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Франко-российская научно-практическая конференция "ЭКОНОМИКА, ПОЛИТИКА, ОБЩЕСТВО: новые вызовы, новые возможности"

Сотрудники лаборатории анализа и выбора решений приняли участие в совместной франко-российской научно-практической конференции "Экономика, политика, общество: новые вызовы, новые возможности"

Помимо участия в заседаниях семинара №5 "Анализ и принятие решений", следующие коллеги представили собственные доклады:

1) Андрей Субочев "k-Устойчивые множества и их свойства" 

2) Фуад Алескеров, Людмила Егорова "Разве это так плохо, что мы не можем распознать Черных Лебедей?" AleskerovEgorova.rtf

3) Александр Карпов "Аксиоматика систем пропорционального представительства"  report Karpov.pdf

Также вниманию сотрудников лаборатории и студентов были представлены доклады французских коллег, ведущих специалистов в области коллективного выбора, теории голосований и принятии решений:

1) Морис Салль (Университет города Кана, Франция, президент общества Social Choice and Welfare)

"Права, коллективный выбор, логика"

2) Винсент Мерлин (Университет города Кана, Франция) 

"Эффективное по большинству представительство граждан в Федеральном Собрании"  report Merlin.pdf

Majority Efficient Representation of the Citizens in a Federal Union

 All the federal unions, like the United States of America or the European Union, face the issue of finding a “good” indirect voting mechanism. In particular, a crucial question is to know how many mandates should be given to each country or state in a two-tier
voting system, given that the majority rule is used at each level. We here propose a new normative criterion to evaluate these voting rules: An apportionment of the seats among the states is majority efficient if the probability of electing the candidate who receives less than 50% of the votes in a two candidate competition over the whole union is minimized. Using computer simulations, we suggest that either the proportional or the square root rule can emerge as an optimal apportionment method depending on the probability model we use to describe the electoral process.

Keywords: federalism, indirect voting, apportionment, paradoxes, power, probability, electoral behavior.

3) Оливье Юдри (Высшая национальная школа телекоммуникаций, Франция)

"О сложности агрегирования предпочтений"

"On the complexity of the aggregation of preferences"

We consider here a problem arising in voting theory: how to aggregate individual preferences (rankings) over a given set of candidates into a collective preference (ranking) which summarizes the individual preferences “as well as possible”? This obviously requires specifying what we mean by “as well as possible”. A usual answer consists in looking for a collective ranking which fulfils some structural properties like transitivity and which minimizes the total number of disagreements with respect to the individual preferences (i.e. the sum, over the set of voters, of the number of disagreements observed between each voter and the collective ranking). In this case (i.e. we want to minimize the sum of the individual disagreements), an optimal collective ranking is called a “median order”.

In a first part of the talk, we study the complexity of the computation of a median order. More precisely, we show that the computation of a median order is usually NP-hard when properties like transitivity are required. In particular, it is the case when the individual preferences are assumed to be linear orders while the median order must be a linear order, a complete preorder or other usual partially ordered relations, at least when the number of voters is large enough.

In the second part of the talk, we study other ways to define the collective ranking. For instance, instead of the total number of the disagreements over the set V of voters, we may consider the maximum number of disagreements over V (in other words, we try to find a collective ranking minimizing the dissatisfaction of the most dissatisfied voter). We show that this kind of problem can sometimes be related to the search of a median order for different kinds of objective functions (including the maximum number of disagreements). We deduce from this relation that the computation of an optimal solution remains NP-hard for several objective functions, when the individual preferences can be any binary relations while the collective ranking must be a linear order or a complete preorder, even if there is only one voter.

Также, французские коллеги приняли участие во внеочередном заседании общемосковского научного семинара "Математические методы анализа решений в экономике, бизнесе и политике" 27 октября. На семинаре выступали:

1) Винсент Мерлин (Университет города Кана, Франция) / Vincent Merlin (University of Caen and CNRS)

The case of two candidate elections I: The axiomatic approach

The objective of this course is to introduce Social Choice theory by focussing on the most simple case, an election between two candidates only. We then consider a finite population of n voters, who have to decide collectively whether candidate A or candidate B is the best one.

After introducing some notations and definitions, we present the characterization of majority vote due to May (1952): May's theorem states that simple majority voting is the only anonymous, neutral, and monotone choice function between two alternatives. We discuss the other possibilities proposed by Fishburn (1973) and Murakami (1968) by relaxing the above mentioned conditions.

At last, we wonder whether there exists, for two candidates, a indirect voting system that would always mimic the result of indirect voting. Recent papers by Chambers (2008) and Bervoets and Merlin (2010) show that the possibilities are not appealing from a democratic point of view.

2) Морис Салль (Университет города Кана, Франция, президент общества Social Choice and Welfare) / Maurice Salles (University of Caen)

"On the origin of social choice theory"

The origin of social choice theory is generally attributed to Condorcet and Borda. However, a number of earlier contributions were made during the Middle Ages and even in Antique Rome. The modern theory of social choice has a double origin: the voting side is just one part of it. Another major part, more associated with mainstream economics, is related to British philosophers at the end of the 18th century establishing the foundations of utilitarianism. I will show how these two aspects are still at the center of the definition of the subject today.

На совместном внеочередном заседании общемосковского научного семинара "Математические методы анализа решений в экономике, бизнесе и политике" и научного семинара "Математическое моделирование" для студентов магистратуры 1 курса по направлению "Математическое моделирование" 1 ноября был представлен доклад Оливье Юдри 

Olivier Hudry http://perso.telecom-paristech.fr/~hudry/

Ecole nationale supérieure des télécommunications

"Tournament solutions"

In voting theory, the result of a paired comparison method as the one suggested by Condorcet [1] can be represented by a tournament T, i.e., a complete asymmetric directed graph, when there is no tie. More precisely, the vertices of T are the candidates of the election, and there is a directed edge from x towards y when a majority of voters prefer x to y.
When there is no Condorcet winner, i.e., a candidate preferred to any other candidate by a majority of voters, it is not always easy to decide who is the winner of the election. Different methods, called tournament solutions (see [3]), have been proposed to define the winners. They differ by their properties and usually lead to different winners.
The aim of this talk is to depict these tournament solutions, to describe their properties and their relationships. Among these properties, we consider combinatorial aspects as well as some algorithmic ones. In particular, we consider the complexity of the most usual tournament solutions: some are polynomial, some are NP-hard (see [2]).

Keywords: voting theory, majority tournament, Copeland solution, maximum likelihood, self-consistent choice rule, Markovian solution, uncovered set, minimal covering set, Banks solution, Slater solution, tournament equilibrium set, eigenvector solution, complexity.