Abstract To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an “optimal” subset of alternatives. In this paper, we provide a quantitative analysis of multiwinner voting rules using methods from the theory of approximation algorithms—we estimate how well multiwinner rules approximate two extreme objectives: a representation criterion defined via the Approval Chamberlin–Courant rule and a utilitarian criterion defined via Multiwinner Approval Voting. With both theoretical and experimental methods, we classify multiwinner rules in terms of their quantitative alignment with these two opposing objectives. Our results provide fundamental information about the nature of multiwinner rules and, in particular, about the necessary tradeoffs when choosing such a rule.

中文翻译：

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基于批准的多赢家规则的功利主义福利和代表保证

摘要 选择合适的多人投票规则是一项艰巨而模糊的任务。根据上下文，选择“最佳”替代方案子集的方式差异很大。在本文中，我们使用近似算法理论中的方法对多赢者投票规则进行了定量分析——我们估计多赢者规则接近两个极端目标的程度：通过 Approval Chamberlin-Courant 规则定义的表示标准和通过多赢家批准投票。使用理论和实验方法，我们根据与这两个对立目标的定量一致性对多赢家规则进行分类。我们的结果提供了关于多赢家规则性质的基本信息，特别是，