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 design a new multi-winner voting rule called the Solid Coalition Refinement (SCR) Rule that simultaneously satisfies committee monotonicity and Dummett's PSC 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 such as Rank-JR and Rank-PJR+ are incompatible with committee monotonicity.

翻译：我们研究基于排序偏好的委员会投票规则，该规则将选民的偏好关系映射到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基础性开放问题，已在多篇文献中被提及。我们设计了一种称为"稳固联盟精炼"(SCR)规则的新多席位投票规则，该规则同时满足委员会单调性、达米特比例代表性准则(PSC)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，因为其他从批准投票中衍生的公平性概念（如Rank-JR和Rank-PJR+）与委员会单调性存在不可兼容性。