提出三类选票指标，量化投票中的共识、多样性与极化程度。
Agreement, Diversity, and Polarization Indices for Approval Elections
- 设计归一化指标，衡量选民在批准投票中的共识度。
- 通过真实选举数据验证，发现不同投票场景的结构差异。
- 适合研究选举制度或社会极化现象的学者使用。
指数是将选举映射到0到1之间的数值函数，用于衡量选举中某种特征的程度。本文旨在为批准投票设计能捕捉选民间共识、多样性与极化的指数，并满足饱和归一化要求：若两个选举仅平均每位选民批准候选人比例不同，但整体结构相似，则指数值应相近。我们提出了若干指数，分析其性质，并应用于（a）构建新的批准投票地图，以及（b）比较来自Pabulib、Preflib等来源的真实选举，揭示其相似性与差异性。
原文摘要 · Abstract (English)
An index is a function that given an election outputs a value between 0 and 1, indicating the extent to which this election has a particular feature. We seek indices that capture agreement, diversity, and polarization among voters in approval elections, and that are normalized with respect to saturation. By the latter we mean that if two elections differ by the fraction of candidates approved by an average voter, but otherwise are of similar nature, then they should have similar index values. We propose several indices, analyze their properties, and use them to (a) derive a new map of approval elections, and (b) show similarities and differences between various real-life elections from Pabulib, Preflib and other sources.
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