In my Ph.D. dissertation, I have studied problems arising in various aspects of preferences: preference modeling, preference learning, and preference reasoning, when preferences concern outcomes ranging over combinatorial domains. Preferences is a major research component in artificial intelligence (AI) and decision theory, and is closely related to the social choice theory considered by economists and political scientists. In my dissertation, I have exploited emerging connections between preferences in AI and social choice theory. Most of my research is on qualitative preference representations that extend and combine existing formalisms such as conditional preference nets, lexicographic preference trees, answer-set optimization programs, possibilistic logic, and conditional preference networks; on learning problems that aim at discovering qualitative preference models and predictive preference information from practical data; and on preference reasoning problems centered around qualitative preference optimization and aggregation methods. Applications of my research include recommender systems, decision support tools, multi-agent systems, and Internet trading and marketing platforms.

Les développements récents en économie du bien-être ouvrent la voie à des méthodes d’évaluations reposant sur d’autres modèles de justice sociale que l’utilitarisme. Leur faisabilité dans les pratiques quotidiennes d’évaluation des interventions de santé pose question : l’objectif de cette thèse est de contribuer d’y répondre. Pour cela nous nous sommes intéressés à trois cas pratiques. L’objectif du Chapitre I est de comparer les méthodologies d’évaluation de trois agences publiques d’évaluation, le NICE (Grande-Bretagne), l’IQWiG (Allemagne) et le KCE (Belgique), pour identifier les positions en matière de justice sociale qui en découlent. Le Chapitre II propose d’étudier le dilemme moral que suscite le phénomène d’adaptation des préférences dans l’évaluation deux dispositifs de compensation du handicap. Trois options sont avancées résoudre ce dilemme, elles s’appuient sur les théories de la justice sociale égalitaristes. Enfin, le Chapitre III démontre la faisabilité de l’approche revenu équivalent-santé, développée par Fleurabey, dans l’aide à la décision publique, au sujet des traitements antihypertenseurs en prévention primaire / Welfare economics encompasses other public choice theories besides utilitarianism, like egalitarian social justice theory. Whether these economic frameworks provide practical tools that could be used in health technology assessment is an ongoing debate, and this study aim to contribute to answer this question. The aim of the first chapter is to review health economic evaluation guidelines and compare methods from three national health technology assessment agencies - NICE (England and Wales), IQWiG (Germany) and KCE (Belgium) - and to assess what social justice principles are implied by their methodological choices. The second chapter studies the moral dilemma raised by adaptive preferences in growth hormones treatment and bilateral cochlear implants. Three options are put forward to solve this dilemma: they are grounded on egalitarian social justice theories. The objective of the third chapter is to provide evidence about the feasibility of assessment based on equivalent income approach, developed by M. Fleurbaey, in the context of public decision making. For this application case, we focussed on antihypertensive treatments in primary prevention

