F Cadini

E Zio

L R Golea

C A Petrescu

APPLICATION OF MULTI-OBJECTIVE GENETIC ALGORITHMS TO TWO CASE STUDIES OF RELIABILITY EFFICIENCY ANALYSIS AND OPTIMAL EXPANSION OF ELECTRICAL TRANSMISSION NETWORKS

Keywords: critical infrastructures, reliability efficiency, group closeness centrality measure, multi-objective genetic algorithms

Two applications of multi-objective genetic algorithms to the analysis and optimization of electrical transmission networks are reported to show the potential of these combinatorial optimization schemes in the treatment of highly interconnected, complex systems. In a first case study, an analysis of the topological structure of an electrical power transmission system of literature is carried out to identify the most important groups of elements of different sizes in the network. The importance is quantified in terms of group closeness centrality. In the second case study, an optimization method is developed for identifying strategies of expansion of an electrical transmission network by addition of new lines of connection which are optimally identified with respect to the objectives of improving the transmission reliability, while maintaining the investment cost limited.

INTRODUCTION

Society is heavily dependent on many technological, natural and even social complex systems which are hierarchies of networks of components (also called nodes, vertices or elements) interacting through links (also called edges, arcs or connections). The apparent ubiquity of networks leads to a fascinating set of problems common to biological, ecological, technological and social complex systems, regarding how the underlying network topology influences the system behavior and its robustness to faults and attacks. In this regard, the identification and quantification of their vulnerabilities, i.e. the set of flaws and weaknesses in the design, implementation, operation, and/or management of an infrastructure system or its elements that renders them susceptible to destruction or incapacitation when exposed to a hazard or threat, becomes crucial for designing the adequate protections, mitigation and emergency actions against their failures [START_REF]Proceedings of the International Workshop on Complex Network and Infrastructure Protection[END_REF][START_REF] Rocco | Multiobjective evolutionary optimisation of the protection of complex networks exposed to terrorist hazard[END_REF][START_REF]Vulnerability, Reliability and Safety of Complex Networks and Critical Infrastructures, Special Sessions I and II[END_REF].

Given the complexity of these highly distributed and interconnected infrastructures, performing a systematic analysis of their vulnerability and robustness to failure becomes difficult if one resorts only to traditional probabilistic safety assessment (PSA) methods, so that new complementary approaches of network analysis are emerging for characterizing the network resistance to failure and identifying its most vulnerable elements [START_REF] Cadini | Using centrality measures to rank the importance of the components of a complex network infrastructure[END_REF][START_REF] Freeman | Centrality in Social Networks: Conceptual Clarification[END_REF][START_REF] Hines | A centrality measure for electrical networks[END_REF][START_REF] Koonce | Bulk power risk analysis: Ranking infrastructure elements according to their risk significance[END_REF][START_REF] Newmann | The structure in function of complex networks[END_REF][START_REF] Zio | Vulnerability analysis of a power transmission system[END_REF][START_REF] Rocco | Implementation of Multiple-Objective Optimization for Vulnerability Analysis of Complex Networks[END_REF]. To this aim, indicators of both the global reliability of the network and of the centrality of its elements have been introduced [START_REF] Zio | Computational methods for reliability and risk analysis[END_REF]. In particular, the global reliability efficiency indicators measure how well connected are the nodes of the network accounting not only for the topology of the network, but also for the failure probabilities of all the connections; this indicator differs from the classical reliability definition in that it represents general properties of the system and it is not defined with respect to a specific system task.

On the other hand, various measures of importance of the network elements can be defined, which capture different structural aspects of the interconnection paths among network nodes. Recently, these measures have been extended to rank the importance of groups of elements for taking into account the potential synergies between elements whose individual centrality may not be so relevant and dealing with the risk associated to changes in network technical specifications which typically impact groups of components [START_REF] Zio | Computational methods for reliability and risk analysis[END_REF].

Another direction of improvement in the definition of network importance measures regards the representation of the actual physical behavior of the system, e.g. in terms of the electric power or hydraulic flow in the network, etc [START_REF] Rocco | A Flow Importance Measure with Application to an Italian Transmission Power System[END_REF].

In this paper, two applications of multi-objective genetic algorithms (MOGAs) are reported with regards to the analysis and optimization of electrical transmission networks. In the first case study, the electrical transmission network system of the IEEE (Institute of Electrical and Electronic Engineers) 14 BUS (a portion of the American Electric Power System) is considered [START_REF] Christie | The IEEE 14 BUS data can be found on[END_REF] and a MOGA is used to solve an optimization problem in which the decision variables identify groups of components and the objectives are to maximize the importance of the groups while minimizing their dimension. This formulation guides the MOGA search towards the identification of the most important single components, couples of components, triplets, and so forth in the topological structure of the network.

In the second case study, a MOGA is developed for identifying strategies of expansion of an electrical network in terms of new lines of connection to add for improving the reliability of its transmission service, while maintaining limited the investment cost. The typical large size of electrical networks offers a combinatorial number of potential solutions of new connections, so that classical optimization techniques become inapplicable. For this reason, we resorted to a MOGA driven by the objectives of maximizing the network global reliability efficiency [START_REF] Zio | From Complexity Science to Reliability Efficiency: A New Way of Looking at Complex Network Systems and Critical Infrastructures[END_REF] and minimizing the cost of the added connections. To realistically restrict the search space to small numbers of new connections the so-called guided multi-objective genetic algorithm (G-MOGA) has been applied. In this approach, the search is based on the guided domination principle which allows to change the shape of the dominance region specifying maximal and minimal trade-offs between the different objectives so as to efficiently guide the MOGA towards Pareto-optimal solutions within these boundaries [START_REF] Zio | Optimal power system generation scheduling by multiobjective genetic algorithms with preferences[END_REF]. The performance of this search approach is tested on a case study based on the IEEE (Institute of Electrical and Electronic Engineers) RTS (Reliability Test System) 96 [START_REF] Billinton | Reliability assessment of electric power systems using Monte Carlo methods[END_REF].

The paper is organized as follows. Section 2 presents the group closeness centrality measure which can be used to quantify the importance of groups of nodes. The concept of network global reliability efficiency is also presented. A short introduction to the basic concepts behind the optimization procedure by Multi-Objective Genetic Algorithms is given in Section 3. In Section 4 and Section 5, the case studies regarding the IEEE 14 BUS network system and IEEE RTS 96 are presented and solved by MOGA. Conclusions on the outcomes of the analysis are eventually drawn in Section 6.

TOPOLOGICAL GROUP CLOSENESS CENTRALITY AND GLOBAL

RELIABILITY EFFICIENCY

Mathematically, the topological structure of a network can be represented as a graph ) , G( K N with N nodes connected by K edges. The connections are defined in an NN  adjacency matrix   ij a whose entries are 1 if there is an edge joining node i to node j and 0 otherwise.

Depending on the specific definition, a centrality measure describes the way in which a node interacts/communicates with the rest of the network, thus providing a way of prioritization of the importance of the nodes for network communication. To evaluate the role played by a group of nodes with respect to its connectivity, the group closeness centrality [START_REF] Everett | The centrality of groups and classes[END_REF], C C (g), is considered; this measure is based on the idea that a node can quickly interact with all other nodes if it is easily accessible by (close to) all others. If ij d is the topological shortest path length between nodes i and j (i.e., the minimum number of arcs on a path connecting them), the closeness of a group g of g N

nodes is the inverse of the node's mean distance from the members of the group to all vertices outside the group:

g g C , C (g) ij i N j N NN d     (1)
This measure is normalized by dividing the distance score into the number of non-group members, with the result that larger numbers indicate greater centrality.

When the group consists of a single node, the group closeness centrality is the same as the individual node closeness centrality [START_REF] Hines | A centrality measure for electrical networks[END_REF], [START_REF] Sabidussi | The Centrality Index of a Graph[END_REF][START_REF] Wasserman | Social Networks Analysis[END_REF].

To capture the failure behavior of the network, the reliability of its connecting edges is included in the framework of analysis by means of the formalism of weighted networks, the weight ij w associated to the edge between the pair of nodes i and j being its reliability:

ij T ij pe    (2)
where ij  is the failure rate of edge ij linking nodes i and j and T is a reference time ( 1 T  year, in this work).

On the basis of the adjacency and reliability matrices   ij a and   ij p (or the complementary failure probability matrix   ij q ), the matrix of the most reliable path lengths   ij rd can be computed [START_REF] Zio | From Complexity Science to Reliability Efficiency: A New Way of Looking at Complex Network Systems and Critical Infrastructures[END_REF]:

  11 min min 1 ij ij ij ij ij mn mn mn mn rd pq                           (3)
where the minimization is done with respect to all paths ij  linking nodes i and j and the product extends to all the edges of each of these paths. Note that 1 ij rd    , the lower value corresponding to the existence of a perfectly reliable path connecting i and j (i.e. 1, 0 mn mn p q mn ij     ) and the upper value corresponding to the situation of no paths connecting i and j (i.e. 0, 1 mn mn pq  ).

