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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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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/plural.pdf
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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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Find related papers by JEL classification:
  • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
  • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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  1. Besley, Timothy & Coate, Stephen, 1997. "An Economic Model of Representative Democracy," The Quarterly Journal of Economics, MIT Press, vol. 112(1), pages 85-114, February.
  2. Brams, Steven J. & Fishburn, Peter, 1998. "Voting Procedures," Working Papers 98-30, C.V. Starr Center for Applied Economics, New York University.
  3. Börgers, Tilman & Janssen, Maarten C.W., 1995. "On the dominance solvability of large cournot games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 297-321.
  4. Francesco De Sinopoli, 2000. "Sophisticated voting and equilibrium refinements under plurality rule," Social Choice and Welfare, Springer, vol. 17(4), pages 655-672.
  5. Jonathan Levin & Barry Nalebuff, 1995. "An Introduction to Vote-Counting Schemes," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 3-26, Winter.
  6. 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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  8. Forsythe, Robert, et al, 1996. "An Experimental Study of Voting Rules and Polls in Three-Candidate Elections," International Journal of Game Theory, Springer, vol. 25(3), pages 355-83.
  9. Marx, Leslie M. & Swinkels, Jeroen M., 1997. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 18(2), pages 219-245, February.
  10. Lepelley, Dominique, 1993. "On the probability of electing the Condorcet," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 105-116, February.
  11. 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.
  12. Roger B. Myerson, 2000. "Comparison of Scoring Rules in Poisson Voting Games," Econometric Society World Congress 2000 Contributed Papers 0686, Econometric Society.
  13. David P. Myatt, 2000. "The New Theory of Strategic Voting," Econometric Society World Congress 2000 Contributed Papers 1586, Econometric Society.
  14. DE SINOPOLI, Francesco & TURRINI, Alessandro, . "A remark on voters' rationality in a model of representative democracy," CORE Discussion Papers RP -1562, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. 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).
  16. Roger B. Myerson & Robert J. Weber, 1988. "A Theory of Voting Equilibria," Discussion Papers 782, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  17. 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.
  18. 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).
  19. Mariotti, Marco, 2000. "Maximum Games, Dominance Solvability, and Coordination," Games and Economic Behavior, Elsevier, vol. 31(1), pages 97-105, April.
  20. Borgers, Tilman, 1992. "Iterated Elimination of Dominated Strategies in a Bertrand-Edgeworth Model," Review of Economic Studies, Wiley Blackwell, vol. 59(1), pages 163-76, January.
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Cited by:

  1. Francesco Sinopoli & Giovanna Iannantuoni, 2008. "Extreme voting under proportional representation: the multidimensional case," Social Choice and Welfare, Springer, vol. 30(3), pages 401-417, April.
  2. Bryan McCannon, 2009. "Can the majority lose the election?," Review of Economic Design, Springer, vol. 13(4), pages 305-317, December.
  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. 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.
  5. 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.
  6. 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.
  7. 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.
  8. De Sinopoli, Francesco, 2004. "A note on forward induction in a model of representative democracy," Games and Economic Behavior, Elsevier, vol. 46(1), pages 41-54, January.
  9. 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.
  10. 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.
  11. Ben Lockwood & Eric Le Borgne, 2003. "Do Elections Always Motivate Incumbents? Experimentation vs. Career Concerns," IMF Working Papers 03/57, International Monetary Fund.
  12. M. Braham & F. Steffen, 2007. "The Chairman’s Paradox Revisited," Social Choice and Welfare, Springer, vol. 28(2), pages 231-253, February.
  13. 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.
  14. 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.
  15. Dellis, Arnaud, 2010. "Weak undominance in scoring rule elections," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 110-119, January.
  16. 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, vol. 42(1), pages 17-30, January.

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