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On stable outcomes of approval, plurality, and negative plurality games

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  • Francesco Sinopoli
  • Giovanna Iannantuoni
  • Carlos Pimienta

Abstract

We prove two results on the generic determinacy of Nash equilibrium in voting games. The first one is for negative plurality games. The second one is for approval games under the condition that the number of candidates is equal to three. These results are combined with the analogous one obtained in De Sinopoli (Games Econ Behav 34:270–286, 2001 ) for plurality rule to show that, for generic utilities, three of the most well-known scoring rules, plurality, negative plurality and approval, induce finite sets of equilibrium outcomes in their corresponding derived games—at least when the number of candidates is equal to three. This is a necessary requirement for the development of a systematic comparison amongst these three voting rules and a useful aid to compute the stable sets of equilibria Mertens (Math Oper Res 14:575–625, 1989 ) of the induced voting games. To conclude, we provide some examples of voting environments with three candidates where we carry out this comparison. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Francesco Sinopoli & Giovanna Iannantuoni & Carlos Pimienta, 2015. "On stable outcomes of approval, plurality, and negative plurality games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 889-909, April.
  • Handle: RePEc:spr:sochwe:v:44:y:2015:i:4:p:889-909
    DOI: 10.1007/s00355-014-0866-z
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    References listed on IDEAS

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    1. Lucia Buenrostro & Amrita Dhillon & Peter Vida, 2013. "Scoring rule voting games and dominance solvability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 329-352, February.
    2. Francesco De Sinopoli, 2000. "Sophisticated voting and equilibrium refinements under plurality rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 655-672.
    3. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    4. 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.
    5. De Sinopoli, Francesco, 2001. "On the Generic Finiteness of Equilibrium Outcomes in Plurality Games," Games and Economic Behavior, Elsevier, vol. 34(2), pages 270-286, February.
    6. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-769, May.
    7. Mertens, Jean-Francois, 1992. "The small worlds axiom for stable equilibria," Games and Economic Behavior, Elsevier, vol. 4(4), pages 553-564, October.
    8. Park, In-Uck, 1997. "Generic Finiteness of Equilibrium Outcome Distributions for Sender-Receiver Cheap-Talk Games," Journal of Economic Theory, Elsevier, vol. 76(2), pages 431-448, October.
    9. Dhillon, Amrita & Lockwood, Ben, 2004. "When are plurality rule voting games dominance-solvable?," Games and Economic Behavior, Elsevier, vol. 46(1), pages 55-75, January.
    10. Peter Fishburn & Steven Brams, 1981. "Approval voting, Condorcet's principle, and runoff elections," Public Choice, Springer, vol. 36(1), pages 89-114, January.
    11. Francesco Sinopoli & Giovanna Iannantuoni & Carlos Pimienta, 2014. "Counterexamples on the Superiority of Approval versus Plurality," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(5), pages 824-834, October.
    12. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    13. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    14. 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.
    15. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
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    Cited by:

    1. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.

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    Keywords

    C72; D72;

    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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