Approval-based voting with mixed goods

IF 0.5 4区经济学 Q4 ECONOMICS Social Choice and Welfare Pub Date : 2024-02-27 DOI:10.1007/s00355-024-01511-8

引用次数: 0

Abstract

We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This setting generalizes both the well-studied model of multiwinner voting and the recently introduced model of cake sharing. Under approval votes, we propose two variants of the extended justified representation (EJR) notion from multiwinner voting, a stronger one called EJR for mixed goods (EJR-M) and a weaker one called EJR up to 1 (EJR-1). We extend three multiwinner voting rules to our setting—GreedyEJR, the method of equal shares (MES), and proportional approval voting (PAV)—and show that while all three generalizations satisfy EJR-1, only the first one provides EJR-M. In addition, we derive tight bounds on the proportionality degree implied by EJR-M and EJR-1, and investigate the proportionality degree of our proposed rules.

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混合商品的认可型投票

摘要我们考虑了一种投票情况，在这种情况下，需要投票的资源可能既包括不可分割的物品，也包括可分割的物品。这种情况概括了已被广泛研究的多赢家投票模型和最近引入的分蛋糕模型。在赞成票下，我们提出了多赢家投票中扩展的合理表示（EJR）概念的两个变体，一个较强的变体称为混合物品的 EJR（EJR-M），另一个较弱的变体称为最多为 1 的 EJR（EJR-1）。我们将三种多赢家投票规则扩展到我们的设置中--GreedyEJR、均等份额法（MES）和比例批准投票（PAV）--并证明虽然所有三种概括都满足 EJR-1，但只有第一种概括提供了 EJR-M。此外，我们还推导出了 EJR-M 和 EJR-1 所隐含的比例度的严格界限，并研究了我们所提规则的比例度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Social Choice and Welfare Multiple-

CiteScore

1.60

自引率

11.10%

发文量

期刊介绍： Social Choice and Welfare explores all aspects, both normative and positive, of welfare economics, collective choice, and strategic interaction. Topics include but are not limited to: preference aggregation, welfare criteria, fairness, justice and equity, rights, inequality and poverty measurement, voting and elections, political games, coalition formation, public goods, mechanism design, networks, matching, optimal taxation, cost-benefit analysis, computational social choice, judgement aggregation, market design, behavioral welfare economics, subjective well-being studies and experimental investigations related to social choice and voting. As such, the journal is inter-disciplinary and cuts across the boundaries of economics, political science, philosophy, and mathematics. Articles on choice and order theory that include results that can be applied to the above topics are also included in the journal. While it emphasizes theory, the journal also publishes empirical work in the subject area reflecting cross-fertilizing between theoretical and empirical research. Readers will find original research articles, surveys, and book reviews.Officially cited as: Soc Choice Welf

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