IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v153y2025icp345-358.html

Axiomatic analysis of approval-based scoring rules

Author

Listed:
  • Bardal, Tuva
  • Endriss, Ulle

Abstract

Approval-based scoring rules require participants to submit ballots that correspond to the candidates they approve of, and each candidate then receives some score from each ballot it appears on. One particularly natural class of approval-based scoring rules is the class of size-approval rules. For rules in this class, each ballot is weighted based on the number of candidates it contains. We provide a deep axiomatic analysis of the class of size-approval rules and related classes of approval-based scoring rules. We organise existing work by shedding light on the exact role played by core axioms involved in previous characterisations of size-approval rules, while also providing multiple new characterisations of the same class and its closest relatives. We furthermore provide an original characterisation of even-and-equal cumulative voting, the most paradigmatic representative of the size-approval voting rules, where each ballot's weight is inversely proportional to its size.

Suggested Citation

  • Bardal, Tuva & Endriss, Ulle, 2025. "Axiomatic analysis of approval-based scoring rules," Games and Economic Behavior, Elsevier, vol. 153(C), pages 345-358.
    • Handle: RePEc:eee:gamebe:v:153:y:2025:i:c:p:345-358
    DOI: 10.1016/j.geb.2025.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825625000971
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2025.07.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Gerald J. Glasser, 1959. "Game Theory and Cumulative Voting for Corporate Directors," Management Science, INFORMS, vol. 5(2), pages 151-156, January.
    2. Bhagat, Sanjai & Brickley, James A, 1984. "Cumulative Voting: The Value of Minority Shareholder Voting Rights," Journal of Law and Economics, University of Chicago Press, vol. 27(2), pages 339-365, October.
    3. Carlos Alós-Ferrer, 2006. "A Simple Characterization of Approval Voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 621-625, December.
    4. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    5. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2009. "Size approval voting," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1187-1210, May.
    6. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    7. Chris Dong & Patrick Lederer, 2023. "Refined Characterizations of Approval-based Committee Scoring Rules," Papers 2312.08799, arXiv.org, revised Mar 2024.
    8. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    9. Florian Brandl & Dominik Peters, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Post-Print hal-03816040, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lederer, Patrick, 2024. "Bivariate scoring rules: Unifying the characterizations of positional scoring rules and Kemeny's rule," Journal of Economic Theory, Elsevier, vol. 218(C).
    2. Chris Dong & Patrick Lederer, 2023. "Refined Characterizations of Approval-based Committee Scoring Rules," Papers 2312.08799, arXiv.org, revised Mar 2024.
    3. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2014. "Non-anonymous ballot aggregation: An axiomatic generalization of Approval Voting," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 69-78.
    4. Aziz, Haris & Lederer, Patrick & Lu, Xinhang & Suzuki, Mashbat & Vollen, Jeremy, 2025. "Approximately fair and population consistent budget division via simple payment schemes," Games and Economic Behavior, Elsevier, vol. 154(C), pages 208-225.
    5. Susumu Cato & Stéphane Gonzalez & Eric Rémila & Philippe Solal, 2022. "Approval voting versus proportional threshold methods: so far and yet so near," Working Papers halshs-03858356, HAL.
    6. Martínez, Ricardo & Moreno, Bernardo, 2017. "Qualified voting systems," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 49-54.
    7. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    8. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    9. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2009. "Size approval voting," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1187-1210, May.
    10. Pivato, Marcus, 2014. "Formal utilitarianism and range voting," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 50-56.
    11. Chris Dong & Patrick Lederer, 2023. "Characterizations of Sequential Valuation Rules," Papers 2302.11890, arXiv.org.
    12. Ginsburgh, Victor & Moreno-Ternero, Juan D. & Weber, Shlomo, 2017. "Ranking languages in the European Union: Before and after Brexit," European Economic Review, Elsevier, vol. 93(C), pages 139-151.
    13. Trevor Leach & Robert C. Powers, 2020. "Majority rule on j-rich ballot spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 639-655, April.
    14. Haris Aziz & Patrick Lederer & Xinhang Lu & Mashbat Suzuki & Jeremy Vollen, 2024. "Approximately Fair and Population Consistent Budget Division via Simple Payment Schemes," Papers 2412.02435, arXiv.org, revised Jul 2025.
    15. Carlos Alós-Ferrer & Michele Garagnani & Jaume García-Segarra, 2025. "The framing of elections: cooperation vs. competition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 65(2), pages 363-385, September.
    16. José Alcantud & Annick Laruelle, 2014. "Dis&approval voting: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 1-10, June.
    17. Patrick Lederer, 2025. "Robust Voting Rules on the Interval Domain," Papers 2509.04874, arXiv.org.
    18. Duddy, Conal & Piggins, Ashley, 2013. "Collective approval," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 190-194.
    19. Federica Ceron & Stéphane Gonzalez, 2019. "A characterization of Approval Voting without the approval balloting assumption," Working Papers halshs-02440615, HAL.
    20. Salvatore Barbaro & Anna-Sophie Kurella, 2025. "Dichotomous Preferences: Concepts, Measurement, and Evidence," Working Papers 2506, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:153:y:2025:i:c:p:345-358. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.