The group reliability closeness centrality can then be computed as in equation 1, with ij rd replacing

. ij d
The global reliability efficiency RE[G] of the graph G can also be defined as [14]:

    , G, 1 RE[G] 1/ 1 ij i j i j rd NN     (4)
In practical terms, the global reliability efficiency indicates how well connected are the nodes of the network taking into account their connection failure probability. For example, the design of a network with very few but highly reliable connections between the nodes is preferable with respect to a densely connected design with connections characterized by large failure rates.

MULTI-OBJECTIVE GENETIC ALGORITHMS

Genetic Algorithms (GAs) are optimization methods aiming at finding the global optimum of a set of real objective functions,

 

F f( ) ,  of one or more decision variables,

 

Uu  , possibly subject to various linear or non linear constraints. The terminology adopted in GAs contains many terms borrowed from biology, suitably redefined to fit the algorithmic context. Thus, GAs operate on a set of (artificial) chromosomes, which are strings of numbers, generally sequences of binary digits Typically, several possibly conflicting objective functions f ( ), i  i = 1, 2,…, n f , must be evaluated in correspondence of each decision variable vector U in the search space. In this case, the GA search proceeds by comparing the solutions in terms of the concepts of Pareto optimality and dominance [START_REF] Goldberg | Genetic algorithms in search, optimization, and machine learning[END_REF]: with reference to a maximization problem proposed, a solution

a U is said to dominate b U if   1, 2,..., ,f ( ) f ( ) f i a i b i n U U    and (5)
  1, 2,..., ,f ( ) f ( ). f j a j b j n U U   
In all other cases of decision variable vectors which are not dominated by any other of a given set, including when to make tradeoffs within this set, rather than taking into account the full range of every decision variable.

  1, 2,..., ,f ( ) f ( ) f l a l b l n U U    ,

CASE STUDY 1 4.1 IEEE 1BUS electrical transmission network

The topological structure of the electrical transmission network system of the IEEE 14 BUS is considered for the analysis of the importance of groups of components, measured in terms of reliability closeness centrality. The system considered represents a portion of the American Electric

Power System and consists of 14 bus locations connected by 20 lines and transformers. The topology of the system can be represented by the graph G(14,20) of Figure 1.

Identification of most central groups of nodes by MOGA

Let the generic centrality measure of a group of nodes be indicated as:

12 C( , , , )

N x x x  (6)
with x i = 1 if i belongs to the group, x i = 0 otherwise. For example, in a network with 3 N  components, C(1,0,0) indicates the centrality of the first node alone; C(0,0,1) indicates the centrality of the third node alone; C(1,0,1) indicates the centrality of the pair made of the first and third nodes.

In a network with

N nodes, the number of groups (single nodes, pairs, triplets, and so forth) that in principle can be formed is 2 N . A complete centrality analysis of all groups to find the most central is therefore impractical for large networks.

To overcome this obstacle, the task of determining the most central groups of components can be framed as an optimization problem with respect to the two following objectives:

1 1 2 Max f ( ) C( , , , ) N x x x  x x (7) 2 1
Min f ( ) [START_REF] Newmann | The structure in function of complex networks[END_REF] with x i = 1 if i belongs to the group, x i = 0 otherwise. The need for introducing the second objective is due to the fact that inevitably the more nodes in a group, the higher its centrality and impact on the network; hence, a search directed only by the centrality of the groups (objective f 1 (x)), with no control on their sizes (objective f 2 (x)) would favor large groups, whose simultaneous failure or attack is however not likely. By introducing the second objective, which favors small groups, the search is guided to finding the most central groups preferably of small size, i.e., the single nodes, pairs, triplets and so forth.

N i i x    x x
A Genetic Algorithm (GA) can be devised to address the above optimization task. In the most typical applications of GAs, every proposal of solution, represented by the vector x of the independent decision variables (control parameters), is coded in a so-called chromosome, constituted by so-called genes, each one coding one decision variable of x; a binary coding is widely used. Differently from these typical applications, the decision variables (x 1 , x 2 ,…, x N ) of the optimization problem considered in this paper are already in the form of a binary string. Therefore, single-gene chromosomes are used, directly coding the composition of the group. The dimension of the chromosome is equal to the number of nodes in the network. Table 1 shows two examples of chromosome coding for a system of 14 nodes.

0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0
Corresponding nodes in the group 4,6,9

1,6,8,9,13

There are two kinds of operations performed in the genetic algorithms search for optimal solutions: i) genetic operations, that mimic the process of heredity of genes to create new offsprings (i.e., new solutions) at each generation and ii) evolution operations, which mimic the process of Darwinian evolution to create populations from generation to generation. The two basic types of genetic operators, i.e., crossover and mutation, provide the basic search mechanism of the GA and depend on the chromosome representation used. Crossover takes two individuals (i.e., two solutions) and produces two new individuals while mutation alters one individual to produce a single new solution.

To use a GA for Multiobjective Optimization (MO) entails comparing two solutions with respect to the multiple objectives considered [START_REF] Carlos | A multiobjective genetic algorithm for RAMS + C optimization with uncertain variables[END_REF], [START_REF] Toshinsky | A method to improve multiobjective genetic algorithm optimization of a self-fuel-providing LMFBR by niche induction among nondominated solutions[END_REF]. In the case of a single-objective, the comparison is trivial: a vector solution x is better than another one, say y , if the corresponding objective function (fitness) value f(x) is greater than f(y). A multiobjective optimization problem, instead, deals with n f objective functions f i (•), i = 1, 2,…, n f ; this requires that two solutions x and y are compared in terms of dominance of one solution over the other with respect to all n f objectives [START_REF] Sawaragi | Theory of multiobjective optimization[END_REF]. The multiobjective optimality search process, converges on a Pareto-optimal set of nondominated solutions, which provides a spectrum of possible choices for the decision-maker to a posteriori identify his or her preferred solution.

Table 2 summarizes the details of the implementation of the MOGA operators described in Section 3 along with a number of parameters that control the operation of the genetic algorithm such as the population size (i.e., the size of the evolving set of candidate solutions) and the number of generations (i.e., the duration of the evolution process). The optimization runs were performed starting from an initial random population. 2 shows the results obtained on the importance of the group in terms of reliability closeness centrality. In the Figure, the values of the objective functions in correspondence of all the nondominated groups of nodes contained in the MOGA archive at convergence are shown to identify the two-dimensional Pareto-optimal surface (circles). The results are compared for validation with those obtained by exhaustive computation of all groups of nodes, i.e., the computation of the group reliability closeness centrality measure for all the possible combinations of n out of N nodes; due to the fact that the number of groups obtained is 2 N , its implementation is feasible here thanks to the small size of the network but would require impractical computational resources for large networks. Actually, different groups of equal size can have the same centrality measure value: Table 3 reports all the nondominated solutions contained in the archive, identified by the MOGA. For the groups composed of one, three and five nodes, there is only one combination that maximizes the reliability closeness centrality measure; on the other hand, there is more than one solution for the groups with sizes two, four and six to ten; this allows choosing the solution most suitable for a given purpose, e.g. system upgrade by components renewal, replacement, or redundancy allocation in order to use effectively the budget available.

In the present case, the smallest group with maximal reliability closeness is of size 10 and there are 2 of these. The group {1, 2, 3, 5, 7, 10, 11, 12, 13, 14} is particularly interesting because it does not contain the highly central node {4} and contains the node {1} that have the smallest individual reliability closeness centrality measure, as it can be seen in Table 4. To gain an engineering feeling of the impact on the network transmission performance resulting from the failure of the nodes of a group of a given reliability closeness centrality value, the relative global reliability efficiency variation of the network is reported in Figure 3. The relative variation of the global reliability efficiency due to the removal of a group of nodes is computed as the difference between the values of the global reliability efficiency (Equation 4) of the network with all the nodes of the group (and all the incident arcs) removed and of the original network with no nodes removed, normalized to the latter. The results show that there is a strong relation between the size of the groups removed and the efficiency of the network and that the most reliability-close central groups (i.e., those in the Pareto front) are indeed the most important also from the point of view of the negative impact on the network global reliability efficiency, when they fail.

