{"title":"Christian Klamler’s ”A distance measure for choice functions” [Social Choice and Welfare 30 (2008) 419–425]: a correction","authors":"","doi":"10.1007/s00355-023-01497-9","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>An extensive choice over <em>X</em> is a function assigning to any subset <em>S</em> of <em>X</em> a possibly empty subset of <em>S</em>. Klamler (Soc Choice Welf 30:419–425, 2008) shows that the operation of symmetric difference induces a metric on the family of extensive choices over <em>X</em>, and this metric is characterized by five axioms <span>A1</span>–<span>A5</span>. We provide counterexamples to Klamler’s result, suggest a slight modification of axioms <span>A4</span> and <span>A5</span> to obtain a correct characterization, and finally observe that axiom <span>A4</span> is redundant.</p>","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"32 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-03-14","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/s00355-023-01497-9","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
An extensive choice over X is a function assigning to any subset S of X a possibly empty subset of S. Klamler (Soc Choice Welf 30:419–425, 2008) shows that the operation of symmetric difference induces a metric on the family of extensive choices over X, and this metric is characterized by five axioms A1–A5. We provide counterexamples to Klamler’s result, suggest a slight modification of axioms A4 and A5 to obtain a correct characterization, and finally observe that axiom A4 is redundant.
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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