扩展委员会选举模型，支持正负投票并定义两种比例公平准则
Proportional Committee Elections with Positive and Negative Votes
- 引入正负投票机制，更贴近在线投票实际
- 提出两类比例公平公理，分别针对不同投票逻辑
- 验证了Phragmén、PAV等规则在新框架下的公平性表现
传统委员会选举中，选民仅批准候选人，目标是根据偏好选出k名胜者。近年来研究聚焦于实现比例代表制。本文探讨在更具表达力的设置下——允许选民反对候选人（常见于在线投票平台）的比例性概念。我们提出两种概念上不同的负票解释：第一种认为阻止不赞成候选人当选与支持赞成候选人同等重要；第二种将赞成与反对分开处理，各自享有独立的公平保障。针对每种思路，我们引入相应的比例性公理，并检验其在Phragmén规则、成比例批准投票（PAV）及等份额法（MES）的适当变体下的可满足性。
原文摘要 · Abstract (English)
In the classic committee election setting each voter approves a subset of candidates and the goal is to select $k$ winners based on these preferences. A central focus of recent research in the area has been to achieve proportional representation. In this work, we explore notions of proportionality in a more expressive setting that allows voters to vote against candidates---a common feature on online polling platforms and beyond. We propose two conceptually distinct interpretations of negative votes, resulting in different perspectives of proportionality. In the first, preventing the election of disapproved candidates is as important to voters as electing approved ones. In the second, approvals and disapprovals are treated separately, with each receiving its own fairness guarantees. For each approach, we introduce suitable axioms capturing proportionality and examine their satisfiability by appropriate variants of Phragmén's rule, Proportional Approval Voting rule (PAV), and the Method of Equal Shares (MES).
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