CASE STUDY 2 5.1 IEEE RTS 96 electrical transmission network

The transmission network system IEEE RTS 96 (Figure 4) [START_REF] Billinton | Reliability assessment of electric power systems using Monte Carlo methods[END_REF]

Optimal network expansion by MOGA

A MOGA has been constructed for identifying the best improvements in the connection of the network, aimed at increasing its global reliability efficiency in transmission at acceptable costs. The improvements are obtained by addition of new lines between nodes with no direct connection in the original network. Given the lack of geographical information on the nodes locations, for simplicity and with no loss of generality, three typologies of lines have been arbitrarily chosen as the minimum, the mean and the maximum values of the failure rates of the transmission lines taken from [START_REF] Billinton | Reliability assessment of electric power systems using Monte Carlo methods[END_REF]: In practical applications only a limited number of lines can be added, due to the large investment costs and other physical constraints. To drive the genetic search towards low cost solutions (i.e., low number of added lines) maximal and minimal trade-offs to the two objectives of the optimization (network global reliability efficiency and cost) can be defined within a Guided Multi-Objective Genetic Algorithm (G-MOGA) scheme, [START_REF] Zio | Optimal power system generation scheduling by multiobjective genetic algorithms with preferences[END_REF]. The preferential optimization has been performed by using G-MOGA, with the same population size, evolution procedures and parameters of the previous search. In this approach, the search is guided by defining the maximal and minimal trade-offs that allow to identify a precise section of the Pareto front. The values of the trade-off parameters have been set by trial-and-error to 12 331.3157 a  and 21 0 a  ; the search converges to a small number of solutions in a Pareto front which is more concentrated on low cost networks, characterized by a limited number of added connections (asterisks in Figure 6).

CONCLUSIONS

This paper has illustrated the use of MOGA in the analysis of complex, interconnected network systems.

First, the electrical transmission network system of the IEEE 14 BUS has been analyzed by MOGA to identify the importance of groups of components, measured in terms of their centrality in the structure of interconnection paths. The results obtained using the group reliability closeness centrality measure as importance indicator have shown that the groups classified as most central indeed contain the nodes of individual highest centrality but may also include nodes with a relatively low centrality. The groups most important from the point of view of group reliability closeness have been shown to be also the most vulnerable to direct attacks, by a crude procedure of removal of nodes and arcs one at a time.

Then, a MOGA for improving the electrical transmission network IEEE RTS 96 has been implemented with the objective of identifying the lines to be added for maximizing the network transmission reliability efficiency, while maintaining the investment costs limited. A preferential procedure of optimization has been performed by using G-MOGA for individuating realistic network expansion solutions made of few new transmission lines.

The original contributions of the paper lie in i) the innovative bit coding strategies within a MOGA approach; ii) the definition of the appropriate objective functions for efficiently handling the combinatorial optimization; iii) the adoption of the guided search, to realistically steer the optimization towards practically implementable solutions of network improvement; iv) the engineering analysis and implementation of the results of the otherwise "blind" MOGA automatic optimization. The case studies have been chosen purposely for the simplicity of the structure of the networks, which has allowed the verification of the proposed approach, which demonstrates the coherence of the MOGA searches with respect to the physical behavior of the two networks.

From the point of view of the physical analysis of the electrical transmission system which the networks represent, some limitations affect the results obtained. These limitations are all related to the fact that the analysis performed focuses only on the topological features of the network, thus neglecting its physical characteristics; this is not realistic for electrical transmission networks.

Work is currently undergoing in establishing effective ways of bringing these physical characteristics into the topological analysis.

Acknowledgments:

(bits) 0 and 1 ,

 1 coding the values of the decision variables. The values of the objective functions in correspondence of the values of the decision variables of a chromosome, give the fitness of that chromosome. The GA search is performed by constructing a sequence of populations of chromosomes, the individuals of each population being the children of those of the previous population and the parents of those of the successive population. The initial population is generated by randomly sampling the bits of all the strings; at each step in the search sequence, the new population is obtained by probabilistically manipulating the strings of the old population with fitness-improving rules which mimic genetic evolution. The search sequence continues until a preestablished optimality termination criterion is reached.

U

  are nondominated with respect to this set within the entire search space, are said to be Pareto efficient and constitute the so called Pareto optimal front or Pareto set, which is the object of the optimization. From an engineering point of view, restricting the attention to the set of choices that are Pareto efficient allows a designer

Figure 1 .

 1 Figure 1. Graph representation of the IEEE 14 BUS transmission network

Figure 2 .

 2 Figure 2. Results of the multi-objective search of the most central groups of nodes in terms of reliability

Figure 3 .

 3 Figure 3. Relative variation of the global reliability efficiency as a function of group closeness centrality

Figure 4 ,

 4 Figure 4, with 230/138 kV tie stations at Buses 11, 12 and 24.

Figure 4 .Figure 5

 45 Figure 4. IEEE RTS 96 transmission network

Figure 5 .

 5 Figure 5. The IEEE RTS 96 graph representation



  The addition of a new line requires an investment cost assumed inversely proportional to the failure rate. The network cost can be then defined as:The reliability cost of the original IEEE RTS 96 is   C G 332.0120  in arbitrary monetary units and the reliability efficiency is  RE G 0.2992 , which is a relatively high value representative of a globally reliable network.The network global reliability efficiency and cost are adopted as objective functions in the MOGA optimization of the network improved structure.From the algorithmic point of view, a proposal of improvement amounts to changing from 0 to 1 the values of the elements in the adjacency matrix corresponding to the added connections. The only physical restriction for adding direct new connections is that the connected nodes must be at the same voltage level (138 or 230 kV), otherwise the addition of a transformer would also be needed. From the genetic algorithm point of view, the generation of proposals of network improvements can be achieved by manipulating a population of chromosomes, each one with a number of bits equal to 214 which is double the number of zeros (i.e., the number of missing direct connections ij) in the upper triangular half of the symmetric adjacency matrix {a ij }. The bits are dedicated to each missing direct connection ij so as to code the three different available types of lines with failure rates λ 1 , λ 2 and λ 3 : in other words, the bit-string (00) is used to code the absence of connection, (01) connection line with a λ 1 -type line,[START_REF] Rocco | Implementation of Multiple-Objective Optimization for Vulnerability Analysis of Complex Networks[END_REF] connection with a λ 2 -type line and (11) connection with a λ 3 -type line. The initial population of 200 individuals is created by uniformly sampling the binary bit values. During the genetic search, each time a new chromosome is created, the corresponding matrices {a ij } and {p ij } are constructed to compute the values of the two objective functions, network global reliability efficiency and cost of the associated improved network.

Figure 6

 6 Figure 6 shows the Pareto dominance front (squares) obtained by the MOGA at convergence after 10 3 generations; the circle represents the original network with RE[G] 0.2992  and

Figure 6 .

 6 Figure 6. Pareto front reached by the MOGA

Table 1 .

 1 Examples of chromosomes coding groups of nodes in a network of 14 nodes

Chromosome coding (14 bits)

	1	2	3	4	5	6	7	8	9	10 11 12 13 14

Table 2 .

 2 MOGA parameters and rules

	Number of chromosomes 200
	Number of generations	200
	Selection	Fit-Fit
	Replacement	Children-parents
	Mutation probability	0.001
	Crossover probability	1
	Number of generations	15
	without elitist selection
	Fraction of parents chosen	0.25
	with elitist selection

Table 3 .

 3 Pareto optimal results of the multi-objective search for reliability closeness centrality groups

	Group	Group	Components
	reliability	Size
	closeness
	centrality
	0.303	1	4
	0.47	2	(4, 6), (6, 9)
	0.562	3	(2, 6, 9)
	0.602	4	(1, 2, 6, 9), (1, 3, 6, 9), (2, 3, 6, 9)
	0.659	5	(1, 2, 3, 6, 9)
	0.688	6	(1, 2, 3, 6, 7, 9), (1, 2, 3, 6, 8, 9)
	0.761	7	(1, 2, 3, 5, 7, 10, 13), (1, 2, 3, 5, 7, 11, 13), (1, 2, 3, 6,
			7, 10, 13), (1, 2, 3, 6, 7, 10, 14), (1, 2, 3, 6, 7, 11, 13),
			(1, 2, 3, 6, 7, 11, 14)
	0.802	8	(1, 2, 3, 5, 7, 10, 11, 13), (1, 2, 3, 5, 7, 10, 12, 13), (1,
			2, 3, 5, 7, 11, 12, 14), (1, 2, 3, 6, 7, 10, 11, 13), (1, 2, 3,
			6, 7, 10, 12, 13), (1, 2, 3, 6, 7, 11, 12, 14) …
	0.868	9	(1, 2, 3, 5, 7, 10, 11, 12, 13), (1, 2, 3, 5, 7, 10, 11, 13,
			14), (1, 2, 3, 6, 7, 11, 12, 13, 14) …
	0.99	10	(1, 2, 3, 5, 7, 10, 11, 12, 13,

Table 4 .

