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The expanding approvals rule: improving proportional representation and monotonicity

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  • Haris Aziz

    (UNSW Sydney and Data61 CSIRO)

  • Barton E. Lee

    (UNSW Sydney and Data61 CSIRO)

Abstract

Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to look towards the single transferable vote (STV) rule as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open problem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. In this paper, we first present a taxonomy of proportional representation axioms for general weak order preferences, some of which generalise and strengthen previously introduced concepts. We then present a rule called the expanding approvals rule (EAR) that satisfies properties stronger than the central PR axiom satisfied by STV, can handle indifferences in a convenient and computationally efficient manner, and also satisfies better candidate monotonicity properties. In view of this, our proposed rule seems to be a compelling solution for achieving proportional representation in voting settings.

Suggested Citation

  • Haris Aziz & Barton E. Lee, 2020. "The expanding approvals rule: improving proportional representation and monotonicity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 1-45, January.
    • Handle: RePEc:spr:sochwe:v:54:y:2020:i:1:d:10.1007_s00355-019-01208-3
    DOI: 10.1007/s00355-019-01208-3
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    Cited by:

    1. Aziz, Haris & Lee, Barton E., 2022. "A characterization of proportionally representative committees," Games and Economic Behavior, Elsevier, vol. 133(C), pages 248-255.
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    3. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.
    4. Kamesh Munagala & Zeyu Shen & Kangning Wang, 2021. "Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule," Papers 2106.00091, arXiv.org.
    5. Dominik Peters & Grzegorz Pierczy'nski & Piotr Skowron, 2020. "Proportional Participatory Budgeting with Additive Utilities," Papers 2008.13276, arXiv.org, revised Oct 2022.

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