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Analysis of Approval Voting in Poisson Games

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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 - IMT - Institut Mines-Télécom [Paris] - SU - Sorbonne Université)

  • Antonin Macé

    (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS Paris - 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, PSE - La plante et son environnement - INRA - Institut National de la Recherche Agronomique - UP11 - Université Paris-Sud - Paris 11 - INA P-G - Institut National Agronomique Paris-Grignon - CNRS - Centre National de la Recherche Scientifique)

  • Matias Nunez

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - 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," Working Papers halshs-02049865, HAL.
  • Handle: RePEc:hal:wpaper: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(1), pages 102-114, March.
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    More about this item

    Keywords

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