 4 Individual reliability closeness centrality

	Node	Reliability closeness
		centrality
	4	0.3031
	9	0.2998
	5	0.2835
	7	0.2742
	6	0.2716
	14	0.253
	10	0.2448
	13	0.2448
	11	0.2371
	2	0.2272
	8	0.2184
	12	0.2081
	3	0.1793
	1	0.1723

Table 5

 5

lists the five solutions of lowest cost identified by the G-MOGA search: the added connections improve the network global reliability efficiency and they do so with relatively small costs.

Table 5 .

 5 The five solutions on the Pareto front obtained by the G-MOGA

	G-MOGA
	Reliability Efficiency	Cost
	0.3072	337.6
	0.3168	339.4
	0.3186	339.4
	0.3187	339.4
	0.3193	339.4

This work has been funded by the Foundation pour une Culture de Securite Industrielle of Toulouse, France, under the research contract AO2006-01.


Cécile Barnaud

Annemarie Van Paassen

Guy Trébuil

Tanya Promburom

François Bousquet

Dealing with power games in a companion modelling process: lessons from community water management in Thailand highlands

Keywords: Participatory approach, social inequities, power relations, cultural differences, critical system perspective, creative learning, negotiation, companion modelling, water management, northern Thailand

Although stakeholder participation is expected to promote equitable and sustainable natural resource management, lessons from the past tell us that more careful attention needs to be paid to achieving equitable impacts. Now the question is how to address social inequities and power asymmetries. Some authors emphasize the need for more dialogue, while others prefer a critical perspective, arguing that dialogue might not be sufficient to avert the risk of a process deepening existing social inequities. This article aims to enrich this debate and question the practical implications of the critical perspective through an in-depth analysis of power games in a participatory process.

A Companion Modelling (ComMod) process was conducted in an Akha community of Northern Thailand with a critical perspective, i.e. with a concern for the less influent stakeholders. Simulation tools such as role-playing games were used to mediate a crosscultural learning process among researchers, farmers and administrators about a local irrigation water management problem.

The detailed analysis of power games in this learning and negotiation process reveals that in spite of initial power asymmetries, the poorest farmers of the community started to voice and assert their interests.

Introduction

As in other Southeast Asian countries, Thailand's recent policy-making framework regarding natural resource management favours decentralization and public participation [START_REF] Arghiros | Democracy, Development and Decentralization in Provincial Thailand[END_REF]. This is an important opportunity for ethnic minorities living in the highlands of northern Thailand who have been accused for many years by the Thai majority of degrading the upper watersheds of the country's major basins and had so far limited voice in decisionmaking processes affecting them (Mac Kinnon and Vienne, 1989).

However, stakeholder participation is challenging. Socio-ecosystems are complex and uncertain, with numerous interacting ecological and socio-economic dynamics, and an increasing number of stakeholders with different legitimate perspectives. There is a need for innovative methodologies and tools to enable stakeholders to manage such complex systems.

The companion modelling (ComMod) approach accepts the challenge and proposes to coconstruct simulation tools integrating the different stakeholders' perspectives and to use them to enhance dialogue, collective learning and the exploration of possible scenarios in these complex socio-ecosystems [START_REF] Barreteau | Our companion modelling approach[END_REF][START_REF] Bousquet | An environmental modelling approach. The use of multi-agents simulations[END_REF].

But ComMod, like many other participatory approaches, is confronted with the issue of power inequalities. How to deal with local power differences? More and more authors argue that participatory interventions with little attention for the socio-political context tend to hurt the interests of less powerful stakeholders [START_REF] Nelson | Participation and power[END_REF][START_REF] Wollenberg | Pluralism and the less powerful: accommodating multiple interests in local forest management[END_REF].

Two main postures can be distinguished: those who believe in 'dialogue' and those who promote a 'critical perspective' [START_REF] Faysse | Troubles on the way: an analysis of the challenges faced by multistakeholder platforms[END_REF]. Proponents of dialogue consider the lack of genuine communication as the main obstacle to fruitful collaboration and coordination.

According to them, once this barrier is removed, it is possible to build a common vision through social learning and to achieve a consensus for collective action [START_REF] Pretty | Participatory learning for sustainable agriculture[END_REF][START_REF] Röling | A new practise: facilitating sustainable agriculture[END_REF]. But the promoters of the critical perspective argue that power relations need to be examined prior to the participatory process; otherwise, there is a high risk of the process deepening existing social inequities. These authors consider participation as a negotiation process rather than a social learning process [START_REF] Edmunds | A Strategic Approach to Multistakeholder Negociations[END_REF][START_REF] Leeuwis | Reconceptualizing Participation for Sustainable Rural Development: Towards a Negotiation Approach[END_REF]. However, the "dialogue" and "critical" perspectives are not necessarily antagonist. Social learning is indeed the basis for creative and integrative negotiation processes [START_REF] Leeuwis | Communication for rural innovation. Rethinking agricultural extension[END_REF].

This article aims to enrich the debate about the way to deal with power inequities in participatory processes through an in-depth analysis of power dynamics in a ComMod experiment that adopted a critical posture. This ComMod experiment aimed to facilitate learning and negotiation about an irrigation water sharing problem in an Akha community in the highlands of northern Thailand. Given the importance of cultural differences among the participants in this cultural context, this paper emphasizes the role of cultural differences in power games in mediated cross-cultural learning processes. This article starts with a presentation of the fundamental principles of the ComMod approach, our conceptual framework based on critical systems thinking and the ComMod methodology implemented at this site. A second section describes the initial socio-political and cultural context and analyses the expression and evolution of power games in the facilitated learning and negotiation process. The article ends with a discussion on the potential, limits and perspectives for the improvement of the ComMod approach to level the playing field and give voice to the perspective of the marginalized. Following [START_REF] Webler | The Craft and Theory of Public Participation[END_REF] advice, we not only focus on what works, but also analyse why it works and how it could work better.

Conceptual framework and research methodology

Fundamental principles of the ComMod approach

ComMod is a participatory action research approach developed since the mid 1990's by a group 5 a researchers that use simulation tools to deal with complex systems in the field of management of renewable resources and the environment [START_REF] Barreteau | Our companion modelling approach[END_REF][START_REF] Bousquet | An environmental modelling approach. The use of multi-agents simulations[END_REF]. ComMod researchers focus on the complexity and uncertainty of their research objects, and on the existence of multiple, legitimate perspectives, including those produced by scientific expertise. ComMod aims to integrate these different perspectives in an iterative process of understanding, confrontation and analysis. It can have two possible aims: to learn about systems or to support concerted processes in these systems. The ComMod approach applies a cyclical approach, alternating modelling and field activities, with systematic feedback to local stakeholders and discussion of assumptions backing the modelling work. This approach is fundamentally adaptive in order to take into account the local stakeholders' preoccupations, perspectives and interests. In the past decade, it has been applied in many places globally (see for example [START_REF] D'aquino | Using Self-Designed Role-Playing Games and a Multi-Agent System to Empower a Local Decision-Making Process for Land Use Management: The SelfCormas Experiment in Senegal[END_REF][START_REF] Etienne | Sylvopast : a multiple target role playing game to assess negotiation processes in sylvopastoral management planning[END_REF] and at a dozen sites in Southeast Asia (Bousquet et al., 2005). Because ComMod researchers differ slightly in their theoretical perspective and consequently in the research methodology they embrace, the ones we adopted in this study are presented below.

The ComMod action research presented in this paper was conducted by the first, third and fifth authors of this paper (some ComMod researchers) in the context of the PhD thesis of the first author (the main facilitator of the ComMod process). The fourth author facilitated the gaming sessions in Thai language. The second author joined the team afterwards to conduct an external evaluation of this ComMod process, in addition to the evaluation conducted by the first author along the process. Therefore, in this paper, "we" means both the people who conducted this process and the people who analyzed it.

Theoretical framework: a critical systems approach

Systems thinking has enabled various disciplines to attain a more holistic, interdisciplinary perspective on reality. Nowadays, three major strands of systems thinking can be identified: hard, soft and critical [START_REF] Flood | Enhancing the process of methodology choice in Total Systems Intervention (TSI) and improving chances of tackling coercion[END_REF]. Soft systems thinking was developed in reaction to the technology oriented hard systems thinking which assumes that, to remain 5 Approximately 40 researchers belonging to diverse organizations from diverse countries and with diverse disciplinary background objective, researchers should stay outside the system they are studying. Based on a constructionist epistemology, soft systems thinking focuses on the various interpretations of a given situation by stakeholders and emphasizes the need for collective learning among them [START_REF] Checkland | Systems thinking, systems practice[END_REF]. So far, ComMod researchers have opted for a soft systems approach. In this experiment and in this paper, we opt for a critical systems perspective. Also based on a constructionist epistemology, critical systems thinking emerged in reaction to the failure of soft and hard systems thinking to deal with coercive situations and to address power imbalances among stakeholders [START_REF] Ulrich | Beyond methodology choice: critical systems thinking as critically systemic discourse[END_REF]. Core commitments in critical systems thinking include [START_REF] Jackson | Systems approaches to management[END_REF]:

-Critical awareness: a never-ending attempt to uncover hidden assumptions, -Social awareness and human emancipation: to prevent coercion and exercise of power from distorting communication to promote a more equitable distribution of power, -Complementarity: the acknowledgement that various systems approaches tend to provide different rationalities which complement each other.

