{"title":"Condorcet domains on at most seven alternatives","authors":"Dolica Akello-Egwel , Charles Leedham-Green , Alastair Litterick , Klas Markström , Søren Riis","doi":"10.1016/j.mathsocsci.2024.12.002","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mrow><mi>n</mi><mo>≤</mo><mn>7</mn></mrow></math></span> alternatives.</div><div>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.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"133 ","pages":"Pages 23-33"},"PeriodicalIF":0.5000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Social Sciences","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165489624001045","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
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 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.
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.
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