Relaxed notions of Condorcet-consistency and efficiency for strategyproof social decision schemes

IF 0.5 4区经济学 Q4 ECONOMICS Social Choice and Welfare Pub Date : 2024-04-01 DOI:10.1007/s00355-024-01519-0

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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.

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防策略社会决策方案的康德塞特一致性和效率的宽松概念

摘要社会决策方案（SDS）将一组选民对某组 m 个备选方案的偏好映射为备选方案的概率分布。吉巴德（Gibbard，《计量经济学》，45（3）：665-681，1977 年）对无策略 SDS 进行了开创性的描述，暗示不存在无策略的康德塞特扩展，只有随机独裁才满足事后效率和无策略性。后者被称为随机独裁定理。我们分别引入了康德赛特胜者概率的下限和帕累托主导替代方案概率的上限，从而放宽了康德赛特一致性和事后效率。然后，我们证明了随机化的谷轮规则是唯一匿名、中立且不受策略影响的 SDS，它能保证康德赛特获胜者的概率至少为 2/m。其次，我们证明了吉巴德随机独裁定理的持续加强：我们赋予帕累托主导的备选方案的概率越小，得到的 SDS 就越接近随机独裁。最后，我们证明了唯一能最大化康德赛特获胜者概率，同时最小化帕累托主导替代方案概率的匿名、中立和无策略的 SDS 是均匀随机独裁和随机科普兰规则的混合物。

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来源期刊

Social Choice and Welfare Multiple-

CiteScore

1.60

自引率

11.10%

发文量

期刊介绍： Social Choice and Welfare explores all aspects, both normative and positive, of welfare economics, collective choice, and strategic interaction. Topics include but are not limited to: preference aggregation, welfare criteria, fairness, justice and equity, rights, inequality and poverty measurement, voting and elections, political games, coalition formation, public goods, mechanism design, networks, matching, optimal taxation, cost-benefit analysis, computational social choice, judgement aggregation, market design, behavioral welfare economics, subjective well-being studies and experimental investigations related to social choice and voting. As such, the journal is inter-disciplinary and cuts across the boundaries of economics, political science, philosophy, and mathematics. Articles on choice and order theory that include results that can be applied to the above topics are also included in the journal. While it emphasizes theory, the journal also publishes empirical work in the subject area reflecting cross-fertilizing between theoretical and empirical research. Readers will find original research articles, surveys, and book reviews.Officially cited as: Soc Choice Welf

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