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Unequivocal Majority and Maskin-Monotonicity

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  • Pablo Amoros

    () (Department of Economic Theory, Universidad de Málaga)

Abstract

The unequivocal majority of a social choice rule F is the minimum number of agents that must agree on their best alternative in order to guarantee that this alternative is the only one prescribed by F. If the unequivocal majority of F is larger than the minimum possible value, then some of the alternatives prescribed by F are undesirable (there exists a different alternative which is the most preferred by more than 50% of the agents). Moreover, the larger the unequivocal majority of F, the worse these alternatives are (since the proportion of agents that prefer the same different alternative increases). We show that the smallest unequivocal majority compatible with Maskin-monotonicity is n-((n-1)/m), where n=3 is the number of agents and m=3 is the number of alternatives. This value represents no less than 66.6% of the population.

Suggested Citation

  • Pablo Amoros, 2008. "Unequivocal Majority and Maskin-Monotonicity," Working Papers 2008-3, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    • Handle: RePEc:mal:wpaper:2008-3
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    References listed on IDEAS

    as
    1. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    2. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 13-33.
    3. Eyal Baharad & Shmuel Nitzan, 2003. "The Borda rule, Condorcet consistency and Condorcet stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 685-688, October.
    4. Weber, James S, 1993. "An Elementary Proof of the Conditions for a Generalized Condorcet Paradox," Public Choice, Springer, vol. 77(2), pages 415-419, October.
    5. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    6. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    7. Orhan Erdem & M. Sanver, 2005. "Minimal monotonic extensions of scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 31-42, October.
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    More about this item

    Keywords

    Maskin-monotonicity; Majority; Condorcet winner;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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