates at different times on the election day, in the first and second round, and with respect to previous elections. We find a significant decrease in turnout of around 3 to 4 percentage points after the exit polls' publication which is suggestive of a causal effect, although similar trends were observed in previous elections. The effect is stronger in departments close to the Belgian border shortly after the release of the exit polls. We do not find clear evidence that either candidate benefited from the decrease in turnout, yet we cannot exclude the presence of a small underdog effect which reduced the winning margin by around 1 percentage point.

Introduction

Elections take place under a given degree of uncertainty concerning the outcome. If the uncertainty is drastically reduced, will citizens still make the effort to vote? We study this question in the context of the 2017 French presidential elections, by exploiting the early release of exit polls by foreign media.

While in France it is forbidden to publish exit polls before polling stations close, foreign media do not abide by this law. In particular, Belgian and Swiss francophone media regularly report exit polls from French elections while voting is still taking place. For tight elections, this information often comes late and is presented with abundant words of caution concerning its precision. However, the circumstances of the 2017 second-round elections, with the exit polls pointing to a landslide victory for Emmanuel Macron1 , allowed these media to disclose the results earlier and with an unusual degree of confidence. For example, Belgian broadcaster RTBF reported already at 16:00 that, according to the exit polls in their possession, Macron was clearly ahead and would beat Marine Le Pen with at least 60% of the votes. The announcement was quickly picked up by many other foreign media, while polling stations remained open until 19:00 or 20:00.

We use turnout data at 12:00, 17:00 and at end of the day to investigate the effect of this information shock on voting behavior. Voter turnout at 12:00 is not affected by the exit polls' release, while turnout at 17:00 and at end of the day can be. We compare the turnout rates in the second round to those in the first round of the elections, similarly to a difference-in-differences setting. This assumes that citizens vote on average at the same time in the first and second round. In our baseline specifications, we find a significant decrease in turnout with respect to the first round at both 17:00 and at the end of the day, which ranges between 3.1 and 4.1 percentage points. The effect does not change by controlling for rainfall and variation in temperature, which could potentially affect the distribution of voting times between the two rounds.

To validate our results, we compare the trends in turnout to those in the two previous French presidential elections. In 2012 and 2007, the second-round election was more competitive and foreign media reported the exit polls with more conservative claims concerning their precision until a later time in the day. In both years, we observe that the increase in turnout after 12:00 is lower in the second round than in the first. Nonetheless, the triple-differences estimator is significant with respect to the 2012 elections at both 17:00 and at the end of the day, as well as with respect to the 2007 elections at 17:00. This suggests that the decrease in turnout in the second round of the 2017 elections is driven at least in part by the exit polls' publication.

These results give credit to theories of voting as an act which is, at least partially, strategic and instrumental, in contrast to theories of voting as a non-strategic decision motivated by civic duty or by a consumption benefit. A similar decrease in turnout has been found in the US in the 1980 elections, which were called in favor of Reagan while polling stations were still open in the Western states [START_REF] Delli Carpini | Scooping the voters? the consequences of the networks' early call of the 1980 presidential race[END_REF], as well as in the 2000 elections, when Florida was called in favor of Bush while polling stations were still open in the Panhandle counties [START_REF] Lott | The impact of early media election calls on republican voting rates in florida's western panhandle counties in 2000[END_REF]. The results are also in line with Morton et al. (2015), who show that in the French overseas territories, before the 2005 electoral reform, voting after exit polls from the mainland had been published decreased turnout by 11 percentage points.

We complement the analysis by checking whether the effect varies geographically or as a function of the preferences expressed in the first round of the election. With respect to geography, the decrease in turnout at 17:00 is stronger for departments that are closer to Belgium, as measured by the distance from the department's capital to Brussels or to the border. The effect at the end of the day goes in the same direction but it is not statistically significant, a result which could be due to the exit polls being transmitted earlier (i.e. between 16:00 and 17:00) in departments that are closer to Belgium.

We do not observe different effects in departments close to the border with Switzerland, compared to all other departments.