Configuração modelo de features é conhecida por ser uma atividade complexa, demorada e propensa a erros. Esta atividade torna-se ainda mais complicada quando envolve múltiplas partes interessadas no processo de configuração. Trabalhos de pesquisa têm proposto abordagens para ajudar na configuração de modelo de features, mas elas dependem de processos sistemáticos que restringem as decisões de alguns dos stakeholders. Neste trabalho, propomos uma nova abordagem para melhorar o processo de configuração multi-stakeholder, considerando as preferências dos stakeholders expressas através de restrições duras e brandas. Com base em tais preferências, recomendamos diferentes configurações de produto utilizando diferentes estratégias da teoria da escolha social. Nossa abordagem é implementada em uma ferramenta chamada SACRES, que permite criar grupos de stakeholders, especificar preferências dos stakeholders sobre uma configuração e gerar as configurações ideais. Realizamos um estudo empírico para avaliar a eficácia de nossas estratégias no que diz respeito à satisfação individual e justiça entre todos os stakeholders. Os resultados obtidos provem evidência de que estratégias em particular possuem melhor performance em relação à satisfação de grupo, chamadas average e multiplicative considerando as pontuações atribuídas pelos participantes e complexidade computacional. Nossos resultados são relevantes não só no contexto de Linha de Produto de Software, mas também para a Teoria da Escolha Social, dada a instanciação de estratégias de escolha social em um problema prático. / Feature model con guration is known to be a hard, error-prone and timeconsuming activity. This activity gets even more complicated when it involves multiple stakeholders in the con guration process. Research work has proposed approaches to aid multi-stakeholder feature model con guration, but they rely on systematic processes that constraint decisions of some of the stakeholders. In this dissertation, we propose a novel approach to improve the multi-stakeholder con guration process, considering stakeholders' preferences expressed through both hard and soft constraints. Based on such preferences, we recommend di erent product con gurations using di erent strategies from the social choice theory. Our approach is implemented in a tool named SACRES, which allows creation of stakeholder groups, speci cation of stakeholder preferences over a con guration and generation of optimal con guration. We conducted an empirical study to evaluate the e ectiveness of our strategies with respect to individual stakeholder satisfaction and fairness among all stakeholders. The obtained results provide evidence that particular strategies perform best with respect to group satisfaction, namely average and multiplicative, considering the scores given by the participants and computational complexity. Our results are relevant not only in the context software product lines, but also in the context of social choice theory, given the instantiation of social choice strategies in a practical problem.

Configuração modelo de features é conhecida por ser uma atividade complexa, demorada e propensa a erros. Esta atividade torna-se ainda mais complicada quando envolve múltiplas partes interessadas no processo de configuração. Trabalhos de pesquisa têm proposto abordagens para ajudar na configuração de modelo de features, mas elas dependem de processos sistemáticos que restringem as decisões de alguns dos stakeholders. Neste trabalho, propomos uma nova abordagem para melhorar o processo de configuração multi-stakeholder, considerando as preferências dos stakeholders expressas através de restrições duras e brandas. Com base em tais preferências, recomendamos diferentes configurações de produto utilizando diferentes estratégias da teoria da escolha social. Nossa abordagem é implementada em uma ferramenta chamada SACRES, que permite criar grupos de stakeholders, especificar preferências dos stakeholders sobre uma configuração e gerar as configurações ideais. Realizamos um estudo empírico para avaliar a eficácia de nossas estratégias no que diz respeito à satisfação individual e justiça entre todos os stakeholders. Os resultados obtidos provem evidência de que estratégias em particular possuem melhor performance em relação à satisfação de grupo, chamadas average e multiplicative considerando as pontuações atribuídas pelos participantes e complexidade computacional. Nossos resultados são relevantes não só no contexto de Linha de Produto de Software, mas também para a Teoria da Escolha Social, dada a instanciação de estratégias de escolha social em um problema prático. / Feature model con guration is known to be a hard, error-prone and timeconsuming activity. This activity gets even more complicated when it involves multiple stakeholders in the con guration process. Research work has proposed approaches to aid multi-stakeholder feature model con guration, but they rely on systematic processes that constraint decisions of some of the stakeholders. In this dissertation, we propose a novel approach to improve the multi-stakeholder con guration process, considering stakeholders' preferences expressed through both hard and soft constraints. Based on such preferences, we recommend di erent product con gurations using di erent strategies from the social choice theory. Our approach is implemented in a tool named SACRES, which allows creation of stakeholder groups, speci cation of stakeholder preferences over a con guration and generation of optimal con guration. We conducted an empirical study to evaluate the e ectiveness of our strategies with respect to individual stakeholder satisfaction and fairness among all stakeholders. The obtained results provide evidence that particular strategies perform best with respect to group satisfaction, namely average and multiplicative, considering the scores given by the participants and computational complexity. Our results are relevant not only in the context software product lines, but also in the context of social choice theory, given the instantiation of social choice strategies in a practical problem.

