Monotonicity of a profile of rankings with ties

International Conference, IPMU (17th. 2018. Cádiz

Voces Populi and the Art of Listening

The strategy most damaging to many preferential election methods is to give insincerely low rank to the main opponent of one’s favorite candidate. Theorem 1 determines the 3-candidate Condorcet method that minimizes the number of noncyclic profiles allowing this strategy. Theorems 2, 3, and 4 establish conditions for an anonymous and neutral 3-candidate single-seat election to be monotonic and still avoid this strategy completely. Plurality elections combine these properties; among the others "conditional IRV" gives the strongest challenge to the plurality winner. Conditional IRV is extended to any number of candidates. Theorem 5 is an impossibility of Gibbard-Satterthwaite type, describing 3 specific strategies that cannot all be avoided in meaningful anonymous and neutral elections.Preferential Election methods; Plurality Election methods

Alternative characterizations of Boston mechanism

Kojima and Ünver (2011) are the first to characterize the class of mechanisms coinciding with the Boston mechanism for some priority order. By mildly strengthening their central axiom, we are able to pin down the Boston mechanism outcome for every priority order. Our main result shows that a mechanism is outcome equivalent to the Boston mechanism at every priority if and only if it respects both preference rankings and priorities and satisfies individual rationality for schools. In environments where each student is acceptable to every school, respecting both preference rankings and priorities is enough to characterize the Boston mechanism

Figure Skating and the Theory of Social Choice

The rule used by the United States Figure Skating Association and the International Skating Union, hereafter the ISU Rule, to aggregate individual rankings of the skaters by the judges into a final ranking, is an interesting example of a social welfare function. This rule is examined thoroughly in this paper from the perspective of the modern theory of social choice. The ISU Rule is based on four different criteria, the first being median ranks of the skaters. Although the median rank criterion is a majority principle, it is completely at odd with another majority principle introduced in this paper and called the Extended Condorcet Criterion. It may be translated as follows: If a competitor is ranked consistently ahead of another competitor by an absolute majority of judges, he should be ahead in the final ranking. Consistency here refers to the absence of a cycle in the majority relation involving these two skaters. There are actually many cycles in the data of four Olympic Games that were examined. The Kemeny rule may be used to break these cycles. This is not only consistent with the Extended Condorcet Criterion but the latter also proves useful in finding Kemeny orders over large sets of alternatives, by allowing decomposition of these orders. The ISU, the Kemeny, the Borda rankings and the ranking according to the raw marks are then compared on 24 olympic competitions. The four rankings disagree in many instances. Finally it is shown that the ISU Rule may be very sensitive to small errors on the part of the judges and that it does not escape the numerous theorems on manipulation. Some considerations are also offered as to whether the ISU Rule is more or less prone to manipulation than others. La règle utilisée par la United States Figure Skating Association et l'International Skating Union, ci-après la règle de l'ISU, pour agréger les classements des patineurs par chacun des juges en un classement final, est un exemple intéressant de fonction de bien-être social. Cette règle est examinée en détail dans cet article du point de vue de la théorie moderne des choix sociaux. Cette règle repose sur quatre critères, le premier étant le rang médian des patineurs. Bien que ce critère soit en fait un principe majoritaire, il va à l'encontre d'un autre principe majoritaire introduit ici et appelé le Critère de Condorcet généralisé. Il peut être traduit ainsi: Si un compétiteur est classé avant un autre de manière cohérente par une majorité de juges, il devrait l'être dans le classement final. La cohérence réfère à l'absence de cycle dans la relation majoritaire impliquant ces deux compétiteurs. De fait, plusieurs cycles ont été rencontrés dans les données de quatre Jeux olympiques qui ont été examinées. La règle de Kemeny peut être utilisée pour briser ces cycles. Non seulement cette règle est-elle cohérente avec le Critère de Condorcet généralisé mais ce dernier s'avère utile dans la recherche d'ordres de Kemeny sur un grand nombre d'alternatives, en permettant la décomposition de ces ordres. Les classements des patineurs selon les règles de l'ISU, de Kemeny, de Borda et selon les notes brutes sont ensuite comparés pour 24 compétitions olympiques. Les quatre classements sont souvent différents. Finalement, il est démontré que la règle de l'ISU peut être très sensible à de petites erreurs de la part des juges et qu'elle n'échappe pas aux nombreux théorèmes d'impossibilité sur la manipulation. Quelques remarques sont aussi offertes sur la plus ou moins grande susceptibilité de cette règle à la manipulation par rapport à d'autres règles.

A Voting-Based System for Ethical Decision Making

We present a general approach to automating ethical decisions, drawing on machine learning and computational social choice. In a nutshell, we propose to learn a model of societal preferences, and, when faced with a specific ethical dilemma at runtime, efficiently aggregate those preferences to identify a desirable choice. We provide a concrete algorithm that instantiates our approach; some of its crucial steps are informed by a new theory of swap-dominance efficient voting rules. Finally, we implement and evaluate a system for ethical decision making in the autonomous vehicle domain, using preference data collected from 1.3 million people through the Moral Machine website.Comment: 25 pages; paper has been reorganized, related work and discussion sections have been expande

The acclamation consensus state and an associated ranking rule

The study of conditions, under which the existence of an “absolute” best winner can be assured, is a hot topic in the field of social choice. Unanimity is an evident example of a condition under which the winner is obvious. However, many more properties weaker than unanimity have been analysed in literature: the presence of a Condorcet winner, strong stochastic transitivity, the presence of a candidate that Borda dominates all other candidates, etc. Unfortunately, one could easily find a prominent ranking rule, for which the outcome does not agree with these relaxed conditions. In this study, we aim to identify a condition weaker than unanimity, but under which the social outcome is still obvious. This condition, defined as the conjunction of three properties already studied by the present authors and hereinafter referred to as acclamation, will be proven to be a meeting point for the most prominent ranking rules in social choice theory, and will be used for introducing an intuitively appealing ranking rule

A partial taxonomy of judgment aggregation rules, and their properties

The literature on judgment aggregation is moving from studying impossibility results regarding aggregation rules towards studying specific judgment aggregation rules. Here we give a structured list of most rules that have been proposed and studied recently in the literature, together with various properties of such rules. We first focus on the majority-preservation property, which generalizes Condorcet-consistency, and identify which of the rules satisfy it. We study the inclusion relationships that hold between the rules. Finally, we consider two forms of unanimity, monotonicity, homogeneity, and reinforcement, and we identify which of the rules satisfy these properties

Monotonic Incompatibility Between Electing and Ranking

Borda proposed a method that assigns points to each of the m candidates. Condorcet proposed a method that assigns points to each of the m! rankings of candidates. The first is more appropriate for electing, the second is more appropriate for ranking. Each satisfies a different type of monotonicity. These monotonicities are incompatible.Borda a proposé une méthode qui attribue des points à chacun des m candidats. Condorcet a proposé une méthode qui attribue des points à chacun des différents m! classements des candidats. La première est plus appropriée pour élire. La seconde est plus appropriée pour classer. Chacune satisfait une certaine monotonie. Leurs monotonies sont incompatible