Whereas the principle of critical awareness is already explicit in the current ComMod charter, social awareness and human emancipation are not. The objective of this contribution is to analyse the importance of power relations in a ComMod process and to reflect on the pertinence for ComMod researchers to use the critical systems approach.

To analyse the socio-ecological system and changes triggered by the ComMod intervention, we used the theoretical framework described on the Figure 1. The agrarian system theory [START_REF] Mazoyer | Histoire des agricultures du monde: du néolithique à la crise contemporaine (A history of world agriculture: from the neolithic age to the current crisis[END_REF] allowed us to apprehend the historical evolution of socioeconomic differentiation of the resource users and the emergence of different types of farming households, each characterized by specific socio-economic and agro-ecological constraints, interests and strategies [START_REF] Trébuil | Regional Agrarian Systems and Sustainability of Agricultural Production Systems in Thailand[END_REF]. In particular, it provides insight in the differential economic power resources among various farmer types and their respective interests in the negotiation process.

Power theories enabled us to better understand stakeholder relations and interactions. We considered power as a relational concept. People may have power resources, but it is in the interaction that they exert power. [START_REF] Weber | Economy and Society: An Outline of Interpretive Sociology[END_REF] defined power as the chance that an individual in a social relationship can achieve his or her own will even against the resistance of others. This is a 'power over' form of power [START_REF] Vermeulen | Power Tools: Handbook to tools and resources for policy influence in natural resource management[END_REF]. [START_REF] Rowlands | Empowerment examined[END_REF] describes it as 'zero-sum': the more power one person has, the less the other has. Classical dichotomies derived from this definition of power, seeing the powerful on one side and the powerless on the other, are problematic because they do not take into account 'the power of the powerless', and therefore deny the possibility of becoming empowered, as to empower means reinforcing an existing power. However, power is not a simple resource that people have or don't have. There are actually different kinds of resources used to exert different kinds of power forms as well as various possible relational mechanisms in power relationships. Resources to exert power can be categorized into three main types: (a) knowledge, (b) cultural norms and values attributing traditional, legal or charismatic authority to certain roles, and (c) physical resources such as money, natural resources or human resources and skills [START_REF] Giddens | The Constitution of Society: Outline of the Theory of Structuration[END_REF][START_REF] Van Paassen | Bridging the gap: computer model enhanced learning about natural resource management in Burkina Faso[END_REF]. Cultural differences such as the belonging to different ethnic groups fall into the second category, but they also have repercussions in the first and third ones. [START_REF] Boulding | Three Faces of Power[END_REF] characterized power relations according to three mechanisms: the stick, the carrot and the hug. The stick and carrot are familiar metaphors, stick standing for force, and carrot for enticement. Both are coercive forms of power, i.e. 'power over' forms of power. The most innovative concept in Boulding's work is the hug because it provides a variable to look at the empowerment of the disadvantaged and marginalized. The hug is a way to describe integrative or cooperative forms of power, i.e. the power of people joining together and obeying the same principles. This corresponds to 'power to' and 'power from within' forms of power [START_REF] Vermeulen | Power Tools: Handbook to tools and resources for policy influence in natural resource management[END_REF].

Counter power (the power to oppose the oppressors) can be seen as a form of cooperative power of the less powerful stakeholders.

Since our analysis of power relations took place in a context of decentralization, we distinguished two kinds of social interactions: the horizontal interactions among people within a community, and the vertical interactions between villagers and higher level institutions, with the key role of local leaders and representatives at the intersection of these two dimensions.

Following [START_REF] Ribot | Integral local development: accommodating multiple interests through entrustment and accountable representation[END_REF], we highlight the importance of their representation and downward accountability to achieve democratic decentralization.

Apart from a contextual analysis, we also studied the expressions of power relations during the ComMod process. In multi-stakeholder processes, there are several possible expressions of power [START_REF] Faysse | Troubles on the way: an analysis of the challenges faced by multistakeholder platforms[END_REF][START_REF] Leeuwis | Reconceptualizing Participation for Sustainable Rural Development: Towards a Negotiation Approach[END_REF], such as the power:

-To include certain people or not in the process; -To stay away from the process; -To make people aware of a certain issue, making it an issue-at-stake they want to discuss and change; -To impose one's ideas during the discussion by dominating and/or ignoring other people's opinions; -To control the implementation of decisions at a certain administrative level.

Powerful stakeholders often refrain from negotiating if they have a good BATNA (Best Alternative To a Negotiated Agreement, [START_REF] Fisher | Getting To Yes: Negotiating Agreement Without Giving In[END_REF]. In some cases, they only engage in negotiations once the other parties have increased their power base, or when they are forced to do so by powerful actors at a higher hierarchical level.

When negotiations start, the less powerful stakeholders need the capacity to defend their interests. Effective advocacy requires self-confidence, freedom to express oneself, access to information and a thorough understanding of the issue at stake. To attain this capacity, marginalized actors might need to be empowered. [START_REF] Rowlands | Empowerment examined[END_REF] identified three dimensions of empowerment corresponding to three different forms of power:

-Personal empowerment: development of self-confidence and personal capacities corresponding to what [START_REF] Vermeulen | Power Tools: Handbook to tools and resources for policy influence in natural resource management[END_REF] called 'power to', -Relational empowerment: development of skills to influence relationships corresponding to the so-called 'power over' , and -Collective empowerment: learning to work together to achieve more (a 'power from within'). [START_REF] Leeuwis | Reconceptualizing Participation for Sustainable Rural Development: Towards a Negotiation Approach[END_REF] proposed using negotiation theory as a theoretical assumption behind participatory processes to better handle power imbalances and social conflicts. Scholars in the field of negotiation commonly distinguish between compromise and integration [START_REF] Follett | Constructive Conflict[END_REF], cited by Carnevale, 2006). This corresponds to some other authors' distinction between distributive and integrative negotiation [START_REF] Rubin | Models of conflict management[END_REF][START_REF] Van Woerkum | Communicatie en innovatie : een inleiding[END_REF][START_REF] Leeuwis | Communication for rural innovation. Rethinking agricultural extension[END_REF]). In a distributive negotiation, stakeholders tend to stick to their own positions, and finally each side gives up something, meeting midway between opening positions. They simply 'share the cake' in a zero-sum outcome. In contrast, in an integrative negotiation process, the stakeholders creatively reframe the problem to 'enlarge the cake' and identify 'win-win' solutions. This implies a collective learning process in which both sides look beyond their initial positioning to examine the underlying interests determining them. [START_REF] Leeuwis | Communication for rural innovation. Rethinking agricultural extension[END_REF] described a set of tasks necessary to achieve such integrative negotiation: learning about the current situation, increased awareness of a problem to be solved collectively, learning about other stakeholders' perceptions, collective re-phrasing of the nature of the problem, coordination of interests through identification and negotiation of new scenarios to solve the re-phrased problem.

To end with, we referred to Ulrich's critical system perspective to analyse our own way to facilitate the multi-stakeholders process. This author suggests in particular that facilitators of multi-stakeholder processes should be aware of their own biases regarding social inequities and power asymmetries among stakeholders [START_REF] Ulrich | Beyond methodology choice: critical systems thinking as critically systemic discourse[END_REF]. [START_REF] Jackson | Systems approaches to management[END_REF] adds critical system scientists take some distance to study power dynamics first, and then strategically choose for a facilitation method best fit to create awareness and empowerment of the marginalised. In the ComMod cycle described in this paper, the main facilitator was aware of her cultural-ideological stance favouring an equitable process. She structured the RGG and ABM in such a way that the position of the marginalized farmers became visible so they had a chance to voice and assert their interests.

The ComMod action research methodology as applied in the 3 rd ComMod cycle in Mae Salaep, northern Thailand

A cyclical ComMod process was conducted between 2002 and 2007 in the Akha village of Mae Salaep, Chiang Rai Province, upper northern Thailand. In this experiment, the main successive phases of a ComMod cycle were as follows: (i) characterization of the problem, (ii) converting this knowledge into a simulator, and (iii) participatory simulations to question the model assumptions and explore scenarios. We used two different simulation tools: roleplaying games (RPG) and agent-based models (ABM). RPG allows multiple stakeholders to interactively examine the complex systems of which they are part and to experientially test alternative scenarios and solutions to solve the issues-at-stake [START_REF] Duke | Gaming: The Future's Language[END_REF]. But RPGs become costly and time consuming if stakeholders wish to try a spectrum of solutions or need to explore long-term effects of their decisions. To remove this constraint, it is possible to build an associated computerized ABM, similar to the RPG, which is more time-efficient in simulating scenarios. The RPG is then a way to 'open the black box of the model' as it allows the players to understand what the ABM is doing, to validate and criticize it [START_REF] Barreteau | Role-playing games for opening the black box of multi-agent systems: method and lessons of its application to Senegal River valley irrigated systems[END_REF].

