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When are Plurality Rule Voting Games Dominance-Solvable?

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Listed author(s):
  • 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
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. Francesco De Sinopoli, 2000. "Sophisticated voting and equilibrium refinements under plurality rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 655-672.
  2. 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.
  3. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
  4. Timothy Besley & Stephen Coate, 1997. "An Economic Model of Representative Democracy," The Quarterly Journal of Economics, Oxford University Press, vol. 112(1), pages 85-114.
  5. Tilman Börgers, 1992. "Iterated Elimination of Dominated Strategies in a Bertrand-Edgeworth Model," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 163-176.
  6. 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.
  7. De Sinopoli, Francesco & Turrini, Alessandro, 2002. " A Remark on Voters' Rationality in a Model of Representative Democracy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(2), pages 163-170.
  8. David P. Myatt, 2000. "The New Theory of Strategic Voting," Econometric Society World Congress 2000 Contributed Papers 1586, Econometric Society.
  9. 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.
  10. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
  11. 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.
  12. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
  13. Forsythe, Robert & Rietz, Thomas & Myerson, Roger & Weber, Robert, 1996. "An Experimental Study of Voting Rules and Polls in Three-Candidate Elections," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(3), pages 355-383.
  14. Brams, Steven J. & Fishburn, Peter C., 2002. "Voting procedures," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 4, pages 173-236 Elsevier.
  15. Lepelley, Dominique, 1993. "On the probability of electing the Condorcet," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 105-116, February.
  16. 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).
  17. Mariotti, Marco, 2000. "Maximum Games, Dominance Solvability, and Coordination," Games and Economic Behavior, Elsevier, vol. 31(1), pages 97-105, 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. 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.
  20. 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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