Concerning differences in voters' preferences, we observe a greater decrease in turnout following the information shock in departments in which Macron was the most voted candidate in the first round, compared to departments in which he was not. The effect corresponds to an additional reduction of 1.1 percentage points and is weakly significant (p-value: 0.099). On the contrary, the decrease in turnout is not different in departments in which Le Pen was the most voted candidate in the first round, compared to departments in which she was not.

We then looked at departments in which the vote share for the other candidates in the first round was relatively higher. Specifically, given the ideological positions of Macron and Le Pen, left-wing voters could be more tempted by abstention after the exit polls' release, in order to avoid voting for a weakly preferred candidate. We observe indeed that departments with the 50% highest combined share of votes for Benoît Hamon and Jean-Luc Mélenchon -the two major left-wing candidates -have a stronger decrease in turnout. As before, the effect corresponds to a 1.1 percentage points reduction.

Yet, though close to the 10% level, the coefficient is insignificant at conventional levels (p-value: 0.113).

The analysis with respect to the results in the first round informs the debate about the diffusion of opinion polls in the last days of the electoral campaign, as well as that on the early release of exit polls. The standard rationale for banning their publication is that it could alter the election results by affecting asymmetrically the voters of different candidates. Researchers typically distinguish between an underdog or a bandwagon effect, depending on whether the publication of polls give an advantage to the trailing (underdog effect) or to the leading candidate (bandwagon effect). The empirical identification of a causal effect with real elections data is challenging, because voting is secret and because these effects could be driven not only by changes in turnout rates but also by changes in the vote choice.

The literature has traditionally found mixed evidence (see the discussions in [START_REF] Marsh | Back on the bandwagon: the effect of opinion polls on public opinion[END_REF][START_REF] Mcallister | Bandwagon, underdog, or projection? opinion polls and electoral choice in britain, 1979-1987[END_REF][START_REF] Irwin | Bandwagons, underdogs, the titanic, and the red cross: the influence of public opinion polls on voters[END_REF], confirmed recently by findings of both bandwagons [START_REF] Hodgson | Bandwagon effects in british elections, 1885-1910[END_REF][START_REF] Kiss | Identifying the bandwagon effect in two-round elections[END_REF]Morton et al., 2015) and underdog effects [START_REF] Chatterjee | Voting for the underdog or jumping on the bandwagon? evidence from india's exit poll ban[END_REF].2 Based on our results and under the assumption that left-wing voters in the 2017 French elections preferred on average Macron to Le Pen, we cannot exclude a mild underdog effect, according to which Macron's margin of victory could have been slightly higher in the absence of the information shock.

Context

The 2017 French presidential elections took place on April 23 and May 7 2017. Because none of the 11 candidates won an absolute majority in the first round, a second round was held between the two top candidates, Emmanuel Macron (who had obtained 24% of the votes) and Marine Le Pen (21.3%).

Three other candidates received more than 5% of the votes in the first round, namely François Fillon (20%), Jean-Luc Mélenchon (19.6%), and Benoît Hamon (6.4%). In both rounds, polling stations closed at 20:00 in big cities and nearby municipalities, while at 19:00 elsewhere.

While French polling agencies collect regular exit polls data on election days, the law requires French media to not publish them before 20:00. Foreign media do not abide by this rule, and francophone media in Belgium and Switzerland report exit polls along the day, registering a large increase in their websites' visits from France. Our empirical analysis relies on the timing and the degree of confidence with which exit polls were unusually released in the second round of the 2017 elections. Foreign media typically wait for a reasonable degree of confidence before publishing the first exit polls and present them with abundant words of caution if the predicted advantage is not large. As an example, in the first round of the 2017 election, Belgian broadcaster RTBF predicted early in the day that Macron would win a relative majority but waited until around 19:00 to predict that Le Pen was going to be the other candidate qualified to the second round. In the second round, instead, although mentioning that voting was still ongoing, RTBF reported already at around 16:00 that Macron was predicted to win with at least 60% of the votes, and updated his vote share to 62%-64% at around 16:20.

