孔多塞域在最多七个备选项上

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences Pub Date : 2025-01-01 DOI:10.1016/j.mathsocsci.2024.12.002

Dolica Akello-Egwel , Charles Leedham-Green , Alastair Litterick , Klas Markström , Søren Riis

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引用次数: 0

摘要

孔多塞域是避免孔多塞悖论的线性序列集合。本文提出了一种完全枚举所有极大孔多塞域的新算法，并利用超级计算机得到了n≤7个备选项上所有极大孔多塞域的第一个枚举。我们研究了这些域的性质，并利用这项研究解决了关于孔多塞域的几个悬而未决的问题，并提出了几个新的猜想。接下来，我们将我们的结果与投票理论中使用的其他域类型联系起来，例如非独裁和策略证明域。我们所有的数据都在网上免费提供。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Condorcet domains on at most seven alternatives

A Condorcet domain is a collection of linear orders which avoid Condorcet’s paradox for majority voting. We have developed a new algorithm for complete enumeration of all maximal Condorcet domains and, using a supercomputer, obtained the first enumeration of all maximal Condorcet domains on

n \leq 7

alternatives.

We investigate properties of these domains and use this study to resolve several open questions regarding Condorcet domains, and propose several new conjectures. Following this we connect our results to other domain types used in voting theory, such a non-dictatorial and strategy-proof domains. All our data are made freely available on the web.

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来源期刊

Mathematical Social Sciences 数学-数学跨学科应用

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

59 days

期刊介绍： The international, interdisciplinary journal Mathematical Social Sciences publishes original research articles, survey papers, short notes and book reviews. The journal emphasizes the unity of mathematical modelling in economics, psychology, political sciences, sociology and other social sciences. Topics of particular interest include the fundamental aspects of choice, information, and preferences (decision science) and of interaction (game theory and economic theory), the measurement of utility, welfare and inequality, the formal theories of justice and implementation, voting rules, cooperative games, fair division, cost allocation, bargaining, matching, social networks, and evolutionary and other dynamics models. Papers published by the journal are mathematically rigorous but no bounds, from above or from below, limits their technical level. All mathematical techniques may be used. The articles should be self-contained and readable by social scientists trained in mathematics.