{"title":"Group strategy-proof rules in multidimensional binary domains","authors":"Aditya Aradhye, Hans Peters","doi":"10.1007/s00355-024-01523-4","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"125 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Social Choice and Welfare","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00355-024-01523-4","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
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.
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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