Other Belgian and Swiss media published similar results at the same time or slightly later, and the news spread quickly to media in other foreign countries as well as on social networks like Twitter. This information shock, which showed an even bigger margin of victory than the one forecasted by most opinion polls in the previous days, could change citizens' motivation to vote later in the day, in an election that appeared to be already decided. 3

Data and empirical strategy

Our dataset contains turnout rates, election results for each candidate, and the number of registered voter at the department level in 2017, 2012 and 2007, obtained from the French interior ministry. Voter turnout is measured at 12:00, 17:00 and when polling stations closed. We merged these data with weather information for both rounds of the 2017 elections, by collecting daily rainfall and maximum temperature in each department's capital. 4 Our baseline specification compares turnout rates before (at 12:00) and after (at 17:00 and at the closing time) the information shock with respect to the first round in the 2017 elections. As in a difference-in-differences setting, we use turnout rates at 12:00 as the pre-period and turnout rates at 17:00 and at the closing time as post-periods, with the first round as the "control group". This assumes 3 Figure 2 in the online appendix gives a sketch of the information release at different times. The exit polls data mentioned by the foreign media are not public information and cannot be independently verified, since they came from French poll agencies, which were subject to the legal ban. The concerned foreign media, however, did publicly defend their sources as reliable, and the data turned out to be correct ex-post in both rounds of the 2017 elections. In our reading of online information, RTBF took a major role in diffusing the exit polls early and in defending this choice, with both the editor-in-chief and the director of information arguing publicly for the general interest of this information, see for example https://www.rtbf.be/info/monde/detail presidentielle-francaise -pourquoi-la-rtbf-diffuse-t-elle-les-estimations-de-resultats?id=9587877 and http://www.slate.fr/story/ 144044/presidentielle-francaise-jackpot-belge.

4 Table 5 in the online appendix presents a few summary statistics of our data.

that, if the exit polls had not been released, voter turnout would have followed the same trend as in the first round. Our baseline estimation is therefore:

turnout t,r,d = β 1 time t + β 2 round r + β 3 time t × round r + t,r,d (1)
where turnout t,r,d measures turnout at time t in round r in department d, time t is the indicator for the post-periods, and round r is the indicator for the second round. Standard errors are clustered at the department level and departments are weighted by the number of registered voters. The coefficient of interest is β 3 .

It is however possible that different trends in voting times would have emerged between the two rounds even absent the information shock from foreign media. Figure 1 plots the aggregate turnout rates in the 2007, 2012, and 2017 elections. Unlike in 2017, both in 2007 and in 2012 voter turnout was higher in the second round than in the first. In all three elections, the increase in turnout from 12:00 to 17:00 and to the end of the day appears smaller in the second round than in the first round.

In both 2012 and 2007, however, given the much tighter competition between the two second-round candidates, foreign media published exit polls with smaller margins of victory and used a more agnostic language concerning their precision until a later time. To isolate the effect of the early release of exit polls, we compare the results in 2017 to those in 2012 and 2007 in a triple-differences setting. This analysis assumes that, absent the information shock in 2017, the difference in turnout trends would have been the same as in the two previous elections.

Our second estimation is thus:

turnout y,t,r,d = β 1 time t + β 2 round r + β 3 year y + β 4 times t × round r + β5time t × year y + β 6 round r × year y + β 7 time t × round r × year y + y,t,r,d (2)
where turnout y,t,r,d measures turnout in year y at time t in round r in department d, and year y is the indicator for the year 2017. The coefficients of interest are β 4 for the presence of a similar trend in previous elections and β 7 for the triple-differences estimation.

Results

Table 1 shows the results of our baseline analysis. We observe a significant decrease in voter turnout with respect to the first round, following the exit polls' publication. The estimates of the effect are between a 3.4 and 4.1 percentage points reduction in turnout at 17:00 and between a 3.1 and 3.7 percentage points reduction in turnout at the end of the day, depending on the specification. We find that the result does not hinge on weighing departments by the number of registered voters (column 2).

