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Analysis of Approval Voting in Poisson Games

Author

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  • François Durand

    (Nokia Bell Labs [Espoo], LINCS - Laboratory of Information, Network and Communication Sciences - Inria - Institut National de Recherche en Informatique et en Automatique - Institut Mines-Télécom [Paris] - SU - Sorbonne Université)

  • Antonin Macé

    () (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - 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 - La plante et son environnement - CNRS - Centre National de la Recherche Scientifique - INA P-G - Institut National Agronomique Paris-Grignon - UP11 - Université Paris-Sud - Paris 11 - INRA - Institut National de la Recherche Agronomique)

  • Matias Nunez

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

Abstract

We analyze Approval Voting in Poisson games endowing voters with private values over three candidates. We firsts how that any stable equilibrium is discriminatory: one candidate is commonly regarded as out of contention. We fully characterize stable equilibria and divide them into two classes. In direct equilibria, best responses depend only on ordinal preferences. In indirect equilibria, preference intensities matter. Counter-intuitively, any stable equilibrium violates the ordering conditions, a set of belief restrictions used to derive early results in the literature. We finally use Monte-Carlo simulations to estimate the prevalence of the different sorts of equilibria and their likelihood to elect a Condorcet winner.

Suggested Citation

  • François Durand & Antonin Macé & Matias Nunez, 2019. "Analysis of Approval Voting in Poisson Games," PSE Working Papers halshs-02049865, HAL.
  • Handle: RePEc:hal:psewpa:halshs-02049865
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-02049865
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    References listed on IDEAS

    as
    1. Myerson, Roger B. & Weber, Robert J., 1993. "A Theory of Voting Equilibria," American Political Science Review, Cambridge University Press, vol. 87(01), pages 102-114, March.
    2. Ahn, David S. & Oliveros, Santiago, 2016. "Approval voting and scoring rules with common values," Journal of Economic Theory, Elsevier, vol. 166(C), pages 304-310.
    3. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    4. Jean-François Laslier, 2009. "The Leader rule: a model of strategic approval voting in a large electorate," Post-Print hal-00363218, HAL.
    5. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, January.
    6. Thomas Palfrey & Howard Rosenthal, 1983. "A strategic calculus of voting," Public Choice, Springer, vol. 41(1), pages 7-53, January.
    7. Goertz, Johanna M.M. & Maniquet, François, 2011. "On the informational efficiency of simple scoring rules," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1464-1480, July.
    8. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    9. repec:ulb:ulbeco:2013/162238 is not listed on IDEAS
    10. repec:cup:apsrev:v:91:y:1997:i:01:p:135-147_23 is not listed on IDEAS
    11. 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.
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    Keywords

    Approval voting; Poisson games; Stable equilibria; Monte-Carlo simulations;

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