Configuração modelo de features é conhecida por ser uma atividade complexa, demorada e propensa a erros. Esta atividade torna-se ainda mais complicada quando envolve múltiplas partes interessadas no processo de configuração. Trabalhos de pesquisa têm proposto abordagens para ajudar na configuração de modelo de features, mas elas dependem de processos sistemáticos que restringem as decisões de alguns dos stakeholders. Neste trabalho, propomos uma nova abordagem para melhorar o processo de configuração multi-stakeholder, considerando as preferências dos stakeholders expressas através de restrições duras e brandas. Com base em tais preferências, recomendamos diferentes configurações de produto utilizando diferentes estratégias da teoria da escolha social. Nossa abordagem é implementada em uma ferramenta chamada SACRES, que permite criar grupos de stakeholders, especificar preferências dos stakeholders sobre uma configuração e gerar as configurações ideais. Realizamos um estudo empírico para avaliar a eficácia de nossas estratégias no que diz respeito à satisfação individual e justiça entre todos os stakeholders. Os resultados obtidos provem evidência de que estratégias em particular possuem melhor performance em relação à satisfação de grupo, chamadas average e multiplicative considerando as pontuações atribuídas pelos participantes e complexidade computacional. Nossos resultados são relevantes não só no contexto de Linha de Produto de Software, mas também para a Teoria da Escolha Social, dada a instanciação de estratégias de escolha social em um problema prático. / Feature model con guration is known to be a hard, error-prone and timeconsuming activity. This activity gets even more complicated when it involves multiple stakeholders in the con guration process. Research work has proposed approaches to aid multi-stakeholder feature model con guration, but they rely on systematic processes that constraint decisions of some of the stakeholders. In this dissertation, we propose a novel approach to improve the multi-stakeholder con guration process, considering stakeholders' preferences expressed through both hard and soft constraints. Based on such preferences, we recommend di erent product con gurations using di erent strategies from the social choice theory. Our approach is implemented in a tool named SACRES, which allows creation of stakeholder groups, speci cation of stakeholder preferences over a con guration and generation of optimal con guration. We conducted an empirical study to evaluate the e ectiveness of our strategies with respect to individual stakeholder satisfaction and fairness among all stakeholders. The obtained results provide evidence that particular strategies perform best with respect to group satisfaction, namely average and multiplicative, considering the scores given by the participants and computational complexity. Our results are relevant not only in the context software product lines, but also in the context of social choice theory, given the instantiation of social choice strategies in a practical problem.

Le premier chapitre de cette thèse, intitulé « Optimal Vote Buying » (co-écrit avec Leon Musolff, Princeton University) s’intéresse à la corruption de comités. Il s’agit d’une contribution théorique dans laquelle nous montrons qu’il est généralement peu onéreux de corrompre une large majorité de membres du comité. En effet, lorsque le comité est largement corrompu, les membres considèrent que l’option soutenue par celui qui corrompt le comité sera probablement plébiscitée. Aucun vote ne peut alors faire basculer l’élection et les membres du comité sont prêts à accepter un pot-de-vin modeste en échange de leur vote. Dans le deuxième chapitre (co-écrit avec Emeric Henry, Sciences Po) nous étudions les interactions entre le vote et les normes sociales. Nous analysons un modèle dans lequel un groupe choisit sa propre règle. Dans une première étape, chaque membre vote pour ou contre une règle. Une fois le règlement établi, les membres du groupes choisissent une action dont les conséquences dépendent de la règle choisie. Nous étudions comment le vote et le comportement ultérieur interagissent. Enfin, le dernier chapitre (co-écrit avec Etienne Fize) traite de l’impact du service militaire obligatoire en France sur les comportements politiques. Nous trouvons d’une part que les individus ayant fait leur service militaire sont plus enclins à voter. Pour les élections de 2012, nous estimons que l’effet est de l’ordre de 4 points de pourcentage pour les élections présidentielles et atteint les 9 points pour le second tour des élections législatives. Nous étudions également les conséquences sur les préférences politiques. Nous trouvons que les anciens conscrits sont plus à droite. / In the first chapter (« Optimal Vote Buying » coauthored with Leon Musolff, Princeton University), we analyze a vote buying problem. We show that bribing a supermajority can be cheaper due to pivotal considerations. When a large number of committee members receive a bribe, they do not expect to be pivotal in the election. As a result, it is sufficient to offer them a small amount of money in exchange for their vote. Due to this mechanism, it turns out that the vote buyer generally prefers to bribe a supermajority. In the second chapter (« Voting and contributing when the group is watching » coauthored with Emeric Henry, Sciences Po) we study the interaction between the way members vote on rules and their subsequent behaviors. This analysis applies to groups who choose their own rules and who care about their image. We study how players’ considerations depend on the visibility of the process. We show that multiple norms can emerge. We discuss the problem of a social planner and the implications for welfare. The last chapter (« Military service and political participation » coauthored with Etienne Fize) investigates the impact of the French military service on political behaviors. Exploiting the suspension of mandatory conscription for French men, we find a significant and positive impact of military service on turnout. This effect ranges from 3.6 percentage points for the first round of the presidential election of 2012 to 8.9 percentage points for the second round of the legislative elections. We also investigate the impact of conscription on political preferences and we find that former conscripts are significantly more nationalist and conservative.

