IPCAINT

The objective of Social Choice Theory is to choose an aggregation procedure that translates individual preferences as faithfully as possible into a collective preference. It therefore makes it possible to make a coherent collective decision based on a set of individual preferences, which makes it possible to establish a single choice, a set of choices or even simply to give an evaluation.

Given a group of individuals called upon to choose one option among others, the rule of choice or the collective decision procedure associates a collective ranking with each state of society. The study of the properties of aggregation procedures constitutes the centerpiece of this theory. Indeed, one of the most crucial questions that social choice theory attempts to resolve is that of the choice of an aggregation procedure allowing the avoidance of the absurd or the unreasonable in the decisions of a group of individuals around of a given subject.

Social choice theory draws on fundamental microeconomic principles to explain the decision-making of rational individuals related to economic or other phenomena. In other words, the scope and the social stakes of this theory can interest, in addition to economics and politics, fields as diverse as management, computer science and philosophy. Indeed, the theory of social choice covers, through its vast field of application, a multitude of situations where the problem is formally similar: a group of individuals (experts, judges, jury, voters, etc.) confronted with a set of options (allocation of resources, economic projects, candidates in a contest or in an election, . . .) must reach a collective decision on the basis of opinions and individual interests.

The challenges of collective decisions involving divergent interests and concerns have long been explored. Nevertheless, many specialists agree that interest in the question of collective choice does not date from today but dates back to the end of the 18th century. Thus, two members of the Royal Academy of Sciences of Paris: Borda (1781) and Condorcet (1785) were already wondering about the voting method to be adopted for the election of academicians.

Condorcet’s method has been the subject of numerous works like that of Borda. In a situation involving three or more candidates, this method raises many difficulties, the main one being that of the Condorcet paradox, which is one of the best known paradoxes of social choice theory.

The Condorcet paradox appears when the aggregation, according to the Condorcet rule, of a list of all transitive individual orders leads to an intransitive collective order. In addition to this difficulty, this rule may not lead to the existence of a winner, called a Condorcet winner who would beat all the others with a majority of votes.

At the same time, Borda’s paradox arises when the rule of plurality leads to choosing a candidate who would be beaten by all other candidates in a pairwise comparison (Condorcet’s loser). It also occurs when the plurality rule fails to elect a candidate who would beat all others with a majority of votes (the Condorcet winner).

The two paradoxes, and in particular the Condorcet paradox, have prompted many social choice theorists to formally study the different methods of aggregation. The starting point of this work is generally dated to the end of the 1940s.

The main result of this time is the famous impossibility theorem of Arrow (1951). Arrow shows that there is no procedure for aggregating individual preferences that is likely to guarantee the simultaneous observance of a set of conditions deemed desirable by society. The method adopted by Arrow is an axiomatic approach, the most common approach in social choice theory.

The probabilistic approach also plays an important role in the developments of social choice theory. This probabilistic method finds its origin in the pioneering works of Guilbaud (1952), Campbell and Tullock (1965), DeMeyer and Plott (1970), Gehrlein and Fishburn (1976), etc. The first works in this field were essentially interested in the probability of obtaining or not a Condorcet winner, subject to a certain number of hypotheses on the frequency of appearance of the different types of individual preferences.

The objective of this conference is to present recent contributions in the field of probabilistic analysis of voting rules and decision mechanisms, in the broad sense. We invite contributions on all areas of social choice and game theory that mobilize probabilistic arguments to gain a better understanding of the properties of decision rules.