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Approval-based voting with mixed goods

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xinhang Lu & Jannik Peters & Haris Aziz & Xiaohui Bei & Warut Suksompong, 2024. "Approval-based voting with mixed goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(4), pages 643-677, June.
    • Handle: RePEc:spr:sochwe:v:62:y:2024:i:4:d:10.1007_s00355-024-01511-8
    DOI: 10.1007/s00355-024-01511-8
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    References listed on IDEAS

    as
    1. Haris Aziz & Anna Bogomolnaia & Hervé Moulin, 2019. "Fair Mixing: the Case of Dichotomous Preferences," Post-Print hal-03047451, HAL.
    2. Haris Aziz & Markus Brill & Vincent Conitzer & Edith Elkind & Rupert Freeman & Toby Walsh, 2017. "Justified representation in approval-based committee voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 461-485, February.
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    Cited by:

    1. Haris Aziz & Patrick Lederer & Xinhang Lu & Mashbat Suzuki & Jeremy Vollen, 2024. "Sequential Payment Rules: Approximately Fair Budget Divisions via Simple Spending Dynamics," Papers 2412.02435, arXiv.org.

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