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Two examples of strategic equilibria in approval voting games

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  • DE SINOPOLI, Francesco

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), 1348 Louvain la Neuve, Belgium)

Abstract

In this note we discuss two examples of appoval voting games. The first one, with six voters and three candidates, has a unique stable set,where each voter approves only his most preferred candidate. This strategy coincides with the sophisticated one, while other strategy combinations, leading to different outcomes, are selected by the perfect equilibrium concept. Moreover, this example shows that sophisticated voting, as well as strategic stability, does not imply the election of a Condorcet winner, even if it exists. The second example, with four voters and four candidates, shows that strategic stability does not exclude non sincere strategies. Furthermore, the same results hold in complete neighborhoods of the games considered.

Suggested Citation

  • DE SINOPOLI, Francesco, 1999. "Two examples of strategic equilibria in approval voting games," LIDAM Discussion Papers CORE 1999031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1999031
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    References listed on IDEAS

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    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.
    2. Jean-François Mertens, 1989. "Stable Equilibria---A Reformulation," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 575-625, November.
    3. MERTENS, Jean-François, 1989. "Stable equilibria - a reformulation. Part I. Definition and basic properties," LIDAM Reprints CORE 866, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Peter Fishburn & Steven Brams, 1981. "Approval voting, Condorcet's principle, and runoff elections," Public Choice, Springer, vol. 36(1), pages 89-114, January.
    5. MERTENS, Jean-François, 1991. "Stable equilibria - a reformulation. Part II. Discussion of the definition, and further results," LIDAM Reprints CORE 960, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
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    Cited by:

    1. Dellis, Arnaud & Oak, Mandar P., 2006. "Approval voting with endogenous candidates," Games and Economic Behavior, Elsevier, vol. 54(1), pages 47-76, January.
    2. 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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    More about this item

    Keywords

    Approval voting; sophisticated voting; perfect equilibrium; stable set;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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