基于多数边界的投票规则特征
Characterizations of voting rules based on majority margins
AI总结：
本文研究了基于多数边界的投票规则特性，证明了投票规则基于边界的充要条件是满足偏好平等性公理。
摘要：
在具有排序选票的投票情境中，一个重要投票规则类别是基于边界的规则（也称为配对规则）。一个投票规则是基于边界的，当两个选举产生相同的头对头胜负边界的候选人间结果时，该投票规则在两个选举中都会产生相同的结果。尽管这是一个数学上自然的不变性属性，但将其视为投票规则的规范公理是否合理尚不明确。在本文中，我们针对任何类型的输出投票规则（无论是候选人的集合、排名、概率分布等）探讨这一问题。我们证明，一个投票规则是基于边界的，当且仅当它满足一些具有更清晰规范内容的公理。一个关键公理是所谓的偏好平等性，即如果两个选民都立即将一个候选人x排在另一个候选人y之上，那么如果一个选民切换为将y排在x之上，其对选举结果的影响与另一个选民切换相同，因此每个选民对y优于x的偏好被平等对待。
英文摘要：
In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins of victory or loss between candidates, the voting rule yields the same outcome in both elections. Although this is a mathematically natural invariance property to consider, whether it should be regarded as a normative axiom on voting rules is less clear. In this paper, we address this question for voting rules with any kind of output, whether a set of candidates, a ranking, a probability distribution, etc. We prove that a voting rule is margin-based if and only if it satisfies some axioms with clearer normative content. A key axiom is what we call Preferential Equality, stating that if two voters both rank a candidate $x$ immediately above a candidate $y$, then either voter switching to rank $y$ immediately above $x$ will have the same effect on the election outcome as if the other voter made the switch, so each voter's preference for $y$ over $x$ is treated equally.
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