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Scoring Rules: A Game-Theoretical Analysis

Author

Listed:
  • Francesco De Sinopoli

    (University of Verona)

  • Giovanna Iannantuoni

    (University of Milano-Bicocca)

  • Carlos Pimienta

    (University of New South Wales)

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 (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, 1989) of the induced voting games. To conclude, we provide some examples of voting environments with three candidates where we carry out this this comparison.

Suggested Citation

  • Francesco De Sinopoli & Giovanna Iannantuoni & Carlos Pimienta, 2012. "Scoring Rules: A Game-Theoretical Analysis," Discussion Papers 2012-40, School of Economics, The University of New South Wales.
    • Handle: RePEc:swe:wpaper:2012-40
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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2012-40.pdf
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    References listed on IDEAS

    as
    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. 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.
    3. Mertens, Jean-Francois, 1992. "The small worlds axiom for stable equilibria," Games and Economic Behavior, Elsevier, vol. 4(4), pages 553-564, October.
    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. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    7. 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.
    8. Govindan, Srihari & McLennan, Andrew, 2001. "On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms," Econometrica, Econometric Society, vol. 69(2), pages 455-471, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Approval voting; Plurality voting; Negative plurality; Sophisticated voting; Mertens Stability;
    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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