Multiwinner analogues of the plurality rule: axiomatic and algorithmic perspectives
研究了满足固定多数准则的委员会计分规则，将其定义为多元获胜者版本的简单多数规则，分析了其公理性质，并探讨了多种规则下胜者确定问题的计算复杂性，包括NP难和多项式时间算法。
We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. We argue that rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-k-counting committee scoring rules and show that the fixed-majority consistent rules are a subclass of the top-k-counting rules. We give necessary and sufficient conditions for a top-k-counting rule to satisfy the fixed-majority criterion. We show that, for many top-k-counting rules, the complexity of winner determination is high (formally, we show that the problem of deciding if there exists a committee with at least a given score is $${\mathrm {NP}}$$ NP -hard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.