{"title":"加权择校问题和加权顶层交易循环机制","authors":"Nadja Stroh-Maraun","doi":"10.1016/j.mathsocsci.2024.09.001","DOIUrl":null,"url":null,"abstract":"<div><p>There are a number of school choice problems in which students are heterogeneous according to the number of seats they occupy at the school they are assigned to. We propose a weighted school choice problem by assigning each student a so-called weight and formulate the weighted top trading cycles algorithm (WTTC) to find a matching. The WTTC is strategy-proof and results in a Pareto efficient matching. While the WTTC is a robust extension of the TTC when weights are introduced, it is no longer guaranteed that each student gets a seat at a school even if the overall capacity exceeds the sum of weights. Additionally, the WTTC introduces a trade-off between weights and priorities as a student with a higher weight has a disadvantage to be matched to a particular school compared to a student with the same schools’ priorities but a smaller weight.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 49-56"},"PeriodicalIF":0.5000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000817/pdfft?md5=20c6d6ce7944d3dcfc320f58184efcf4&pid=1-s2.0-S0165489624000817-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Weighted school choice problems and the weighted top trading cycles mechanism\",\"authors\":\"Nadja Stroh-Maraun\",\"doi\":\"10.1016/j.mathsocsci.2024.09.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>There are a number of school choice problems in which students are heterogeneous according to the number of seats they occupy at the school they are assigned to. We propose a weighted school choice problem by assigning each student a so-called weight and formulate the weighted top trading cycles algorithm (WTTC) to find a matching. The WTTC is strategy-proof and results in a Pareto efficient matching. While the WTTC is a robust extension of the TTC when weights are introduced, it is no longer guaranteed that each student gets a seat at a school even if the overall capacity exceeds the sum of weights. Additionally, the WTTC introduces a trade-off between weights and priorities as a student with a higher weight has a disadvantage to be matched to a particular school compared to a student with the same schools’ priorities but a smaller weight.</p></div>\",\"PeriodicalId\":51118,\"journal\":{\"name\":\"Mathematical Social Sciences\",\"volume\":\"132 \",\"pages\":\"Pages 49-56\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0165489624000817/pdfft?md5=20c6d6ce7944d3dcfc320f58184efcf4&pid=1-s2.0-S0165489624000817-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Social Sciences\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165489624000817\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Social Sciences","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165489624000817","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
Weighted school choice problems and the weighted top trading cycles mechanism
There are a number of school choice problems in which students are heterogeneous according to the number of seats they occupy at the school they are assigned to. We propose a weighted school choice problem by assigning each student a so-called weight and formulate the weighted top trading cycles algorithm (WTTC) to find a matching. The WTTC is strategy-proof and results in a Pareto efficient matching. While the WTTC is a robust extension of the TTC when weights are introduced, it is no longer guaranteed that each student gets a seat at a school even if the overall capacity exceeds the sum of weights. Additionally, the WTTC introduces a trade-off between weights and priorities as a student with a higher weight has a disadvantage to be matched to a particular school compared to a student with the same schools’ priorities but a smaller weight.
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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