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Strategic Voting in Multi-Winner Elections with Approval Balloting: A Theory for Large Electorates

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  • Jean-François Laslier

    (PSE - Paris-Jourdan Sciences Economiques - 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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, 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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Karine van Der Straeten

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, Institute advanced for advanced studies in Toulouse - Institute advanced for advanced studies in Toulouse)

Abstract

We propose a theory of strategic voting in multi-winner elections with approval balloting: A fixed number M of candidates are to be elected; each voter votes for as many candidates as she wants; the M candidates with the most votes are elected. We assume that voter preferences are separable and that there exists a tiny probability that any vote might be misrecorded. Best responses involve voting by pairwise comparisons. Two candidates play a critical role: the weakest expected winner and the strongest expected loser. Expected winners are approved if and only if they are preferred to the strongest expected loser and expected losers are approved if and only if they are preferred to the weakest expected winner. At equilibrium, if any, a candidate is elected if and only if he is approved by at least half of the voters. With single-peaked preferences, an equilibrium always exists, in which the first M candidates according to the majority tournament relation are elected. The theory is tested on individual data from the 2011 Regional Government election in Zurich.

Suggested Citation

  • Jean-François Laslier & Karine van Der Straeten, 2016. "Strategic Voting in Multi-Winner Elections with Approval Balloting: A Theory for Large Electorates," PSE Working Papers halshs-01304688, HAL.
    • Handle: RePEc:hal:psewpa:halshs-01304688
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01304688
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    References listed on IDEAS

    as
    1. Jean-François Laslier, 2009. "The Leader Rule," Journal of Theoretical Politics, , vol. 21(1), pages 113-136, January.
    2. Romain Lachat & Jean-François Laslier & Karine van Der Straeten, 2015. "Strategic Voting under Committee Approval: An Application to the 2011 Regional Government Election in Zurich," Working Papers halshs-01168743, HAL.
    3. Myerson, Roger B. & Weber, Robert J., 1993. "A Theory of Voting Equilibria," American Political Science Review, Cambridge University Press, vol. 87(1), pages 102-114, March.
    4. Steven J. Brams & William S. Zwicker & D. Marc Kilgour, 1998. "The paradox of multiple elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(2), pages 211-236.
    5. Jean-François Laslier, 2009. "The Leader rule: a model of strategic approval voting in a large electorate," Post-Print hal-00363218, HAL.
    6. Gehrlein, William V., 1985. "The Condorcet criterion and committee selection," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 199-209, December.
    7. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    8. Brams, Steven J. & Kilgour, D. Marc & Zwicker, William, 1997. "Voting on Referenda: The Separability Problem and Possible Solutions," Working Papers 97-15, C.V. Starr Center for Applied Economics, New York University.
    9. Bock, Hans-Hermann & Day, William H. E. & McMorris, F. R., 1998. "Consensus rules for committee elections," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 219-232, May.
    10. D. Marc Kilgour, 2010. "Approval Balloting for Multi-winner Elections," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 105-124, Springer.
    11. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
    12. Francesco Sinopoli & Bhaskar Dutta & Jean-François Laslier, 2006. "Approval voting: three examples," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(1), pages 27-38, December.
    13. Gilbert Laffond & Jean Lainé & Jean-François Laslier, 1996. "Composition-consistent tournament solutions and social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 75-93, January.
    14. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, June.
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    Cited by:

    1. Markus Brill & Jean-François Laslier & Piotr Skowron, 2018. "Multiwinner approval rules as apportionment methods," Journal of Theoretical Politics, , vol. 30(3), pages 358-382, July.
    2. Baujard, Antoinette & Gavrel, Frédéric & Igersheim, Herrade & Laslier, Jean-François & Lebon, Isabelle, 2018. "How voters use grade scales in evaluative voting," European Journal of Political Economy, Elsevier, vol. 55(C), pages 14-28.
    3. Salvador Barberà & Danilo Coelho, 2024. "Mechanisms to Appoint Arbitrator Panels or Sets of Judges by Compromise Between Concerned Parties," Working Papers 1442, Barcelona School of Economics.
    4. Francesco Sinopoli & Claudia Meroni, 2018. "A concept of sincerity for combinatorial voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 493-512, October.
    5. Joshua C. Yang & Damian Dailisan & Marcin Korecki & Carina I. Hausladen & Dirk Helbing, 2024. "LLM Voting: Human Choices and AI Collective Decision Making," Papers 2402.01766, arXiv.org, revised Aug 2024.

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    Keywords

    Approval Voting; Elections; Voting behavior;
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