AI 中文总结
该研究探讨基于批准的多获胜者选举中“两全其美”公平性，证明事前弱PO、AJR与事后JR互斥，但多个事前代表性保证可兼容，明确公平随机委员会选择的根本局限性。
AI 中文摘要
我们研究基于批准的多获胜者选举中的“两全其美”公平性，探讨能否在实现分数结果的事前保证的同时，让每个实际选出的委员会满足事后代表性公理。近期研究表明，若干事前比例保证可与强事后代表性公理同时实现。我们首先证明，事前弱帕累托最优（weak PO，要求不存在其他分数结果能让所有选民严格受益）与事后正当代表性（JR）互斥。由于分数核心稳定性隐含弱PO，这也排除了将分数核心（分数委员会的核心公平概念）与事后JR结合的可能。我们进一步证明，事前AJR（JR的强平均代表性类似物）与事后JR互斥。积极方面，我们发现分数事前维度仍高度兼容：多个自然事前代表性保证可同时满足，包括分数核心、群体资源比例性、AJR及其严格强化AJR+，以及帕累托最优。因此，即便无法通过JR委员会的随机化实现，仍存在高度公平的分数委员会。我们的结果区分了分数代表性与“两全其美”可实现性，明确了公平随机委员会选择的根本局限性。
英文摘要
We study the best-of-both-worlds fairness in approval-based multi-winner elections, asking whether ex-ante guarantees for a fractional outcome can be implemented while every realized committee satisfies an ex-post representation axiom. Recent work has shown that several ex-ante proportionality guarantees can be achieved together with strong ex-post representation axioms. We first prove that ex-ante weak Pareto optimality (weak PO), which requires that no other fractional outcome makes every voter strictly better off, is incompatible with ex-post justified representation (JR). Since fractional core stability implies weak PO, this also rules out the possibility of combining ex-ante fractional core, a central fairness notion for fractional committees, with ex-post JR. We further show that ex-ante AJR is incompatible with ex-post JR, even though AJR is a much stronger average-representation analogue of JR. On the positive side, we show that the fractional ex-ante side itself remains highly compatible: several natural ex-ante representation guarantees can be satisfied simultaneously, including fractional core, group-resource proportionality, AJR (as well as its strict strengthening AJR+), and Pareto-optimality. Hence, highly fair fractional committees may exist even when they cannot be implemented by randomization over JR committees. Our results separate fractional representation from best-of-both-worlds implementability and identify fundamental limitations of fair randomized committee selection.
Comments29 pages, 2 figures
