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When are Plurality Rule Voting Games Dominance-Solvable?

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  • Dhillon, A.
  • Lockwood, B.

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

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 549.

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Length: 40 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:wrk:warwec:549

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Keywords: VOTING ; GAMES ; DEMOCRACY;

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References

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  1. Börgers, Tilman & Janssen, Maarten C.W., 1995. "On the dominance solvability of large cournot games," Games and Economic Behavior, Elsevier, Elsevier, vol. 8(2), pages 297-321.
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  4. DE SINOPOLI, Francesco, 1998. "Strategic stability and non cooperative voting games: the plurality rule," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1998043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  13. Rajan, Uday, 1998. "Trembles in the Bayesian Foundations of Solution Concepts of Games," Journal of Economic Theory, Elsevier, Elsevier, vol. 82(1), pages 248-266, September.
  14. Dhillon, A. & Lockwood, B., 1999. "When are Plurality Rule Voting Games Dominance-Solvable?," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 549, University of Warwick, Department of Economics.
  15. Mariotti, Marco, 2000. "Maximum Games, Dominance Solvability, and Coordination," Games and Economic Behavior, Elsevier, Elsevier, vol. 31(1), pages 97-105, April.
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Citations

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Cited by:
  1. Bryan McCannon, 2009. "Can the majority lose the election?," Review of Economic Design, Springer, Springer, vol. 13(4), pages 305-317, December.
  2. De Sinopoli, F. & Iannantuoni, G., 2005. "Extreme Voting under Proportional Representation: The Multidimensional Case," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0531, Faculty of Economics, University of Cambridge.
  3. 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.
  4. Francesco De Sinopoli, 2003. "A Note on Forward Induction in a Model of Representative Democracy," CEIS Research Paper, Tor Vergata University, CEIS 21, Tor Vergata University, CEIS.
  5. Lucia Buenrostro & Amrita Dhillon & Peter Vida, 2013. "Scoring rule voting games and dominance solvability," Social Choice and Welfare, Springer, Springer, vol. 40(2), pages 329-352, February.
  6. 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), Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS 201329, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
  7. Vincent Merlin & Jörg Naeve, 2000. "Implementation of Social Choice Functions via Demanding Equilibria," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim, Department of Economics, University of Hohenheim, Germany 191/2000, Department of Economics, University of Hohenheim, Germany, revised 25 Sep 2001.
  8. Eric Le Borgne & Ben Lockwood, 2002. "Candidate Entry, Screening, and the Political Budget Cycle," IMF Working Papers 02/48, International Monetary Fund.
  9. Ben Lockwood & Eric Le Borgne, 2003. "Do Elections Always Motivate Incumbents? Experimentation vs. Career Concerns," IMF Working Papers 03/57, International Monetary Fund.
  10. Dhillon, Amrita & Lockwood, Ben, 2004. "When are plurality rule voting games dominance-solvable?," Games and Economic Behavior, Elsevier, Elsevier, vol. 46(1), pages 55-75, January.
  11. Bag, Parimal Kanti & Sabourian, Hamid & Winter, Eyal, 2009. "Multi-stage voting, sequential elimination and Condorcet consistency," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(3), pages 1278-1299, May.
  12. Joaquín Pérez & Omar De la Cruz, 2014. "Implementation of Jefferson-d’Hondt rule in the formation of a parliamentary committee," Social Choice and Welfare, Springer, Springer, vol. 42(1), pages 17-30, January.
  13. M. Braham & F. Steffen, 2007. "The Chairman’s Paradox Revisited," Social Choice and Welfare, Springer, Springer, vol. 28(2), pages 231-253, February.
  14. Dellis, Arnaud, 2010. "Weak undominance in scoring rule elections," Mathematical Social Sciences, Elsevier, Elsevier, vol. 59(1), pages 110-119, January.
  15. Francesco De Sinopoli & Giovanna Iannantuoni & Carlos Pimienta, 2012. "Scoring Rules: A Game-Theoretical Analysis," Discussion Papers, School of Economics, The University of New South Wales 2012-40, School of Economics, The University of New South Wales.
  16. le Borgne, E. & Lockwood, B., 2000. "Do Elections Always Motivate Incumbents?," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 580, University of Warwick, Department of Economics.

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