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Multiwinner approval rules as apportionment methods

Author

Listed:
  • Markus Brill

    (TUB - Technical University of Berlin / Technische Universität Berlin)

  • Jean-François Laslier

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique)

  • Piotr Skowron

    (UW - Uniwersytet Warszawski [Polska] = University of Warsaw [Poland] = Université de Varsovie [Pologne])

Abstract

During the first round of the 2012 French presidential election, participants in an in situ experiment were invited to vote according to "evaluative voting", which involves rating the candidates using a numerical scale. Various scales were used: (0,1), (-1,0,1), (0,1,2), and (0,1,…,20). The paper studies scale calibration effects, i.e., how individual voters adapt to the scale, leading to possibly different election outcomes. The data show that scales are not linearly equivalent, even if individual ordinal preferences are not inconsistent. Scale matters, notably because of the symbolic power of negative grades, which does not affect all candidates uniformly.

Suggested Citation

  • Markus Brill & Jean-François Laslier & Piotr Skowron, 2018. "Multiwinner approval rules as apportionment methods," PSE-Ecole d'économie de Paris (Postprint) halshs-02087610, HAL.
    • Handle: RePEc:hal:pseptp:halshs-02087610
    DOI: 10.1177/0951629818775518
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    Cited by:

    1. Rosa Camps & Xavier Mora & Laia Saumell, 2019. "The method of Enestr\"om and Phragm\'en for parliamentary elections by means of approval voting," Papers 1907.10590, arXiv.org, revised Mar 2024.
    2. Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐Baptiste Tondji, 2022. "Vaccine and inclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1101-1123, October.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐baptiste Tondji, 2022. "Vaccine and inclusion," Post-Print hal-04257703, HAL.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean-Baptiste Tondji, 2022. "Vaccine and Inclusion," Working Papers 2202E Classification-C62,, University of Ottawa, Department of Economics.
    3. Chris Dong & Patrick Lederer, 2023. "Refined Characterizations of Approval-based Committee Scoring Rules," Papers 2312.08799, arXiv.org, revised Mar 2024.
    4. Markus Brill & Paul Gölz & Dominik Peters & Ulrike Schmidt-Kraepelin & Kai Wilker, 2022. "Approval-based apportionment," Post-Print hal-03816043, HAL.
    5. 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.
    6. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.
    7. Martin Bullinger & Chris Dong & Patrick Lederer & Clara Mehler, 2023. "Participation Incentives in Approval-Based Committee Elections," Papers 2312.08798, arXiv.org.
    8. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    9. Balázs R Sziklai & Károly Héberger, 2020. "Apportionment and districting by Sum of Ranking Differences," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-20, March.
    10. Niclas Boehmer & Markus Brill & Ulrike Schmidt-Kraepelin, 2021. "Selecting Matchings via Multiwinner Voting: How Structure Defeats a Large Candidate Space," Papers 2102.07441, arXiv.org.
    11. Steven J. Brams & Markus Brill & Anne-Marie George, 2022. "The excess method: a multiwinner approval voting procedure to allocate wasted votes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 283-300, February.
    12. Niclas Boehmer & Markus Brill & Ulrike Schmidt-Kraepelin, 2025. "Proportional representation in matching markets: selecting multiple matchings under dichotomous preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(1), pages 179-220, February.
    13. Chris Dong & Patrick Lederer, 2023. "Characterizations of Sequential Valuation Rules," Papers 2302.11890, arXiv.org.
    14. Steven J. Brams & D. Marc Kilgour & Richard F. Potthoff, 2019. "Multiwinner approval voting: an apportionment approach," Public Choice, Springer, vol. 178(1), pages 67-93, January.
    15. Laszlo A. Koczy & Peter Biro & Balazs Sziklai, 2017. "US vs. European Apportionment Practices: The Conflict between Monotonicity and Proportionality," CERS-IE WORKING PAPERS 1716, Institute of Economics, Centre for Economic and Regional Studies.
    16. Torun Dewan & John W. Patty, 2018. "Editors’ Introduction to JTP issue 30.3," Journal of Theoretical Politics, , vol. 30(3), pages 269-271, July.
    17. Pivato, Marcus & Soh, Arnold, 2020. "Weighted representative democracy," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 52-63.
    18. Th'eo Delemazure & Tom Demeulemeester & Manuel Eberl & Jonas Israel & Patrick Lederer, 2022. "Strategyproofness and Proportionality in Party-Approval Multiwinner Elections," Papers 2211.13567, arXiv.org.
    19. Clinton Gubong Gassi, 2024. "Weighted scoring rules for selecting a compatible committee," Working Papers 2024-04, CRESE.

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