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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.

Suggested Citation

  • 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.
  • Handle: RePEc:wrk:warwec:549
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    Cited by:

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    2. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    3. Mr. Ben Lockwood & Mr. Eric Le Borgne, 2003. "Do Elections Always Motivate Incumbents? Experimentation vs. Career Concerns," IMF Working Papers 2003/057, International Monetary Fund.
    4. 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.
    5. Laurent Denant-Boemont & Enrico Diecidue & Olivier l’Haridon, 2017. "Patience and time consistency in collective decisions," Experimental Economics, Springer;Economic Science Association, vol. 20(1), pages 181-208, March.
    6. Elkind, Edith & Grandi, Umberto & Rossi, Francesca & Slinko, Arkadii, 2020. "Cognitive hierarchy and voting manipulation in k-approval voting," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 193-205.
    7. 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.
    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. Sébastien Courtin & Matías Núñez, 2017. "Dominance solvable approval voting games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(6), pages 1047-1068, December.
    10. Francesco Sinopoli & Giovanna Iannantuoni, 2008. "Extreme voting under proportional representation: the multidimensional case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 401-417, April.
    11. Neelam Gohar & Gul E. Saman & Salma Noor & Sehrish Aslam & Maryam Khan & Anam Qadeer & Fawad Qayum, 2019. "Analysis of dynamics of voting system for small number of candidates," Computational and Mathematical Organization Theory, Springer, vol. 25(3), pages 225-246, September.
    12. Kei Kawai & Yasutora Watanabe, 2013. "Inferring Strategic Voting," American Economic Review, American Economic Association, vol. 103(2), pages 624-662, April.
    13. 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;The Society for Social Choice and Welfare, vol. 42(1), pages 17-30, January.
    14. Lucia Buenrostro & Amrita Dhillon & Peter Vida, 2013. "Scoring rule voting games and dominance solvability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 329-352, February.
    15. 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.
    16. Christian Basteck, 2016. "Scoring rules and implementation in iteratively undominated strategies," Working Papers 2016002, Berlin Doctoral Program in Economics and Management Science (BDPEMS).
    17. M. Braham & F. Steffen, 2007. "The Chairman’s Paradox Revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(2), pages 231-253, February.
    18. Mr. Ben Lockwood & Mr. Eric Le Borgne, 2002. "Candidate Entry, Screening, and the Political Budget Cycle," IMF Working Papers 2002/048, International Monetary Fund.
    19. Dellis, Arnaud, 2010. "Weak undominance in scoring rule elections," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 110-119, January.
    20. 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.
    21. Francesco Sinopoli & Giovanna Iannantuoni & Carlos Pimienta, 2015. "On stable outcomes of approval, plurality, and negative plurality games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 889-909, April.
    22. Bryan McCannon, 2009. "Can the majority lose the election?," Review of Economic Design, Springer;Society for Economic Design, vol. 13(4), pages 305-317, December.
    23. Arzumanyan, Mariam & Polborn, Mattias K., 2017. "Costly voting with multiple candidates under plurality rule," Games and Economic Behavior, Elsevier, vol. 106(C), pages 38-50.
    24. Dhillon, Amrita & Kotsialou, Grammateia & Xefteris, Dimitris, 2021. "Information Aggregation with Delegation of Votes," SocArXiv ubk7p, Center for Open Science.
    25. 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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    More about this item

    Keywords

    VOTING ; GAMES ; DEMOCRACY;
    All these keywords.

    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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