{"title":"Nash implementation of supermajority rules","authors":"","doi":"10.1007/s00182-024-00888-1","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>A committee of <em>n</em> experts from a university department must choose whom to hire from a set of <em>m</em> candidates. Their honest judgments about the best candidate must be aggregated to determine the socially optimal candidates. However, experts’ judgments are not verifiable. Furthermore, the judgment of each expert does not necessarily determine his preferences over candidates. To solve this problem, a mechanism that implements the socially optimal aggregation rule must be designed. We show that the smallest quota <em>q</em> compatible with the existence of a <em>q</em>-supermajoritarian and Nash implementable aggregation rule is <span> <span>\\(q=n-\\left\\lfloor \\frac{n-1}{m}\\right\\rfloor\\)</span> </span>. Moreover, for such a rule to exist, there must be at least <span> <span>\\(m\\left\\lfloor \\frac{n-1}{m}\\right\\rfloor +1\\)</span> </span> impartial experts with respect to each pair of candidates.</p>","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"162 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Game Theory","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00182-024-00888-1","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 committee of n experts from a university department must choose whom to hire from a set of m candidates. Their honest judgments about the best candidate must be aggregated to determine the socially optimal candidates. However, experts’ judgments are not verifiable. Furthermore, the judgment of each expert does not necessarily determine his preferences over candidates. To solve this problem, a mechanism that implements the socially optimal aggregation rule must be designed. We show that the smallest quota q compatible with the existence of a q-supermajoritarian and Nash implementable aggregation rule is \(q=n-\left\lfloor \frac{n-1}{m}\right\rfloor\). Moreover, for such a rule to exist, there must be at least \(m\left\lfloor \frac{n-1}{m}\right\rfloor +1\) impartial experts with respect to each pair of candidates.
期刊介绍：
International Journal of Game Theory is devoted to game theory and its applications. It publishes original research making significant contributions from a methodological, conceptual or mathematical point of view. Survey articles may also be considered if especially useful for the field.
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