Social Choice and Welfare最新文献

We present various results about Euclidean preferences in the plane under (ell _1,) (ell _2) and (ell _{infty }) norms. When there are four candidates, we show that the maximum size (in terms of the number of pairwise distinct preferences) of Euclidean preference profiles in ({mathbb {R}}^2) under norm (ell _1) or (ell _{infty }) is 19. Whatever the number of candidates, we prove that at most four distinct candidates can be ranked in the last position of a two-dimensional Euclidean preference profile under norm (ell _1) or (ell _infty ,) which generalizes the case of one-dimensional Euclidean preferences (for which it is well known that at most two candidates can be ranked last). We generalize this result to (2^d) (resp. 2d) for (ell _1) (resp. (ell _infty )) for d-dimensional Euclidean preferences. We also establish that the maximum size of a two-dimensional Euclidean preference profile on m candidates under norm (ell _1) is in (varTheta (m^4),) which is the same order of magnitude as the known maximum size under norm (ell _2.) Finally, we provide a new proof that two-dimensional Euclidean preference profiles under norm (ell _2) for four candidates can be characterized by three inclusion-maximal two-dimensional Euclidean profiles. This proof is a simpler alternative to that proposed by Kamiya et al. (Adv Appl Math 47(2):379–400, 2011).

We consider a setting in which the alternatives are binary vectors and the preferences of the agents are determined by the Hamming distance from their most preferred alternatives. We consider only rules that are unanimous, anonymous, and component-neutral, and focus on strategy-proofness, weak group strategy-proofness, and strong group strategy-proofness. We show that component-wise majority rules are strategy-proof, and for three agents or two components also weakly group strategy-proof, but not otherwise. These rules are even strongly group strategy-proof if there are two or three agents. Our main result is an impossibility result: if there are at least four agents and at least three components, then no rule is strongly group strategy-proof.

The single transferable vote (STV) voting method is used to elect multiple candidates in ranked-choice elections. One weakness of STV is that it fails multiple fairness criteria related to monotonicity and no-show paradoxes. We analyze 1079 local government STV elections in Scotland to estimate the frequency of such monotonicity anomalies in real-world elections, and compare our results with prior empirical and theoretical research about the rates at which such anomalies occur. In 62 of the 1079 elections we found some kind of monotonicity anomaly. We generally find that anomaly rates are similar to prior empirical research and much lower than what most theoretical research has found. Most STV anomalies we find are the first of their kind to be documented in real-world multiwinner elections.

Fishburn’s alternating scheme domains occupy a special place in the theory of Condorcet domains. Karpov (2023) generalised these domains and made an interesting observation proving that all of them are single-peaked on a circle. However, an important point that all generalised Fishburn domains are maximal Condorcet domain remained unproved. We fill this gap and suggest a new combinatorial interpretation of generalised Fishburn’s domains which provide a constructive proof of single-peakedness of these domains on a circle. We show that classical single-peaked domains and single-dipped domains as well as Fishburn’s alternating scheme domains belong to this family of domains while single-crossing domains do not.

Abstract

We introduce semi-flexible majority rules for public good provision with private valuations. Such rules take the form of a two-stage, multiple-round voting mechanism where the output of the first stage is the default alternative for the second stage and the vote-share thresholds used in every round of binary voting (a) vary with the alternative on the table for a public-good level and (b) require a qualified majority for approving the alternative on the table by stopping the procedure. We show that these mechanisms implement the ex post utilitarian optimal public-good level, provided valuations can only be high or low. This public-good level is chosen after all potential socially optimal alternatives have been picked for a voting round. We explore ways to reduce the number of voting rounds and develop a compound mechanism when there are three or more valuation types.

Abstract

Social decision schemes (SDSs) map the preferences of a group of voters over some set of m alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard (Econometrica 45(3):665–681, 1977) implies that there are no strategyproof Condorcet extensions and that only random dictatorships satisfy ex post efficiency and strategyproofness. The latter is known as the random dictatorship theorem. We relax Condorcet-consistency and ex post efficiency by introducing a lower bound on the probability of Condorcet winners and an upper bound on the probability of Pareto-dominated alternatives, respectively. We then show that the randomized Copeland rule is the only anonymous, neutral, and strategyproof SDS that guarantees the Condorcet winner a probability of at least 2/m. Secondly, we prove a continuous strengthening of Gibbard’s random dictatorship theorem: the less probability we put on Pareto-dominated alternatives, the closer to a random dictatorship is the resulting SDS. Finally, we show that the only anonymous, neutral, and strategyproof SDSs that maximize the probability of Condorcet winners while minimizing the probability of Pareto-dominated alternatives are mixtures of the uniform random dictatorship and the randomized Copeland rule.

Welfare and other properties of Berge equilibria are investigated. In particular, we address the questions to what extent Berge equilibrium can select from multiple Nash equilibria; can serve as a substitute for Nash equilibria; can Pareto improve upon Nash equilibrium. Furthermore, some of the recent results on the relation between Berge equilibria and Kantian equilibria are summarized.

In the third decade of the 21st century, digitization and artificial intelligence, global events, challenges from authoritarian states, and difficulties of particular democracies to function properly confront democracy with a new series of challenges and opportunities that will force it to reinvent itself. The last decades have produced an accelerating flow of ideas for new forms of democracy. We survey a long period in the quest for such new forms and point to next inventions for such forms. We suggest to experiment with new ways for democracy to extend the choice of democratic processes that can be implemented in real-life situations, with the beneficial side-effect that democracy might remain the only sustainable structure for self-governing societies.

Abstract

Proportional ranking rules aggregate approval-style preferences of agents into a collective ranking such that groups of agents with similar preferences are adequately represented. Motivated by the application of live Q&A platforms, where submitted questions need to be ranked based on the interests of the audience, we study a dynamic extension of the proportional rankings setting. In our setting, the goal is to maintain the proportionality of a ranking when alternatives (i.e., questions)—not necessarily from the top of the ranking—get selected sequentially. We propose generalizations of well-known ranking rules to this setting and study their monotonicity and proportionality properties. We also evaluate the performance of these rules experimentally, using realistic probabilistic assumptions on the selection procedure.

Abstract

An extensive choice over X is a function assigning to any subset S of X a possibly empty subset of S. Klamler (Soc Choice Welf 30:419–425, 2008) shows that the operation of symmetric difference induces a metric on the family of extensive choices over X, and this metric is characterized by five axioms A1–A5. We provide counterexamples to Klamler’s result, suggest a slight modification of axioms A4 and A5 to obtain a correct characterization, and finally observe that axiom A4 is redundant.