We prove axiomatic characterizations of several important multiwinner rules within the class of approval-based committee choice rules. These are voting rules that return a set of (fixed-size) committees. In particular, we provide axiomatic characterizations of Proportional Approval Voting, the Chamberlin--Courant rule, and other Thiele methods. These rules share the important property that they satisfy an axiom called consistency, which is crucial in our characterizations.

翻译：我们证明了几种重要多赢家规则在基于批准的委员会选择规则类中的公理刻画。这些投票规则会返回一个（固定规模的）委员会集合。具体而言，我们给出了比例批准投票、钱柏林-库朗规则及其他蒂勒方法的公理刻画。这些规则共享一个重要性质，即满足被称为一致性的公理，该公理在我们的刻画中至关重要。