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通过克隆不变性刻画多数规则

Characterizing the Plurality Rule via Clone Invariance

Leo Goto

arXiv 2608.18798首次发表:更新:

AI 中文总结

该研究针对多数规则易受选票分流的问题,引入p-抗克隆性概念并在评分规则类中考察,发现p∈(0,1)时仅平凡规则普遍满足该条件。

AI 中文摘要

多数规则易受相似备选方案间的选票分流影响。与传统认知相悖,我们通过一类特定的克隆独立性条件刻画多数规则。我们进一步引入单参数族p-抗克隆性(p-CR)的概念,并在评分规则类中考察该性质。对于p∈(0,1),至多含三个备选方案的非平凡规则存在,但仅平凡规则普遍满足该条件。

英文摘要

The Plurality rule is vulnerable to vote splitting between similar alternatives. Defying conventional wisdom, we characterize the Plurality rule through a specific type of clone independence condition. We further introduce the notion of a one-parameter family of $p$-Clone Resistance ($p$-CR), and examine the property within the class of scoring rules. For $p \in (0,1)$, nontrivial rules exist with at most three alternatives, but only the Trivial rule generally satisfies the condition.

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