Econ Papers Daily / 期刊论文
序数多赢家投票规则的帕累托效率
Pareto-efficiency of ordinal multiwinner voting rules
摘要
We investigate the Pareto-efficiency of ordinal multiwinner voting rules, that is, voting rules based on ordinal preference profiles over candidates. Defining Pareto-optimality of a committee requires relating the voters’ rankings over individual candidates to their preferences over committees. We consider two well-known extension principles that extend rankings over candidates to preferences over committees: the responsive extension and the lexicographic extension. As the responsive extension outputs partial orders, we consider two Pareto-optimality notions: a committee is possibly (respectively, necessary) Pareto-optimal if it is Pareto-optimal for some (respectively, every) completion of these partial orders. As the lexicographic extension principle outputs a total order, it leads to only one Pareto-optimality notion. We then define several notions of Pareto-efficiency of multiwinner rules, depending on whether some (respectively, all) committees in the output are Pareto-optimal for one of the latter notions. We review what we believe to be a complete list of ordinal multiwinner rules that have been studied in the literature, and identify which Pareto-efficiency notions they satisfy. Our finding is that, somewhat surprisingly, these rules show a huge diversity: some satisfy the strongest notion, some do not even satisfy the weakest one, with many other rules at various intermediate levels.
中文摘要
本文研究了序数多赢家投票规则的帕累托效率，即基于候选人的序数偏好分布的投票规则。定义委员会的帕累托最优性需要将选民对单个候选人的排序与其对委员会的偏好联系起来。我们考虑两种广为人知的扩展原则，将候选人的排序扩展为对委员会的偏好：响应扩展和词典序扩展。由于响应扩展输出偏序，我们考虑两种帕累托最优性概念：一个委员会是可能（分别地，必然）帕累托最优的，如果它对于这些偏序的某些（分别地，所有）完备化是帕累托最优的。由于词典序扩展原则输出全序，它仅导致一种帕累托最优性概念。随后，我们根据输出中的某些（分别地，所有）委员会是否满足上述某种帕累托最优性概念，定义了多赢家规则的若干帕累托效率概念。我们回顾了文献中研究过的、我们认为完整的序数多赢家规则列表，并识别了它们满足哪些帕累托效率概念。我们的发现是，有些出人意料的是，这些规则表现出巨大的多样性：有些满足最强的概念，有些甚至不满足最弱的概念，而许多其他规则则处于各种中间水平。