The learning process stimulated by a given ComMod cycle may raise new questions to be examined in a following cycle with modified RPG and/or associated ABM. This is what happened in the present ComMod experiment (Figure 2). In a first cycle focusing on soil erosion risk [START_REF] Trébuil | Multi-Agent Systems Companion Modeling for Integrated Watershed Management: A Northern Thailand Experience[END_REF], the participating villagers in Mae Salaep identified the expansion of perennial crops as a promising solution, and requested a second cycle focusing on the socio-economic constraints limiting their ability to invest in such crops (Barnaud et al., 2008a). Later on, as these perennial crops required irrigation, the participants requested to explore water management issues in a third ComMod cycle which is the focus of this article. This paper focuses on the third cycle, which started with an analysis of the agrarian and institutional aspects of the water problem: semi-structured interviews were conducted with two dozens of farmers representing the diversity of farming strategies in the village of Mae Salaep, the village headman and the key stakeholders of the sub-district administration (the TAO -Tambon Administrative Organization), i.e. the TAO village representatives, the TAO officers, and the president of the TAO council. The local knowledge acquired with these interviews was used to modify the previous RPG and ABM to focus on the water issue. These simulation tools (presented in details in [START_REF] Barnaud | Evolving simulation and gaming to support collective watershed management in mountainous northern Thailand[END_REF]Barnaud et al., , 2008a[START_REF] Barnaud | Interactive models to catalyze collective water management: a companion modeling approach in northern Thailand[END_REF]) integrated and highlighted the diversity of perspectives and interests regarding the water issue among the different types of farming households. These tools were used in a three-day participatory workshop organized in the village. 12 villagers had been selected and invited by the research team. The main selection criteria were as follows: they represented the diversity of farming strategies in the village regarding the water issue, they were potentially able to defend their interests (communication skills, self confidence reinforced by the presence of closed acquaintances), and the participants of the first and second cycle were selected in priority to ensure the continuity of the whole ComMod process.. On the first day, gaming sessions were organized with the 12 villagers playing a role similar to their real life situation. After a first gaming session played with rules corresponding to the current water use situation, a collective debriefing was organized for the participants to discuss the problems encountered in this gaming session and their possible solutions. Then the facilitator suggested to the 12 villagers-players to present their preferred solution to the TAO president which had also been invited to the workshop. In the afternoon, a second gaming session allowed the villagers to further explore this potential solution by modifying the initial rules of the game. On the second day of the workshop, individual interviews were conducted with the 12 villagers-players to compare researchers' and participants'representations of the situation, to better understand players' behaviour during the gaming sessions, to learn about their individual opinions regarding the collectively discussed issues and to assess the shortterm learning effects of the RPG sessions. On the third day, participatory ABM simulations were conducted in a plenary session with the 12 participants to allow them to further reflect on their preferred scenarios. Three weeks and three months later, more ABM participatory simulations were conducted within smaller and more homogenous groups to accompany the on-going discussions in the village (beyond the 12 participants) which had been stimulated by the three-day workshop.

To assess the dynamic and the effects of the ComMod process, we adopted an interpretive approach, trying to interpret what the participants think and why they act the way they act.

Data on cognitive changes triggered by the ComMod process were obtained via semistructured individual interviews of the 12 participants conducted before the workshop and one day, three weeks and three months after the workshop. These interviews aimed to assess the evolution of the following indicators:

-Stakeholders' perceptions of the issue, -Their perceptions of other stakeholders and their interactions with them, -Their perceptions of the possible scenarios to mitigate the problem at stake. The results of these interviews were analyzed using Atlas.ti, a software facilitating the qualitative analysis of texts.

The analysis of the collective dynamics of the group was based on observations of the participants' behaviour and discourses during the gaming sessions and group debates. Three researchers were observers during the workshop and took note of all the features which seemed interesting to them. A debriefing was organized afterwards with the rest of the facilitation team. Moreover, all the group sessions were video recorded. These videos were not systematically analyzed but their visioning helped to better understand some specific events or to identify elements which would have been overlooked by the observers.

The results of this analysis of the ComMod process are presented in the next sections.

Ecological, socio-political and cultural context

Water management issue

The local irrigation system uses gravity through a network of small PVC pipes connected to the creeks, each creek providing enough water to irrigate from one to three plantations. Due to the recent expansion of irrigated lychee and Oolong tea plantations and the increasing water shortage, social tensions about unequal access to water have heightened within the community. This issue concerned various stakeholders having specific interests, embedded in a specific cultural context and a complex network of power relationships.

Main types of farming households

The integration of farming households into the market economy has led to extensive socioeconomic differentiation (Table 1). Well-off type C farmers are well-off farmers who belong to influential clans of first settlers and sit on the traditional council of elders. Fifteen years ago, when they invested in the first lychee plantations and irrigation facilities in the village, they claimed that the first-come-first-served rule was an ancestral custom to regulate access to water. This rule stipulates that once a farmer has set up water pipes in a creek, other villagers cannot get water from the upstream section. As a result, only this minority of well-off farmers currently has access to water.

Type A and B households belong to smaller and less influential clans. Most of them do not openly question the first-come-first-served rule, including the farmers who invested in lychee plantations and cannot irrigate them. Not only because they do not want to break what is seen as an ancestral community rule, but also because they are (partly) dependent on type C clans, from whom they borrow money or work as hired labourers. In terms of power relations, type C farmers use both traditional authority and physical resources to exert power through enticement over type A and type B farmers (Figure 3).

The Tambon Administrative Organization (TAO)

Villagers asked ComMod researchers to explore the water management issue, and requested the participation of the Tambon (sub-district) Administrative Organization (TAO), because it funds local projects such as the construction of small-scale water infrastructure. These recently empowered administrations, with their council of elected villagers (two representatives per village), have the responsibility to promote participatory decentralization in rural Thailand [START_REF] Arghiros | Democracy, Development and Decentralization in Provincial Thailand[END_REF]. However, there are still obstacles to achieving this desired aim.

Despite the formal decentralisation, Thailand's bureaucracy still adheres to a hierarchical, top-down institutional culture. In our case study, the TAO president used the participatory discourse, but as we will see later, there was a sharp contrast between the discourse and her actual practices, as is often the case in participatory projects [START_REF] Pijnenburg | Keeping it vague. Discourses and practices of participation in rural Mozambique[END_REF]. As for the two TAO representatives, they belong to the local economic elite and their downward accountability to the community was openly questioned as they were regularly accused of taking advantage of their position to serve their own clan's interests. They felt much greater allegiance to upward accountability and defined their role as top-down relays between the sub-district administrators and the villagers. As for the villagers, very few were aware of the role they could play in the proposition and realisation of TAO funded projects.

Village leaders and representatives

Two leaders played a key role in this ComMod cycle. The first one is a TAO representative.

He had recently concluded a deal with an external investor, who bought a large piece of land in the village to plant high value Oolong tea. As this plantation needed a substantial quantity of irrigation water, he was likely to defend his personal interest in the ComMod process. The religious leader of the village Christian community (representing 60% of the village population) also played a key role. He was not only respected as a religious leader but also as a knowledgeable innovator and leader in agricultural matters, actively supporting poor households facing difficulties. His charisma created a federative form of power within the Christian community and among poor villagers. He was the first to raise the idea of using ComMod to discuss water sharing problems.

Cultural issues that played a role in the learning process

Several cultural aspects of the context played a key role in the power games and the collective dynamic of the ComMod process. First, as mentioned before, there was the cultural issue of a western ComMod researcher openly embracing the critical system theory, highligting the situation of the poor in the RPG and ABM simulations. This is all the more important since this participatory process was conducted in a society in which people evade public confrontation and not very used to open participatory deliberations. Akha people do not like conflicts (traditionally, when a conflict would occur among people in a settlement, the whole community would move and settle somewhere else) and although these values tend to erode over time, Akha people remain very much community-oriented [START_REF] Goodman | Meet the Akhas[END_REF]. Moreover, the conversion to Christian religion of half of the villagers of this community (villagers from the upper hamlet) in the last 20 years makes the cultural picture of this participatory process even more plural and complex. There was no real contradiction or conflicts of perspectives between the animist and Christian parts of the community (the upper and the down hamlets), since most of villagers who converted to Christian religion did so more for practical reasons than for ideological reasons ("because every one in this hamlet is Christian" and "because there are less rituals and donations" were the main reasons given by the villagers from the upper hamlet). However, the religious beliefs of the Christian leader influenced his views, discourses and actions in favour of the poorest of the community. Lastly, ethnic minorities living in the uplands of Northern Thailand (the Golden Triangle) have long been considered by the Thai majority as "backwards" people, if not dangerous. Opium dealers, communists, forest destroyers: these clichés about upland ethnic minorities are very common among Thai people and in Thai administrations [START_REF] Ganjanapan | The politics of environment in Northern Thailand: ethnicity and highland development programs[END_REF]. In our case study, if the president of the TAO council was Akha, the TAO officers were all Thai government employees. Their perception of the villagers remained influenced by the above-mentioned clichés. This cultural dimension reinforced stereotyping, limited communication and power asymmetries between villagers and TAO officers.

