How many candidates are needed to make elections hard to manipulate?

In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally. The complexity of manipulating realistic elections where the number of candidates is a small constant was recently studied (Conitzer 2002), but the emphasis was on the question of whether or not a protocol becomes hard to manipulate for some constant number of candidates. That work, in many cases, left open the question: How many candidates are needed to make elections hard to manipulate? This is a crucial question when comparing the relative manipulability of different voting protocols. In this paper we answer that question for the voting protocols of the earlier study: plurality, Borda, STV, Copeland, maximin, regular cup, and randomized cup. We also answer that question for two voting protocols for which no results on the complexity of manipulation have been derived before: veto and plurality with runoff. It turns out that the voting protocols under study become hard to manipulate at 3 candidates, 4 candidates, 7 candidates, or never

Vote and aggregation in combinatorial domains with structured preferences

In many real-world collective decision problems, the set of alternatives is a Cartesian product of finite value domains for each of a given set of variables. The prohibitive size of such combinatorial domains makes it practically impossible to represent preference relations explicitly. Now, the AI community has been developing languages for representing preferences on such domains in a succinct way, exploiting structural properties such as conditional preferential independence. In this paper we reconsider voting and aggregation rules in the case where voters' preferences have a common preferential independence structure, and address the issue of decomposing a voting rule or an aggregation function following a linear order over variables

Compact preference representation and combinatorial vote

In many real-world social choice problems, the set of alternatives is defined as the Cartesian product of (finite) domain values for each of a given set of variables, and these variables cannot be asusmed to be prefentially independent (to take an example, if X is the main dish of a dinner and Y the wine, preferences over Y depends on the value taken for X). Such combinatorial domains are much too large to allow for representing preference relations or utility functions explicitly (that is, by listing alternatives together with their rank or utility); for this reason, artificial intelligence researchers have been developing languages for specifying preference relations or utility functions as compactly as possible. This paper first gives a brief survey of compact representation languages, and then discusses its role for representing and solving social choice problems, especially from the point of view of computational complexity

Boolean Hedonic Games

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen, Norway, July 27-30, 201

Procédure de vote parallèle dans les référendums multiples : une approche expérimentale

Session "Articles"National audienceLes référendums multiples consistent à prendre une décision commune sur chacune d'un ensemble de questions binaires, à partir des préférences d'un ensemble de votants. Demander aux votants leur avis sur toutes les combinaisons de valeurs est pratiquement infaisable, en raison du nombre exponentiellement grand de ces combinaisons ; d'un autre côté, effectuer des votes en parallèle sur chacune des questions peut mener à des résultats fortement paradoxaux. Dans cet article, nous essayons de mesurer à quel point il est sous-optimal de procéder à un tel vote parallèle, en fonction de la règle de vote que l'on veut implémenter, et de la nature des préférences des votants (arbitraires, faiblement séparables ou fortement séparables). Nous utilisons pour cela une expérimentation sur des données generées aléatoirement

Probabilistic Knowledge-Based Programs

International audienceWe introduce Probabilistic Knowledge-Based Programs (PKBPs), a new, compact representation of policies for factored partially observable Markov decision processes. PKBPs use branching conditions such as if the probability of ϕ is larger than p, and many more. While similar in spirit to value-based policies, PKBPs leverage the factored representation for more compactness. They also cope with more general goals than standard state-based rewards, such as pure information-gathering goals. Compactness comes at the price of reactivity, since evaluating branching conditions on-line is not polynomial in general. In this sense, PKBPs are complementary to other representations. Our intended application is as a tool for experts to specify policies in a natural, compact language, then have them verified automatically. We study succinctness and the complexity of verification for PKBPs

Génération de plans à base de connaissances

National audienceLes Knowledge-Based Programs (KBPs) associent représentation des connaissances et pla-nification. Il s'agit de protocoles décrivant les actions à effectuer par un agent, en fonction de son état de connaissance, afin d'atteindre un but donné. Ces plans possèdent une grande expressivité, grâce à l'uti-lisation de la logique modale S5, et une plus grande compacité que les plans classiques. La question de la génération de tels plans n'a été que peu étudiée. Notre objectif est de combler ce manque. Nous pro-posons des algorithmes permettant de générer des KBPs à partir de la spécification d'un état initial, d'un but et d'un ensemble d'actions disponibles. Deux types d'algorithmes sont présentés, par progression, c'est-à-dire en partant de l'état initial pour aller vers le but, et par régression, en partant cette fois-ci du but. Dans les deux cas, un algorithme de recherche en largeur est décrit, ayant la propriété de fournir un plan optimal en nombre d'actions à effectuer dans le pire cas. De même, nous exposons dans les deux cas des algorithmes de recherche en profondeur, dans lesquels une action est choisie pour chaque état de connaissance, par le biais de différentes fonctions heuristiques dont nous montrons certaines propriétés. Nous proposons également des benchmarks adaptés, pour lesquels la planification classique est moins précise, et testons nos algorithmes sur ces problèmes

New Candidates Welcome! Possible Winners with respect to the Addition of New Candidates

In voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number $k$ of new candidates will be added. We give a computational study of this problem, focusing on scoring rules, and we provide a formal comparison with related problems such as control via adding candidates or cloning.Comment: 34 page