The results are also robust to controlling for rain and maximal temperature at the department level (column 3), and hold if we only include departments in which it did not rain (column 4).6

In table 2, we compare turnout trends with those in the previous elections. The significant negative coefficients for the interaction between time and round of the election confirm the graphical evidence in Figure 1 of a similar trend in the two previous elections. The coefficients of the triple interaction are however also significant, both at 17:00 and at the end of the day for the 2012 election as well as at 17:00 for the 2007 election. This suggests that despite the similar trend in voting times in previous elections, the information shock contributed to the decrease in turnout from the first to the second round of the 2017 elections. Specifically, with respect to the 2012 elections, the results show that the exit polls' release is associated to an additional decrease in turnout of 2.8 percentage points at 17:00 and of 1.7 percentage points at end of the day.

Heterogeneous Effects

In this section, we investigate possible heterogeneous effects along two dimensions, namely geography and the preferences expressed in the first round of the elections. We first examine whether the decrease in turnout is stronger in departments that are closer to the borders with Belgium and Switzerland, the two countries with francophone media which regularly publish exit polls during the election day. The rationale is that voters in departments closer to either country might more likely be aware of the exit polls' release. Moreover, some foreign media like RTBF have a radio station whose signal is received in the French departments that are close to the border. Some voters in these departments could therefore be reached in addition to those who actively look for the information online.

Table 3 shows the results of this analysis. For either border, we distinguish between a first set of very close departments and a second larger set of close ones. These include the 4 and 7 closest departments to either Belgium or Switzerland, respectively. 7 Columns 1 and 2 in Table 3 show a significantly greater decrease in participation for the departments close and very close to Belgium, while columns 3 and 4 show that departments close and very close to Switzerland do not significantly differ from all the others. For the Belgian border, the coefficients of interest are negative for turnout measured both at 17:00 and at the end of the day, although only the one at 17:00 is statistically significant. Their magnitude varies between -1.3 and -2.1 percentage points. One possible line of interpretation for the effect being significant only at 17:00 is that the information shock spread earlier to departments who are closer to Belgium, and then more homogeneously to the whole country by the end of the day.

As a second exercise, we investigate the presence of heterogeneous effects with respect to the preferences expressed in the first round of the elections. This analysis points to the main concern of the early release of exit polls, namely that its effect on turnout could be biased in favor of one candidate and therefore alter the representation of the electorate's preferences. Table 4 reports the results. Column 1 shows that, by the end of the day, the decrease in turnout with respect to the first round was greater in departments in which Macron had won a relative majority in the first round, as compared to all other departments. With a p-value of 0.099, this effect is significant at the 10% level.

Its magnitude corresponds to an additional decrease of 1.1 percentage points in turnout. Column 2

shows instead the absence of heterogeneous effects when we compare departments in which Le Pen 7 Figure 3 in the online appendix shows these departments on a map.

had won a relative majority in the first round with all the others.8

We then look at whether the decrease in turnout was stronger in departments in which many voters did not support any of the two second-round candidates. Specifically, given the ideological positions of Macron and Le Pen, voters with left-wing preferences could be more likely to opt for abstention after the information shock, instead of voting for a candidate that was only weakly preferred. In column 3 of Table 4, we find that we cannot exclude such an effect for the turnout measure at 17:00.

Departments which in the first round had the top 50% joint vote share for Benoît Hamon and Jean-Luc

Mélenchon show a larger decrease in turnout after the information shock, compared to departments with the bottom 50% vote share for the two left-wing candidates. As before, the effect corresponds to an additional reduction in turnout of 1.1 percentage points. Though insignificant on conventional levels, with a p-value of 0.113, this effect is close to the 10% level. Finally, column 4 in Table 4 shows the absence of heterogeneous effects between departments with the top and bottom 50% vote share in favor of François Fillon, whose ideological position on the right was in between Macron and Le Pen.

Overall, with respect to the worry that exit polls might alter the representation of preferences through voter turnout, our results point, if anything, to a small underdog effect. In our data, this effect is driven by a greater -but with a weak statistical significance -decrease in turnout in departments in which Macron had won a relative majority in the first round as well as in departments in which leftwing candidates had obtained a higher vote share. We do not find, instead, any evidence suggesting that supporters of the expected loser might abstain at a larger rate.