Analysis of power dynamics in the learning and negotiation process

In this section we analyze the influence and mechanisms of power games at key stages of the ComMod mediated cross-cultural learning and negotiation process.

Structure of the game increased awareness of a problem to be solved collectively

In the first gaming session, the players acted as in reality: the well-off farmers hurried to install water pipes, and did not allow others access to water from the upstream sections. This highlighted the current conflict caused by the first-come-first-served rule and increased the participants' awareness of the problem, its urgency and the need to solve it collectively. As the religious leader said, "the game showed everyone we need to change the water allocation rules. No need to say anything."

This was a key phase in the negotiation process since it determined whose interests would be on the agenda. Before the gaming sessions, well-off (type C) farmers with access to water denied the water problem. They repeatedly noted: 'there is no water problem in the village, everything is all right.' They obviously had a good BATNA (Best Alternative to Negotiated Agreement); a clear interest in maintaining the statu quo rather than exploring the water problem. If the ComMod process had started with a more classical meeting in which discussions prevail, the water-sharing problem might not have emerged as the elite would have been able to dominate discussion and agenda-setting. The game, however, facilitated a different form of communication, which allowed less powerful villagers to raise their problem and to create a collective awareness of its existence.

Exchanges of perceptions on the problem

The ComMod process stimulated participants to share perspectives on the water problem.

Most of participants said the game allowed them to better understand other villagers' situations, problems and/or perceptions (table 2). In particular, some well-off (type C) farmers with water access realized that the first-come-first-served rule would create more and more social tensions under the current expansion of irrigated plantations. Two type A and B farmers said they realized that "many of [them] had the same problem" (the lack of access to water).

At first sight, this may be surprising since villagers in a small community tend to know each other, but as one participant said: "in every day life, every one goes to his fields; we do not have such opportunities to jointly discuss issues." Moreover, several participants noted the game provided some distance from reality and an open playful atmosphere, which both facilitated exchanges about the sensitive and conflicting water issue. This was particularly important in the Akha cultural context of conflict avoidance.

Non-threatening re-framing by integrative negotiation of solutions

The framing of the problem is a crucial step in a negotiation process as it orients people towards certain kinds of solutions [START_REF] Leeuwis | Communication for rural innovation. Rethinking agricultural extension[END_REF]. In this case, when being asked by the facilitator to identify the problem, none of the players mentioned the first-come-first-served rule. The TAO representative dominated the discussions emphasizing the lack of water and suggesting the construction of a single large reservoir above the village catchment. Other participants were sceptical about this proposition since they feared it would only benefit a minority of farmers, but they did not say anything at this stage. The Christian leader kept silent and only expressed himself when the facilitator explicitly asked for other suggestions.

As he would explain later, he knew that it was impossible to question directly the first-comefirst-served rule because well-off clans would have not accepted it. Furthermore, a direct confrontation over this rule would have generated a zero-sum bargaining process in which the villagers would have fought to 'share the cake'; a distributive mode of negotiation in which small farmers had no chance to change the situation. Therefore, he suggested increasing the amount of water available to be able to share it with more people. By creating a win-win situation, he had a chance of getting the attention and support of powerful stakeholders. He suggested building small weirs in several creeks and sharing the water within several water user groups. In interviews, he and other participants interestingly explained that "without new infrastructures, it is impossible to change existing rules." All participants (except one whose plots were above the creeks) raised their hand to vote in favour of this integrative solution. It is important to notice here that the community-oriented Akha way of life deeply influenced the trajectory of this creative learning process. The importance of peace and consensus within the community favoured the acceptance of this win-win solution by the well-off farmers despite their interest in statu quo.

Importance of discussions behind the scenes

The above-mentioned proposal (several small weirs) was tested in the second gaming session.

It stimulated discussions, further supported by hybrid Agent Based Model (ABM) simulations (Barnaud el al, 2008c), regarding how to share water among beneficiaries of the weirs. At the first plenary ABM simulations, the TAO representative used his communication skills and authority to impose his idea, i.e. to share water in amounts proportional to the farmers' plantation size. But three weeks later, when new sets of simulations were organized within smaller and more homogeneous groups, participants had continued discussions among them after the workshop on the water sharing rules and they immediately agreed on sharing equal amounts of water. They added the possibility to temporarily lend out water rights to other farmers in case of excess of water. This shift illustrates the importance of discussions "behind the scenes" in-between ComMod workshops. In particular, as explained below, much of the process of empowerment of the marginalized which progressively led to the emergence of pro-poor solutions occurred "behind the scenes". Moreover, once more at this stage, the procommunity dimension of the Akha culture was influential. Indeed, interviews revealed that an old and respected farmer belonging to a well-off and influential clan said after the workshop to other villagers that he was in favour of an equal way of sharing the water to preserve peace in the community.

Reaching agreement

In a decision-making process, the phase at which the protagonists reach agreement is a determining one. At this stage, in spite of previous phases of improved communication and exchange of perspectives, influential participants (consciously or unconsciously) can exert power to impose their point of view [START_REF] Van Der Veen | Learning natural resource management[END_REF]. This can lead to a simple reproduction of initial power inequities. In our case study, three months after the last ComMod workshop, the TAO representative felt inclined to present his initial idea of the single reservoir to the TAO council rather than the agreed upon solution of several weirs. However, ten months later, the TAO representative and the Christian leader had started to collaborate and they had proposed the TAO council a project that took into account the interests of small farmers with no access to water.

A process which empowered the marginalized

In spite of initial power inequities, the interests of the marginalized were progressively taken into account in the negotiation arena. This was achieved through individual and collective empowerment. Along the process, the participants became more and more aware and selfconfident about the water issue and the TAO village projects. In the interviews, the ideas they expressed about theses issues were more and more elaborate, and during the group discussions, they more and more dared to express their opinion. The development of individual self-confidence is particularly important in the cultural context of northern Thailand, where prejudices against ethnic minorities persist and strongly affect people's notion of self-efficacy. Several villagers (in particular type A farmers) believed that they had neither valuable ideas nor the skills to express them. In this light, it is remarkable that a female participant noted: 'I am so proud. I did not know that I would be able to play the game, to think by myself about solutions'. Furthermore, evaluation interviews revealed that the feeling of collective empowerment was one of the stronger effects of the ComMod process.

Most of the participants explained the ComMod process made them realize that collectively they were 'stronger' or 'more intelligent' than individually. "Without the game, everyone thinks and act on his own. With the game, we discuss and think together, and we can find better solutions", said a B participant. And one step further: less powerful stakeholders realised they could join a charismatic leader to create an alliance and counter power. Most of this counter power was built "behind the scenes" in-between and after the ComMod workshops.

Potential and limits of this critical ComMod process to level the playing field

In this ComMod process, as facilitators, we adopted a critical attitude, i.e. we explicitly took into account power asymmetries to try to facilitate an equitable concerted process. In this section, we identify and discuss the strengths and weaknesses of our cultural-embedded methodological choices. Final questions were: were our methods able to deal with power inequities and include the marginalized? What was the legitimacy of these cultural-embedded choices?

Strengths

First, we argue the need for an initial analysis of power asymmetries among stakeholders in the local socio-political context. Among practitioners of participatory approaches there is a debate about the kind of initial analysis needed before starting a participatory process. In our experiment, the initial analysis allowed us to identify constraints for an equitable concerted process and to mitigate them by adapting the methods and tools we used. A methodological proposition for such an initial analysis is available in (Barnaud et al., 2008b). The formulation of ComMod activities were then guided by the concern for the less powerful actors.

The careful selection of participants was a determining factor to go towards the creation of a level playing field. [START_REF] Edmunds | A Strategic Approach to Multistakeholder Negociations[END_REF] argue not all stakeholders should systematically participate in a multi-stakeholder process.

