We study committee voting rules under ranked preferences, which map the voters' preference relations to a subset of the alternatives of predefined size. In this setting, the compatibility between proportional representation and committee monotonicity is a fundamental open problem that has been mentioned in several works. We address this research question by designing a new committee voting rule called the Solid Coalition Refinement (SCR) rule that simultaneously satisfies committee monotonicity and Dummett's Proportionality for Solid Coalitions (PSC) property as well as one of its variants called inclusion PSC. This is the first rule known to satisfy both of these properties. Moreover, we show that this is effectively the best that we can hope for as other fairness notions adapted from approval voting are incompatible with committee monotonicity. For truncated preferences, we prove that the SCR rule still satisfies PSC and a property called independence of losing voter blocs, thereby refuting a conjecture of Graham-Squire et al. (2024). Finally, we discuss the consequences of our results in the context of rank aggregation.

翻译：我们研究排序偏好下的委员会投票规则，该规则将选民的偏好关系映射至预定义规模的备选方案子集。在此背景下，比例代表制与委员会单调性之间的兼容性是一个被多篇文献提及的基础性开放问题。我们通过设计一种名为"稳固联盟精化"（SCR）的新型委员会投票规则来探讨这一研究问题，该规则同时满足委员会单调性、达梅特的稳固联盟比例性（PSC）性质及其变体——包容性PSC。这是首个已知同时满足这些性质的规则。此外，我们证明这实际上是我们所能期望的最佳结果，因为从批准投票中衍生的其他公平性概念与委员会单调性互不相容。对于截断偏好，我们证明SCR规则仍满足PSC性质及"失败选民集团独立性"特性，从而否定了Graham-Squire等人（2024）的猜想。最后，我们讨论了研究结果在排名聚合背景下的意义。