Conclusion

On French election days, francophone foreign media in neighboring countries regularly release exit polls in order to attract online readers from France, where the publication of such information is forbidden until voting is over. Whether this early release of information has an impact on the electoral outcome is of key importance to safeguard a fair electoral process. We exploited the circumstances of the 2017 second-round presidential elections to investigate this issue. A predicted landslide victory of Emmanuel Macron against Marine Le Pen allowed the concerned media to release the exit polls earlier than usual and to present the election as de facto decided even if voting was still taking place. By comparing turnout rates at different times in the day with respect to the first round and to previous elections, we estimate a reduction of 3.1-4.1 percentage points in turnout from the exit polls' release.

Consistently with Belgian media being a major source of the information shock, the reduction in turnout affects the departments close to the Belgian border earlier, before spreading more homogeneously across the country. The decrease in participation also seems to have involved Macron's supporters and left-wing voters in the first round more than Le Pen's supporters and right-wing voters. While the magnitude and statistical significance of the effect suggests that the heterogeneity has not been severe, the possibility of altering the true representation of preferences calls for attention on such electoral interference as well as for further investigation of its empirical relevance. Note: Includes voter turnout for the 2017 French presidential elections for all French mainland departments. P-values are in parentheses, based on standard errors clustered at the department level. Baseline is the turnout at 12:00 in the first round. Closure is at either 19:00 or 20:00. Column 1, 3 and 4 are weighted by registered voter population, column 2 is unweighted. Weather trends include the maximum temperature and the amount of rainfall at the department capital in that day interacted with the time. Column 4 only includes departments where it did not rain in the first or second round. Turnout data from the French Ministry of Interior. 4)

Figure 4: Map of departments by the winning candidate in the first round (see Table 4) Source: The Guardian. Correction: in the original map, the department of Alpes-Maritimes was wrongly assigned to Le Pen

  5

Figure 1 :

 1 Figure 1: Voter turnout at different times of the day in the first and the second round of the French presidential elections.

Figure 2 :Figure 3 :

 23 Figure 2: Sketch of the information available on the RTBF network and on twitter on the second round election day, 7 May 2017

Table 1 :

 1 Voter turnout at different times of the day for the first and the second round of the 2017 French presidential elections. Includes voter turnout for the French presidential elections for all French mainland departments in 2017 and 2012 (column 1) and in 2017 and 2007 (column 2). P-values are in parentheses, based on standard errors clustered at the department level. Baseline is the turnout at 12:00 in the first round in 2012 (column 1) and 2007 (column 2). Closure is at either 19:00 or 20:00. Weighted by registered voter population. Turnout data from the French Ministry of Interior.

	Dependent variable:	Voter turnout
		Comparing 2012 Comparing 2007
		to 2017	to 2017
		(1)	(2)
	17h	42.30 * * *	42.70 * * *
		(0.000)	(0.000)
	Closure	53.07 * * *	54.29 * * *
		(0.000)	(0.000)
	2nd Round	2.362 * * *	3.066 * * *
		(0.000)	(0.000)
	17h X 2nd Round	-0.986 * * *	-1.735 * * *
		(0.006)	(0.000)
	Closure X 2nd Round	-1.781 * * *	-3.091 * * *
		(0.000)	(0.000)
	2017	0.250	-2.490 * * *
		(0.561)	(0.000)
	17h X 2017	-1.413 * * *	-1.815 * * *
		(0.003)	(0.001)
	Closure X 2017	-1.604 * * *	-2.822 * * *
		(0.000)	(0.000)
	2nd Round X 2017	-2.678 * * *	-3.382 * * *
		(0.000)	(0.000)
	17h X 2nd Round X 2017	-2.835 * * *	-2.086 * * *
		(0.000)	(0.000)
	Closure X 2nd Round X 2017	-1.659 * * *	-0.349
		(0.000)	(0.488)
	Constant (Turnout at 12h, 1st round)	28.30 * * *	31.04 * * *
		(0.000)	(0.000)
	Weighted	Yes	Yes
	Weather trends	No	No
	Observations	1152	1152
	Departments	96	96
	Note:

Table 2 :

 2 Comparing voter turnout at different times of the day for the first and the second round of the 2017 French presidential elections with previous elections. Includes voter turnout for the 2017 French presidential elections for all French mainland departments. P-values are in parentheses, based on standard errors clustered at the department level. Department very close to Belgium ("Very close to BE") include the departments Nord, Aisne, Ardennes, and Pas de Calais. Departments close to Belgium ("Close BE") include those before and Meuse, Meurthe et Moselle, and Somme. Departments very close to Switzerland ("Very close CH") include Haute Savoie, Ain, Jura, and Doubs. Departments close to Switzerland ("Close BE") include those before and Belfort, Haut Rhin, and Savoie. Baseline is the turnout at 12:00 in the first round. Closure is at either 19:00 or 20:00. Weighted by registered voter population. Turnout data from the French Ministry of Interior.

	Dependent variable:	Voter turnout in the 2017 French Presidential Elections
		(1)	(2)	(3)	(4)
	17h	40.81 * * *	40.83 * * *	41.03 * * *	41.05 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	Closure	51.65 * * *	51.68 * * *	51.60 * * *	51.66 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	2nd Round	0.519	0.503	0.647	0.689
		(0.281)	(0.297)	(0.191)	(0.167)
	17h X 2nd Round	-3.660 * * *	-3.655 * * *	-3.842 * * *	-3.863 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	Closure X 2nd Round	-3.677 * * *	-3.696 * * *	-3.690 * * *	-3.750 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	Very close BE	-1.265
		(0.397)
	17h X Very close BE	1.509
		(0.225)
	Closure X Very close BE	-1.566
		(0.431)
	2nd Round X Very close BE	2.539 *
		(0.077)
	17h X 2nd Round X Very close BE	-1.693 *
		(0.059)
	Closure X 2nd Round X Very close BE	-1.337
		(0.222)
	Close BE		-0.932
			(0.453)
	17h X Close BE		0.944
			(0.387)
	Closure X Close BE		-1.516
			(0.356)
	2nd Round X Close BE		2.691 * *
			(0.028)
	17h X 2nd Round X Close BE		-2.066 * * *
			(0.009)
	Closure X 2nd Round X Close BE		-1.471
			(0.119)
	Very close CH			1.710
				(0.136)
	17h X Very close CH			-2.816 * * *
				(0.002)
	Closure X Very close CH			-2.236 * *
				(0.011)
	2nd Round X Very close CH			0.743
				(0.589)
	17h X 2nd Round X Very close CH			2.126
				(0.142)
	Closure X 2nd Round X Very close CH			1.144
				(0.411)
	Close CH				1.781 * *
					(0.036)
	17h X Close CH				-2.215 * *
					(0.011)
	Closure X Close CH				-2.502 * * *
					(0.003)
	2nd Round X Close CH				0.00778
					(0.995)
	17h X 2nd Round X Close CH				1.439
					(0.188)
	Closure X 2nd Round X Close CH				1.659
					(0.139)
	Constant	28.61 * * *	28.60 * * *	28.45 * * *	28.41 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	Weighted	Yes	Yes	Yes	Yes
	Weather trends	Yes	Yes	Yes	Yes
	Observations	576	576	576	576
	Departments	96	96	96	96
	Note:

Table 3 :

 3 Voter turnout at different times of the day for the first and the second round of the 2017 French Presidential Elections: Heterogeneous effects with respect to geography. Includes voter turnout for the 2017 French presidential elections for all French mainland departments. P-values are in parentheses, based on standard errors clustered at the department level. "Macron first" includes the 41 departments where Macron won a relative majority in the first round. "Le Pen first" includes the 46 departments where Le Pen won a relative majority in the first round. "Left top 50%" includes departments where the combined vote share of the left candidates Hamon and Mélenchon is above the median. "Fillon top 50%" includes departments where the vote share of the right candidate Fillon is above the median. Baseline is the turnout at 12:00 in the first round. Closure is at either 19:00 or 20:00. Weighted by registered voter population. Turnout data from the French Ministry of Interior.

