We propose strike mechanisms as a solution to the classical problem of Hurwicz and Schmeidler (1978) and Maskin (1999) according to which, in two-person societies, no Pareto efficient rule is ...Nash-implementable. A strike mechanism specifies the number of alternatives that each player vetoes. Each player simultaneously casts these vetoes and the mechanism selects randomly one alternative among the non-vetoed ones. For strict preferences over alternatives and under a very weak condition for extending preferences over lotteries, these mechanisms are deterministic-in-equilibrium. They Nash implement a class of Pareto efficient social choice rules called Pareto-and-veto rules. Moreover, under mild richness conditions on the domain of preferences over lotteries, any Pareto efficient Nash-implementable rule is a Pareto-and-veto rule and hence is implementable through a strike mechanism.
Nous proposons divers modèles dont le but est d’expliquer la formation des stéréotypes. Un stéréotype est interprété comme un jugement émis par un observateur à propos d’un groupe d’individus ou ...d’objets. Pour chaque membre du groupe, on suppose que l’on observe une caractéristique appartenant à un ensemble dénombrable. La formation des stéréotypes est alors modélisée par une fonction de perception. Dans notre modèle de base, une fonction de perception combine trois étapes : 1) les caractéristiques sont codées numériquement de telle sorte que plus le nombre associé à une caractéristique est élevé, plus cette caractéristique est en accord avec le stéréotype étudié, 2) le vecteur de nombres ainsi obtenu est agrégé de manière cohérente en un nombre unique et enfin 3) ce nombre unique est comparé à un seuil et le stéréotype est accepté dès lors que le seuil est dépassé. Nous donnons une caractérisation des fonctions de perception qui entrent dans le cadre de ce modèle. Nous examinons enfin diverses extensions du modèle de base. JEL Codes: C44, D70.
In a world where voters not only rank the alternatives but also qualify them as “approved” or “disapproved”, we observe that majoritarianism in preferences and majoritarianism in approvals are ...logically incompatible. We show that this observation generalises to the following result: every aggregation rule that respects unanimity and decomposes the aggregation of preferences and approvals is dictatorial. Our result implies an incompatibility between ordinal and evaluative approaches to social choice theory under 2 weak assumptions: respect for unanimity and independence of evaluation of each alternative. We describe possibilities when the latter assumption is relaxed. On the other hand, our impossibility generalises to the case where there are more than the two evaluative levels of “approved” and “disapproved”.
Compromising as an equal loss principle Cailloux, Olivier; Napolitano, Beatrice; Sanver, M. Remzi
Review of economic design,
09/2023, Volume:
27, Issue:
3
Journal Article
Peer reviewed
Open access
A social choice rule aggregates the preferences of a group of individuals over a set of alternatives into a collective choice. The literature admits several social choice rules whose recommendations ...are supposed to reflect a compromise among individuals. We observe that all these compromise rules can be better described as
procedural compromises
, i.e., they impose over individuals a willingness to compromise but they do not ensure an outcome where everyone has effectively compromised. We revisit the concept of a compromise in a collective choice environment with at least three individuals having strict preferences over a finite set of alternatives. Referring to a large class of spread measures, we view the concept of compromise from an
equal loss
perspective, favoring an outcome where every voter concedes as equally as possible. As such, being a compromise may fail Pareto efficiency, which we ensure by asking voters to concede as equally as possible among the Pareto efficient alternatives. We show that Condorcet consistent rules, scoring rules (except antiplurality) and Brams-Kilgour compromises (except fallback bargaining) all fail to ascertain an outcome which is a compromise. A slight restriction on acceptable spread measures suffices to extend the negative result to antiplurality and fallback bargaining. This failure also prevails for social choice problems with two individuals: all well-known two-person social choice rules of the literature, namely, fallback bargaining, Pareto and veto rules, short listing and veto rank, fail to pick ex-post compromises. We conclude that there is a need to propose and study rules that satisfy this equal loss, or outcome oriented, notion of a compromise.
Although they exclude any possibility of a compromise ex-post, uniform random dictatorship methods provide a solution to conflicts of interest that guarantees an ex-ante fairness. Axiomatic ...characterizations of random dictatorships in the classical literature of social choice theory use strategy-proofness. In a probabilistic framework that embeds tops-onlyness and anonymity, for three or more alternatives, we provide a characterization that uses an independence condition instead: uniform random dictatorship is the only social choice rule that is efficient and independent. This characterization also establishes that under efficiency and anonymity, independence and strategy-proofness are equivalent. In the particular case of two alternatives, independence becomes vacuous and we propose a characterization without independence.
May's theorem shows that if the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule. We show that if ...the set of alternatives contains three or more alternatives only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash's version of "independence of irrelevant alternatives" for the domain of problems that have strict Condorcet winners. We show also that no rule satisfies the four conditions for domains that are more than slightly larger.
We propose simple models aiming at explaining the formation of stereotypes. A stereotype is an overall judgment brought by an observer over a group of individuals or objects. For each member of the ...group, we suppose that we observe a characteristic that belongs to a denumerable set. The formation of a stereotype about the group is governed by a perception function. Our basic model consists in decomposing a perception function into three steps: 1) characteristics are recoded numerically so that higher numbers mean a higher support for the stereotype, 2) this vector of numbers is consistently aggregated into a single number, and 3) this number is compared to a threshold and the stereotype is accepted if the threshold is exceeded. We characterize perception functions that can be explained using such a model. We then study various extensions of our basic model.
Nous proposons divers modèles dont le but est d’expliquer la formation des stéréotypes. Un stéréotype est interprété comme un jugement émis par un observateur à propos d’un groupe d’individus ou d’objets. Pour chaque membre du groupe, on suppose que l’on observe une caractéristique appartenant à un ensemble dénombrable. La formation des stéréotypes est alors modélisée par une fonction de perception. Dans notre modèle de base, une fonction de perception combine trois étapes: 1) les caractéristiques sont codées numériquement de telle sorte que plus le nombre associé à une caractéristique est élevé, plus cette caractéristique est en accord avec le stéréotype étudié, 2) le vecteur de nombres ainsi obtenu est agrégé de manière cohérente en un nombre unique et enfin 3) ce nombre unique est comparé à un seuil et le stéréotype est accepté dès lors que le seuil est dépassé. Nous donnons une caractérisation des fonctions de perception qui entrent dans le cadre de ce modèle. Nous examinons enfin diverses extensions du modèle de base.
Abreu and Sen (J Econ Theory 50(2):285–299, 1990) provide a necessary condition, called Condition
α
, which is almost sufficient for a social choice rule to be implementable via subgame perfect ...equilibria. Yet, it is not straightforward to check the satisfaction of Condition
α
. We contribute in this direction by establishing a nuanced picture over the subgame perfect implementability of compromise rules, as a function of the compromise threshold. This contrasts with scoring rules that all fail to be subgame perfect implementable and with several Condorcet rules which are subgame perfect implementable.
We revisit the incompatibility of anonymity and neutrality in single-valued social choice. We first analyze the irresoluteness outlook these two axioms together with Pareto efficiency impose on ...social choice rules and deliver a method to refine irresolute rules without violating anonymity, neutrality, and efficiency. Next, we propose a weakening of neutrality called
consequential neutrality
that requires resolute social choice rules to assign each alternative to the same number of profiles. We explore social choice problems in which consequential neutrality resolves impossibilities that stem from the fundamental tension between anonymity, neutrality, and resoluteness.
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