A well-known fact about positional election procedures is that its ranking of m alternatives can change when some of the alternatives are removed from consideration—given a positional procedure on each of 2, 3, …, m alternatives and a collective preference order for each distinct subset of the m alternatives. Saari has established that with few exceptions, we can find a voter profile for which the collective preference order for each subset under the according positional procedure is the one given. However, Saari's results do not quantify the likelihood of finding such voter profiles. For small numbers of alternatives, William Gehrlein developed a statistical model to explore the probabilities that particular collective preference orders on subsets of alternatives can occur for large electorates. One goal of this research is to determine whether changes in the collective preference order as alternatives are removed can be considered to be the norm or an outlier for positional procedures. This dissertation extends the research headed by Gehrlein in two directions. One, I generalize his statistical model to explore probabilities for iterated election procedures. Gehrlein's model previously produced results only for three alternatives and in limited cases for four alternatives. I have extended this model to produce results for up to five alternatives, including analysis of instant-runoff voting and runoff elections. Two, Gehrlein's model required specific conditions on the probability distribution of individual voter preferences across the population. I relax this assumption so that for any probability distribution of individual voter preferences across the population, I can explore the probability that a collective preference order is inconsistent with the outcomes when alternatives are removed. These results provide a foundation for discussing the impact of removing alternatives on elections across all large electorates. I also apply these results to two recent United States elections wherein a third-party candidate received a significant share of the votes: the 1992 U.S. Presidential election and the 1998 Minnesota Gubernatorial election. Overall, my research will suggest that as the number of alternatives increases, the likelihood of finding changes in the collective preference order as alternatives are removed will approach one.