	Dependent variable:	Turnout in the 2017 French Presidential Elections
		(1)	(2)	(3)	(4)
	17h	40.00 * * *	41.48 * * *	40.15 * * *	41.10 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	Closure	49.50 * * *	53.12 * * *	50.72 * * *	51.09 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	2nd Round	0.389	0.725 * *	0.604	1.128 * *
		(0.601)	(0.047)	(0.362)	(0.046)
	17h X 2nd Round	-3.629 * * *	-3.793 * * *	-3.048 * * *	-4.082 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	Closure X 2nd Round	-3.189 * * *	-4.112 * * *	-3.161 * * *	-3.949 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	Macron first	-1.955 * *
		(0.010)
	17h X Macron first	1.927 * *
		(0.023)
	Closure X Macron first	4.180 * * *
		(0.000)
	2nd Round X Macron first	0.555
		(0.455)
	17h X 2nd Round X Macron first	-0.371
		(0.599)
	Closure X 2nd Round X Macron first	-1.134 *
		(0.099)
	Le Pen first		1.783 * *
			(0.018)
	17h X Le Pen first		-1.234
			(0.151)
	Closure X Le Pen first		-3.617 * * *
			(0.000)
	2nd Round X Le Pen first		-0.101
			(0.907)
	17h X 2nd Round X Le Pen first		-0.0303
			(0.967)
	Closure X 2nd Round X Le Pen first		0.849
			(0.254)
	Left Top 50%			-1.014
				(0.200)
	17h X Left Top 50%			1.355
				(0.110)
	Closure X Left Top 50%			1.384
				(0.206)
	2nd Round X Left Top 50%			-0.0664
				(0.929)
	17h X 2nd Round X Left Top 50%			-1.121
				(0.113)
	Closure X 2nd Round X Left Top 50%			-0.702
				(0.293)
	Fillon Top 50%				0.298
					(0.717)
	17h X Fillon Top 50%				-0.332
					(0.707)
	Closure X Fillon Top 50%				0.848
					(0.447)
	2nd Round X Fillon Top 50%				-0.919
					(0.198)
	17h X 2nd Round X Fillon Top 50%				0.616
					(0.391)
	Closure X 2nd Round X Fillon Top 50%				0.366
					(0.591)
	Constant	29.45 * * *	27.72 * * *	29.09 * * *	28.36 * * *
		(0.000)	(0.000)	(0.000)	(0.000)
	Weighted	Yes	Yes	Yes	Yes
	Weather trends	Yes	Yes	Yes	Yes
	Observations	576	576	576	576
	Departments	96	96	96	96
	Note:

Table 4 :

 4 Voter turnout at different times of the day for the first and the second round of the 2017 French presidential elections: Heterogeneous effects with respect to voting behavior in the first round.A Online Appendix (not intended for publication) Turnout and voting data from the French Ministry of Interior. Weather measured at the department capital.

	Variable	Mean Std. Dev. Min.	Max.
	Final voter turnout round 1	80.072	2.648	67.239 84.290
	Final voter turnout round 2	76.681	2.759	63.45 80.930
	Indicator of rain in round 1	0.01	0.102	0	1
	Maximum temperature in round 1 17.896	4.236	1	27
	Indicator of rain in round 2	0.552	0.5	0	1
	Maximum temperature in round 2 16.625	3.616	10	26
	First round vote shares:
	Emmanuel Macron	23.029	3.486	16.46	34.83
	Marine Le Pen	22.589	5.935	4.99	35.67
	Jean-Luc Mélenchon	19.18	3.12	13.78	34.02
	François Fillon	19.647	3.402	12.75	29.14
	Benoît Hamon	6.068	1.387	3.44	10.91
	Second round vote shares:
	Emmanuel Macron	63.884	8.484	47.09 89.680
	Marine Le Pen	36.131	8.496	10.32	52.91
	N		96
	Note:

Table 5 :

 5 Summary Statistics Includes voter turnout for the 2017 French presidential elections for all French mainland departments. P-values are in parentheses, based on standard errors clustered at the department level. Column 1 shows the baseline regression with the weather trends. Column 2 test for a difference in the trends between departments where iy never rained and departments where it rained in either of the two rounds. Baseline is the turnout at 12:00 in the first round. Closure is at either 19:00 or 20:00. Weighted by registered voter population. Turnout data from the French Ministry of Interior.

