{"title":"On the decomposability of fractional allocations","authors":"Shurojit Chatterji , Peng Liu","doi":"10.1016/j.mathsocsci.2024.10.002","DOIUrl":null,"url":null,"abstract":"<div><div>A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 79-89"},"PeriodicalIF":0.5000,"publicationDate":"2024-10-28","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/S0165489624000908","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 common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.
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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