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When are plurality rule voting games dominance-solvable?

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  • Dhillon, Amrita
  • Lockwood, Ben

Abstract

This paper studies the dominance-solvability (by iterated deletion of weakly dominated strategies) of plurality rule voting games. For K > 3 alternatives and n > 3 voters, we find sufficient conditions for the game to be dominance-solvable (DS) and not to be DS. These conditions can be stated in terms of only one statistic of the game, the largest proportion of voters who agree on which alternative is worst in a sequence of subsets of the original set of alternatives. When n is large, "almost all" games can be classified as either DS or not DS. If the game is DS, a Condorcet Winner always exists when n > 4, and the outcome is always the Condorcet Winner when the electorate is sufficiently replicated.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 46 (2004)
Issue (Month): 1 (January)
Pages: 55-75

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Handle: RePEc:eee:gamebe:v:46:y:2004:i:1:p:55-75

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. Tim Besley & Stephen Coate, . ""An Economic Model of Representative Democracy''," CARESS Working Papres 95-02, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
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  11. DE SINOPOLI, Francesco & TURRINI, Alessandro, 1999. "A remark on voters’ rationality in Besley and coate model of representative democracy," CORE Discussion Papers 1999027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Rajan, Uday, 1998. "Trembles in the Bayesian Foundations of Solution Concepts of Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 248-266, September.
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  14. DE SINOPOLI, Francesco, 1998. "Strategic stability and non cooperative voting games: the plurality rule," CORE Discussion Papers 1998043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Gehrlein, William V. & Lepelley, Dominique, 1998. "The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 271-283, April.
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  18. Francesco De Sinopoli, 2000. "Sophisticated voting and equilibrium refinements under plurality rule," Social Choice and Welfare, Springer, vol. 17(4), pages 655-672.
  19. 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.
  20. Mariotti, Marco, 2000. "Maximum Games, Dominance Solvability, and Coordination," Games and Economic Behavior, Elsevier, vol. 31(1), pages 97-105, April.
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Citations

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Cited by:
  1. De Sinopoli, F. & Iannantuoni, G., 2005. "Extreme Voting under Proportional Representation: The Multidimensional Case," Cambridge Working Papers in Economics 0531, Faculty of Economics, University of Cambridge.
  2. Bag, Parimal Kanti & Sabourian, Hamid & Winter, Eyal, 2009. "Multi-stage voting, sequential elimination and Condorcet consistency," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1278-1299, May.
  3. Vincent Merlin & Jörg Naeve, 2000. "Implementation of Social Choice Functions via Demanding Equilibria," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 191/2000, Department of Economics, University of Hohenheim, Germany, revised 25 Sep 2001.
  4. DE SINOPOLI, Francesco, 1999. "A note on forward induction in a model of representative democracy," CORE Discussion Papers 1999060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Sébastien Courtin & Matias Nùnez, 2013. "Dominance Solvable Approval Voting Games," THEMA Working Papers 2013-27, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  6. Ben Lockwood & Eric Le Borgne, 2003. "Do Elections Always Motivate Incumbents? Experimentation vs. Career Concerns," IMF Working Papers 03/57, International Monetary Fund.
  7. Laurent Denant-Boèmont & Enrico Diecidue & Olivier L'Haridon, 2013. "Patience and Time Consistency in Collective Decisions," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201329, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
  8. M. Braham & F. Steffen, 2007. "The Chairman’s Paradox Revisited," Social Choice and Welfare, Springer, vol. 28(2), pages 231-253, February.
  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. Bryan McCannon, 2009. "Can the majority lose the election?," Review of Economic Design, Springer, vol. 13(4), pages 305-317, December.
  11. Le Borgne, Eric & Lockwood, Ben, 2000. "Candidate Entry, Screening, and the Political Budget Cycle," The Warwick Economics Research Paper Series (TWERPS) 582, University of Warwick, Department of Economics.
  12. 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.
  13. 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.
  14. Dellis, Arnaud, 2010. "Weak undominance in scoring rule elections," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 110-119, January.
  15. le Borgne, E. & Lockwood, B., 2000. "Do Elections Always Motivate Incumbents?," The Warwick Economics Research Paper Series (TWERPS) 580, University of Warwick, Department of Economics.

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