arXiv:2601.20779cs.GTcs.AI2026-01被引 1

研究近似克隆候选人在选举中的影响,发现多数规则不满足该性质。

Independence of Approximate Clones

  • 提出两种量化近似克隆的方法,评估其对投票结果的影响。
  • 四人以上选举中,现有克隆无关规则均不满足近似克隆无关。
  • 三人选举时有积极结果,实证显示近似克隆在真实数据中常见。

在序数选举中,若每位选民将两个候选人相邻排列,则称其为完美克隆。克隆无关性公理要求移除其中一个克隆不应改变选举结果。该公理在社会选择理论中被广泛研究,已有若干投票规则(如IRV、Ranked Pairs和Schulze)被证明满足此性质。然而,现实中完美克隆极少出现,尤其在大规模政治选举中。本文研究序数选举中近似克隆的不同定义,提出两种衡量接近程度的度量方式,并分析已知克隆无关规则在何种条件下也具备近似克隆无关性。结果表明:在至少四个候选人的选举中,这些规则在一般情况下不满足近似克隆无关性;但在三人选举中存在更积极的结果。此外,基于苏格兰地方选举、迷你陪审团审议及花样滑冰裁判评分三个真实数据集的实证研究表明,近似克隆在某些情境下较为普遍,且候选人间越接近完美克隆,其移除对结果的影响越小,尤其是对原本满足完美克隆无关性的规则而言。

原文摘要 · Abstract (English)

In an ordinal election, two candidates are said to be perfect clones if every voter ranks them adjacently. The independence of clones axiom then states that removing one of the two clones should not change the election outcome. This axiom has been extensively studied in social choice theory, and several voting rules are known to satisfy it (such as IRV, Ranked Pairs and Schulze). However, perfect clones are unlikely to occur in practice, especially for political elections with many voters. In this work, we study different notions of approximate clones in ordinal elections. Informally, two candidates are approximate clones in a preference profile if they are close to being perfect clones. We discuss two measures to quantify this proximity, and we show under which conditions the voting rules that are known to be independent of clones are also independent of approximate clones. In particular, we show that for elections with at least four candidates, none of these rules are independent of approximate clones in the general case. However, we find a more positive result for the case of three candidates. Finally, we conduct an empirical study of approximate clones and independence of approximate clones based on three real-world datasets: votes in local Scottish elections, votes in mini-jury deliberations, and votes of judges in figure skating competitions. We find that approximate clones are common in some contexts, and that the closest two candidates are to being perfect clones, the less likely their removal is to change the election outcome, especially for voting rules that are independent of perfect clones.

投票机制社会选择近似克隆

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