L’apport principal de cette thèse réside dans l’évaluation de la vulnérabilité d’un certain nombre de règles de voteà la violation de deux propriétés ; nous nous appuyons pour cela sur l’approche axiomatique de la théorie du choixsocial, qui permet d’étudier le comportement d’un mécanisme de choix social vis-à-vis d’un jugement de valeurémis par l’économiste. La symétrie inverse ("reversal symmetry") est la première propriété examinée. A la suite destravaux de Saari [150], nous évaluons deux catégories de règles de vote en prenant cette propriété comme critèrede décision : d’une part, les règles positionnelles simples et d’autre part les règles positionnelles à deux tours. Plusprécisément, nous calculons la probabilité d’occurrence de ce phénomène à la fois en domaine universel (c’est-à-direlorsque les individus peuvent exprimer n’importe quel ordre de préférence), et en domaine restreint (lorsque deshypothèses supplémentaires sont introduites sur la manière dont les votants classent les « candidats » à l’élection).Nous examinons le cas de trois candidats, de quatre candidats ainsi que le contexte d’élections à un très grandnombre de votants, en faisant tendre ce nombre vers l’infini.La seconde thématique est consacrée à l’examen du comportement de la règle de Dodgson face à la propriété d’homogénéité.Nous proposons une méthode de calcul simple et systématique du score de Dodgson. Nous distinguonsensuite différentes classes de profils pour lesquels cette règle est susceptible d’être vulnérable à cette propriété. Afinde compléter notre recherche, des fréquences de violation de cette propriété par la règle de Dodgson sont fournies. / The contribution of this thesis lies in the evaluation of the vulnerability of a number of voting rules to the violationof two properties of the theory of social choice. We rely on the axiomatic approach of social choice theory to examinethe behavior of a social choice procedure according to a value judgment (or axiom) emitted by the economist.Reversal symmetry is the first property studied. Following the works of Saari [150], we evaluate two families ofvoting by using this property as the decision criterion : the simple scoring rules on the one hand, and the scoringrules with runoff on the other hand. We do probability calculations to evaluate how frequent this phenomenon is,in the three-candidate case under universal domain as well as under a restricted domain, and we also tackle thefour-candidate case and the infinite number of voters case.The second topic is devoted to the study of the Dodgsonrule according to the homogeneity axiom. We introduce a simple and systematic method for the computation ofthe Dodgson score. We distinguish various classes of profiles at which that rule may be vulnerable to this property.Further, frequencies of violation of this property by the Dodgson rule are provided.

This thesis studies ultrafilters and their various applications in topology, social choice theory and construction of a nonstandard universe. First of all, we introduce basic properties of ultrafilters and show how to use them to construct nonstandard framework. Next, we prove Arrow's impossibility theorem which states that every electoral system with a finite set of voters satisfying certain natural conditions necessarily admits at least one dictator who determines the society's preferences. However, if the set of voters is infinite, this is not true anymore and ultrafilters play a key role in the proof. We present two counterexamples in the infinite case using nonstandard framework. A similar theorem holds in the case where the preferences are real functions. Again, we show two examples of electoral systems that are not dictatorial - one using Banach limits and the other using hyperfinite sums. Finally, we use the ultrafilters to construct the Čech-Stone compactification of natural numbers. We show that the nonstandard enlargement of natural numbers equipped with suitable topology is the Čech-Stone compactification of the set of natural numbers. 1

To evaluate voting rules, it would be good to know what universe election outcomes are drawn from. Election theorists have postulated that elections might be drawn from various stochastic preference models, including the IC and IAC conditions, but these models induce empirically contradicted predictions. We use two distinct data sets, FairVote and German Politbarometer survey. Based on the data information, we suggest approaches that differ from those probabilistic models to better approximate the actual data in Chapter 3 and 4. Chapter 5 applies the spatial model for four-candidate in a three-dimensional setting. We also offer a significant gap between the actual and simulated data under the IAC conditions by comparing their statistical characteristics. / Doctor of Philosophy / Through the 1884 Third Reform Act, the plurality rule (or first-past-the-post system) runs to elect parliament members for the first time. More than a hundred years passed after the Act, and election theorists have suggested various alternatives, the plurality rule is the second most used rule worldwide for national elections for now. One main reason is that researchers do not reach an agreement on the best alternative rule. Theorists have evaluated different voting rules under probabilistic assumptions, but real-world examples contradict the predictions of these models. In this dissertation, we suggest different approaches provide a better approximation to the actual data. In Chapter 3 and 4, we go backward: analyze how voters of each preference order are distributed in real data first, then set a model for estimating the frequency of paradox. In chapter 5, we extend an existing model with higher dimensionality. Then using the model, we offer empirical evidence showing the gap between the actual and simulated data under a popular probabilistic model.