Approval-based voting with mixed goods

Xinhang Lu, Jannik Peters, Haris Aziz, Xiaohui Bei and Warut Suksompong ()
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Xinhang Lu: University of New South Wales
Jannik Peters: Technische Universität Berlin
Haris Aziz: University of New South Wales
Xiaohui Bei: Nanyang Technological University
Warut Suksompong: National University of Singapore

Social Choice and Welfare, 2024, vol. 62, issue 4, No 2, 643-677

Abstract: 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.

Date: 2024
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DOI: 10.1007/s00355-024-01511-8

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