{"title":"Extensions of partial priorities and stability in school choice","authors":"Minoru Kitahara , Yasunori Okumura","doi":"10.1016/j.mathsocsci.2024.06.002","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a school choice matching model where priorities for schools are represented by binary relations that may not be linear orders. Even in that case, it is necessary to construct linear orders from the original priority relations to execute several mechanisms. We focus on the (linear order) extensions of the priority relations, because a matching that is stable for an extension profile is also stable for the profile of priority relations. We show that if the priority relations are partial orders, then for each stable matching for the original profile of priority relations, an extension profile for which it is also stable exists. Furthermore, if there are multiple stable matchings that are ranked by Pareto dominance, then there is an extension for which all these matchings are stable. We apply the result to a version of efficiency adjusted deferred acceptance mechanisms.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"131 ","pages":"Pages 1-4"},"PeriodicalIF":0.5000,"publicationDate":"2024-06-27","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/S0165489624000532","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 school choice matching model where priorities for schools are represented by binary relations that may not be linear orders. Even in that case, it is necessary to construct linear orders from the original priority relations to execute several mechanisms. We focus on the (linear order) extensions of the priority relations, because a matching that is stable for an extension profile is also stable for the profile of priority relations. We show that if the priority relations are partial orders, then for each stable matching for the original profile of priority relations, an extension profile for which it is also stable exists. Furthermore, if there are multiple stable matchings that are ranked by Pareto dominance, then there is an extension for which all these matchings are stable. We apply the result to a version of efficiency adjusted deferred acceptance mechanisms.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
