Which set of agents plays a key role? An impossibility in transforming binary relations

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences Pub Date : 2024-02-23 DOI:10.1016/j.mathsocsci.2024.02.003

Takahiro Suzuki, Masahide Horita

引用次数: 0

Abstract

When provided with the performance ranking of multiple sets of agents as input, which set of agents is expected to play the key role? To address this question, we introduce a new rule (transformation rule) that maps a performance ranking over sets of agents into a contributing ranking over sets of agents. Preference extension (PE) and social ranking problem (SRP) represent two special cases. We prove an impossibility theorem: in a sufficiently rich environment, there is no transformation rule that satisfies ceteris paribus weak dominance, self-reflection, and triple-acyclicity. The impossibility is novel in that it is degenerated in PE/SRP models.

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哪一组代理人起着关键作用？转换二元关系的不可能性

当输入多组代理的绩效排名时，哪一组代理会发挥关键作用？为了解决这个问题，我们引入了一个新规则（转换规则），它可以将一组代理的绩效排名映射为一组代理的贡献排名。偏好扩展（PE）和社会排名问题（SRP）代表了两种特殊情况。我们证明了一个不可能性定理：在一个足够丰富的环境中，不存在满足弱支配性、自省性和三重椭圆性的转化规则。这种不可能性的新颖之处在于，它在 PE/SRP 模型中退化了。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Social Sciences 数学-数学跨学科应用

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

59 days

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.