Sampford 分配法满足阈值单调性
Sampford Apportionment Satisfies Threshold Monotonicity
- UNSW Sydney（新南威尔士大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明 Sampford 分配法满足阈值单调性，解决 Correa 等人猜想，并证明在至少七个政党时无配额尊重且事前比例的方法满足成对阈值单调性。
AI中文摘要：
分配问题将固定数量的立法席位按各政党得票比例进行分配。随机化可以在每次实现中满足配额，并在期望上满足精确比例性，但这些要求仅决定了各政党的边际席位分布。我们研究阈值单调性，该性质要求：当联盟内每个标准配额弱增加且联盟外每个标准配额弱减少时，联盟的新席位总数在随机占优意义上支配其旧席位总数。我们证明 Sampford 分配法满足阈值单调性，从而解决了 Correa 等人（2024）提出的阈值单调性猜想。作为该结果的补充，我们证明：当存在至少七个政党时，没有任何满足配额且事前比例性的方法满足成对阈值单调性，即使对于不相交的联盟也是如此。这一不可能性结论无论该方法是否具有完全支持均成立。
英文摘要：
Apportionment distributes a fixed number of legislative seats among political parties in proportion to their vote shares. Randomization can satisfy quota in every realization and exact proportionality in expectation, but these requirements determine only the parties' marginal seat distributions. We study threshold monotonicity, which requires that when every standard quota inside a coalition weakly increases and every standard quota outside it weakly decreases, the coalition's new seat total stochastically dominates its old one. We prove that Sampford apportionment satisfies threshold monotonicity, resolving the threshold-monotonicity conjecture of Correa et al. (2024). Complementing this result, we prove that no quota-respecting, ex-ante proportional method satisfies pairwise threshold monotonicity even for disjoint coalitions when there are at least seven parties. This impossibility applies whether or not the method has full support.
