基于认可的委员会选举中的候选人弃权单调性
Candidate Resignation Monotonicity in Approval-Based Committee Elections
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中文总结 AI 辅助
该研究针对基于认可的委员会选举，提出弃权单调性概念，证明多数主流ABC规则不满足该属性，设计的最大支付规则（MPR）可满足其松弛形式，且PAV规则易受战略操纵影响。
中文摘要 AI 辅助
基于认可的委员会（ABC）选举依据选民的认可偏好选出固定规模的候选人委员会。我们研究当选成员可能弃权的场景，并形式化弃权单调性：当弃权后重新运行投票规则时，弃权单调规则必须仍选出所有剩余的原获胜候选人。我们表明，许多主流ABC规则不满足该属性；通过将我们的概念与之前关于候选集动态变化的ABC选举研究相联系，我们证明了正当代表（JR）公理与弃权单调性不兼容。结果表明，分数委员会投票不存在此问题：基于在选举实例的网络表示中使用最大流的规则可同时满足代表公理和弃权单调性。我们设计了最大流的整数版本——最大支付规则（MPR），并证明其满足弃权单调性的松弛形式，该形式仅要求存在某种替换弃权候选人的方式以保证PJR+公理。MPR在一般情况下的计算是NP难的，但在结构化领域中可处理。最后，我们研究战略场景：一名落败候选人可能引入新的弱势候选人参与选举以试图成为获胜者。我们表明，所有弃权单调规则以及许多序列规则对此具有免疫力，但PAV规则可通过这种方式被操纵。
英文摘要
Approval-based committee (ABC) elections select a fixed-size committee of candidates based on voters' approval preferences. We study a setting where elected members may resign and formalize resignation monotonicity: when we re-run the voting rule after resignations, a resignation monotone rule must still elect all remaining previously winning candidates. We show that many prominent ABC rules fail this property, and by connecting our notion to prior work on ABC elections with dynamic candidate sets, we show that the justified representation (JR) axiom is incompatible with resignation monotonicity. It turns out that fractional committee voting does not suffer from this issue: rules based on using maximum flows in the network representation of an election instance can satisfy both representation axioms and resignation monotonicity. We design an integral version of maximum flow, the Maximum Payment Rule (MPR), and show that it satisfies a relaxed form of resignation monotonicity that only requires there to be some way of replacing the resigning candidates in a way that guarantees the PJR+ axiom. MPR is NP-hard to compute in general, but becomes tractable in structured domains. Finally, we study a strategic setting where a losing candidate may introduce new weak candidates to the election to try to become a winner. We show that all resignation monotone rules as well as many sequential rules are immune, but that the PAV rule can be manipulated in this way.