	Dependent variable	Voter turnout
		(1)	(2)
	17h	40.93 * * *	40.42 * * *
		(0.000)	(0.000)
	Closure	51.52 * * *	51.23 * * *
		(0.000)	(0.000)
	2nd Round	0.603	-0.232
		(0.214)	(0.666)
	17h X 2nd Round	-3.747 * * *	-3.908 * * *
		(0.000)	(0.000)
	Closure X 2nd Round	-3.618 * * *	-3.547 * * *
		(0.000)	(0.000)
	Rain	-1.183
		(0.236)
	17h X Rain	-0.537
		(0.425)
	Closure X Rain	-0.149
		(0.845)
	Max. temperture (std)	1.189 * *	0.920
		(0.016)	(0.110)
	17h X Max. temperture (std)	-1.162 * * *	-1.394 * * *
		(0.001)	(0.000)
	Closure X Max. temperture (std)	-1.308 * * *	-1.435 * * *
		(0.003)	(0.001)
	Never rained		1.324
			(0.215)
	17h X Never rained		1.235
			(0.209)
	Closure X Never rained		0.694
			(0.537)
	2nd Round X Never rained		0.242
			(0.743)
	17h X 2nd Round X Never rained		-0.459
			(0.534)
	Closure X 2nd Round X Never rained		-0.430
			(0.546)
	Constant	28.51 * * *	27.95 * * *
		(0.000)	(0.000)
	Weighted	Yes	Yes
	Observations	576	576
	Departments	96	96
	Note:

Table 6 :

 6 Voter turnout at different times of the day for the first and the second round of the 2017 French Presidential Elections: Full specification with weather trends.

As also forecasted by most opinion polls, whose average result on the day before the election was 61.79% in favor of Macron. See for example https://en.wikipedia.org/wiki/Opinion polling for

the 2017 French presidential election

These unconclusive results are echoed by the mixed findings in the experimental literature[START_REF] Levine | The paradox of voter participation? a laboratory study[END_REF][START_REF] Großer | Public opinion polls, voter turnout, and welfare: an experimental study[END_REF][START_REF] Morton | What motivates bandwagon voting behavior: altruism or a desire to win?[END_REF] as well as by theoretical work highlighting potential drivers of both effects[START_REF] Herrera | Turnout across democracies[END_REF][START_REF] Grillo | Risk aversion and bandwagon effect in the pivotal voter model[END_REF]. These contributions also clarify that the empirical observation of a null or weak total effect might be due to different effects offsetting each other rather than to the absence of any effect.

For example, in 2012 Belgian broadcaster RTBF reported at around 17:20 a predicted vote share of 52%-53% for Hollande against Sarkozy, mentioning the possibility of change. Also, note that polling stations elsewhere than in big cities closed at 18:30 in 2012 and at 18:00 in 2007, while at 19:00 in 2017.

We report the coefficients of all the weather controls in Table6in the online appendix as well as the comparison between departments where it never rained and those where it rained (which is insignificant). We note that on the day of the first round elections it rained (lightly) only in one department's capital; hence all raining variation comes from the second-round elections.

In the first round, Macron won a relative majority in 41 departments, while Le Pen won a relative majority in 46 departments. Figure4in the online appendix shows the geographical distribution of such departments.

This work has been supported by the French National Research Agency Grants ANR-17-EURE-0020 and by the Excellence Initiative of Aix-Marseille University A*MIDEX. We are grateful to Julie Lassébie who obtained the data. We thank Julie Lassébie, Julieta Peveri, and Marc Sangnier for their helpful comments. Eva Raiber is a Research Affiliate at the Centre for Economic Policy Research (CEPR, London).