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Scoring Rules: A Game-Theoretical Analysis

  • Francesco De Sinopoli

    ()

    (University of Verona)

  • Giovanna Iannantuoni

    ()

    (University of Milano-Bicocca)

  • Carlos Pimienta

    ()

    (University of New South Wales)

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.

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File URL: http://research.economics.unsw.edu.au/RePEc/papers/2012-40.pdf
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Paper provided by School of Economics, The University of New South Wales in its series Discussion Papers with number 2012-40.

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Length: 23 pages
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:swe:wpaper:2012-40
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  1. Dhillon, A. & Lockwood, B., 1999. "When are Plurality Rule Voting Games Dominance-Solvable?," The Warwick Economics Research Paper Series (TWERPS) 549, University of Warwick, Department of Economics.
  2. Lucia Buenrostro & Amrita Dhillon & Peter Vida, 2013. "Scoring rule voting games and dominance solvability," Social Choice and Welfare, Springer, vol. 40(2), pages 329-352, February.
  3. MERTENS, Jean-François, 1990. "The "small worlds" axiom for stable equilibria," CORE Discussion Papers 1990007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Roger B. Myerson, 2000. "Comparison of Scoring Rules in Poisson Voting Games," Econometric Society World Congress 2000 Contributed Papers 0686, Econometric Society.
  6. Francesco Sinopoli & Bhaskar Dutta & Jean-François Laslier, 2006. "Approval voting: three examples," International Journal of Game Theory, Springer, vol. 35(1), pages 27-38, December.
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