In the committee voting setting, a subset of $k$ alternatives is selected based on the preferences of voters. In this paper, our goal is to efficiently compute ex-ante fair probability distributions (or lotteries) over committees. Since it is not known whether a lottery satisfying the desirable fairness property of fractional core is polynomial-time computable, we introduce a new axiom called group resource proportionality (GRP), which strengthens other fairness notions in the literature. We characterize our fairness axiom by a correspondence with max flows on a network formulation of committee voting. Using the connection to flow networks revealed by this characterization, we then introduce voting rules which achieve fairness in conjunction with other desirable properties. The redistributive utilitarian rule satisfies ex-ante efficiency in addition to our fairness axiom. We also give a voting rule which maximizes social welfare subject to fairness by reducing to a minimum-cost maximum-flow problem. Lastly, we show our fairness property can be obtained in tandem with strong ex-post fairness properties -- an approach known as best-of-both-worlds fairness. We strengthen existing best-or-both-worlds fairness results in committee voting and resolve an open question posed by Aziz et al. (2023). These findings follow from an auxiliary result which may prove useful in obtaining best-of-both-worlds type results in future research on committee voting.

翻译：在委员会投票场景中，需根据选民偏好从备选方案中选出包含$k$个方案的子集。本文旨在高效计算满足事前公平性的委员会概率分布（即抽签机制）。鉴于目前尚不确定满足分数核心这一理想公平性质的抽签机制是否能在多项式时间内计算，我们提出了一种称为群体资源比例性（GRP）的新公理，该公理强化了现有文献中的其他公平性概念。我们通过委员会投票网络建模中最大流问题的对应关系，刻画了该公平公理的特征。基于此特征揭示的流网络关联性，我们进一步提出了能同时实现公平性与其他理想特性的投票规则。再分配功利主义规则在满足我们提出的公平公理之外，还实现了事前效率性。我们还通过归约为最小成本最大流问题，给出了在公平约束下最大化社会福利的投票规则。最后，我们证明了所提出的公平性质可与强事后公平性质协同实现——这种方法被称为"两全其美"公平性。我们强化了委员会投票中现有的两全其美公平性结果，并解决了Aziz等人（2023）提出的开放性问题。这些结论源自一项辅助性结果，该结果可能对未来委员会投票研究中获取两全其美类型的结果具有重要价值。