If not yet empowered prior to such an exercise, the less powerful ones might not be able to properly defend their interests. This is the reason why we started the ComMod process at the village level, only integrating stakeholders of higher institutional levels when villagers felt comfortable and explicitly requested the presence of these decision-makers. When selecting the participants, we also tried to avoid the representation of a category of stakeholders by a single, shy person. For example, several women would have felt intimidated and shy when being alone, but in company of acquaintances they were more self-confident and talkative. Moreover, ComMod provides an opportunity to meet and exchange to a specific set of participants; the selection of participants hence influences the alliances that emerge during the process. For example, the identification and the active involvement of key stakeholders such as the Christian leader, who was particularly bottom-up minded and had sufficient charismatic authority to stimulate people to follow him, proved to be crucial.

To increase the self-confidence and capacity of participants to express their opinions, they should genuinely understand the model in use and for so participate in its construction. Some ComMod researchers think it is better not to prepare a model and RPG in advance, so as not to impose their science-based perspective, but to build the conceptual model from scratch in plenary discussions with the stakeholders. However, in this ComMod experiment, we considered in plenary discussions village elite would probably impose their perception and set the agenda, so it was decided to construct the model from the information gathered via individual interviews with farmers of all farm categories. Disadvantage of this approach is that participants need time to build self-confidence before they dare to criticise the researchers' model. But advantage is that the researchers can take care to represent all stakeholders' interests, also those of the marginalized, in the RPG and ABM. In this way, we could put the issues-at-stake for the marginalized on the agenda. Despite the Akha culture of conflict avoidance, it was accepted the ComMod scientist visualised the confronting situation via the RPG and ABM simulations. This enabled the farmers to tackle the issue. [START_REF] Wollenberg | Pluralism and the less powerful: accommodating multiple interests in local forest management[END_REF] underline participatory approaches often fail to tackle power inequities because they try to reach a consensus too fast. This experiment demonstrated how important it was to move beyond the first apparent consensus when facilitating the plenary discussions, as it often reflected the interest of the most powerful participants. This is especially important in Akha and Thai cultures that emphasize respect for hierarchy. To move beyond the 'initial public consensus', we also conducted individual interviews and small group discussions alongside plenary discussions. This provided the participants the opportunity to freely express and further articulate their opinions. Typically, in a plenary session, participants stated they lacked water as they had no money to buy PVC pipes, while in individual interviews the same persons quickly incriminated the first-come-first-served rule.

As most conflicts are not solved in public but behind the scenes [START_REF] Fisher | Getting To Yes: Negotiating Agreement Without Giving In[END_REF], the continual and iterative nature of the ComMod process is a feature favouring the re-framing of matter, gradual articulation of opinions, empowerment of less vocal and the integration of multiple interests. If the ComMod process had stopped after a single gaming workshop, we would have missed the opportunity to monitor and support the individual and collective empowerment processes needed to attain a fair village discussion and a more equitable solution.

Limits and perspectives for improvement

All the factors mentioned above allowed some usually voiceless people to participate in the elaboration of a new project at the village level. However, the question remains what impact this will actually have on the life of this community? What perspectives for improvements did this experiment suggest?

Only 12 villagers participated to the third ComMod cycle on water management. They were selected by the research team to be representative of the different types of farming households in the village, but they were not considered by the other villagers as their representatives or spokespersons. Therefore, no village-level decisions could be formally taken during the ComMod workshops. The discussions among the 12 participants more or less diffused across other villagers since a TAO village project was finally designed at the village level. However, several participants mentioned that 'those who played the game now think differently, in a more cooperative way, but those who did not play the game do not all think the same way.' This was considered a main limit of this ComMod process. However, it is difficult to organize gaming sessions with more than 15-20 participants, and it would be too costly to multiply their number. A first solution could be a game that the villagers could play autonomously without guidance of researchers. The effect of multiple use of such a game highly depends on the commitment and training of a local facilitator. To attain a fair discussion it is important to have a skilled facilitator, readily available to regularly play the game and closely monitor village discussions, working on empowerment of the marginalised and integration of perspectives. Such a 'champion' may be difficult to find. The religious leader was initially identified as such a potential local facilitator but in spite of his general support of the ComMod approach, he finally refused to ensure this heavy task. The TAO representative expressed his interest to be such a facilitator, but the research team considered that the risk was too high that he manipulates the process to serve his own interests. Another option could be to call village meetings after each workshop to present and discuss the results in an interactive way to all villagers. A new combination of RPG and ABM was tested for such a purpose in a ComMod experiment conducted in another province of northern Thailand (Barnaud et al., 2008b).

Second, this ComMod experiment failed to stimulate a genuine bottom-up dialogue between the villagers and their TAO president. If the process reinforced the villagers' ability to make creative and concerted suggestions to the TAO, it did not reinforce the ability of TAO officers and managers to genuinely listen to villagers. In spite of her discourse on participation, the TAO president arrived late at the ComMod workshop and discouraged rather than listened to the villagers. Later on, when the villagers finally submitted their project to the TAO council, she refused to fund it. Greater efforts should be pursued to know the front-office and backoffice discourse of these key actors, to raise their awareness and interest in the potential of a deliberative ComMod process enabling them to arrive at better informed, sustainable decisions. At this stage of the decentralisation process, most Thai organisations and officers

are not yet ready to participate in a truly bottom-up dialogue. The training of a new generation of local administrators in the potential, limits and risks of participatory approaches may change their appreciation and promote their critical use.

Conclusion

This experiment illustrates the pertinence of taking power games into account in participatory processes. The case shows it is not always enough to put stakeholders together around a table to achieve a fair and equitable concerted process. This paper calls for a critical companion modelling approach, paying attention to power relations, in which the socio-political system is carefully analysed and monitored to identify the main constraints militating against an equitable concerted process, and to creatively adapt existing methods and tools to mitigate them.

However, such a posture raises several questions. Here a foreign process designer used her cultural space for manoeuvre to put the issue of equity on the agenda. Beside the practical question of the costs and feasibility of a preliminary in-depth analysis of power relations, it raises the key question of the facilitators' involvement and commitment. Is it legitimate for researchers to be involved in processes that modify power games in the negotiation arena by empowering the powerless participants? If not, should they adopt a neutral posture? But this experiment shows that facilitators' neutrality is an illusion: overlooking power relations entails the risk of increasing social inequities. Moreover, claiming facilitators' neutrality is insidious as unconscious choices drive the process without being examined. Systematically expressing and examining the facilitators' choices is a demanding but wiser course to adopt. If facilitators make explicit their cultural or ideological embedded biases and methodological choices, these choices can be rejected or accepted as legitimate by stakeholders. This way, the social legitimacy of the process can be progressively built, being in itself an important result of the cross-cultural learning process.

List of figures and tables

FigureFigure 2 .

 2 Figure 1. Conceptual analytical framework

Figure 1 .

 1 Figure 1. Conceptual analytical framework

Table 1 .

 1 Characteristics of the main types of farming households in Mae Salaep 1) l labour unit is equivalent to 300 working days per year.(2) In 2005, the local household survival threshold (to meet the household basic needs) was assessed at 210 US dollars/household/year, and the annual income from minimum wages paid to city workers was 750 US dollars/year. Figure 3. Initial power relations among the local participants in the ComMod process implemented in 2005 at Mae Salaep.

	Farm type		A. Vulnerable landless	B. Self-sufficient &	C. Relatively large &
				or very smallholders	medium-sized farms	diversified farms
	Size (ha/labour (1) )		0.4 -0.8	0.8 -2.4	1.3 -3.2
	Main crops		Maize (for cash)	Upland rice (for family	Paddy rice (for family
					consumption), maize,	consumption), maize,
					small	and	rainfed	extensive	irrigated
					plantations of Assam	plantations of lychee,
					tea or lychee	Oolong and/or Assam
						tea
	Off-farm employment	To meet basic family	To mitigate fluctuations	To raise cash and invest
				needs	of farming incomes	on the farm
	Total annual household	200	420	1,160
	cash	income	(US
	Dollars/year) (2)
	Investment capacity	Nil	Weak	Significant

(

Table 2 .

 2 Participants' answers to the question "did the process allow you to learn something about other participants?"

		Number of participants who
	Categories of answers	gave this answer
		(types of farmers)
	Realized that when all people discuss together, they can find	4
	better solutions	(1 A, 2 B, 1 C)
	Realized that other people had problems similar to his/her	2
	problems regarding water	(1 A, 1 B)
	Better understood the situation and perception of other	4
	participants regarding water	(2 B, 2 C)
	Better understood the practices of other participants	2
	regarding water	(2 B)
	Did not learn much about other participants	1
		(1 A)

Table 1 .

 1 Characteristics of the main types of farming households in Mae Salaep, Chiang Rai Province, northern Thailand Table 2. Participants' answers to the question "did the process allow you to learn something about other participants?"

Acknowledgements

The authors gratefully thank the Challenge Program Water and Food of the CGIAR, the Asia IT&C Initiative of the European Union and the Thai-French Bilateral Scientific Cooperation Programme for their financial support.