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Unequivocal majority and Maskin-monotonicity

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  • Pablo Amorós

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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.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 33 (2009)
Issue (Month): 4 (November)
Pages: 521-532

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Handle: RePEc:spr:sochwe:v:33:y:2009:i:4:p:521-532

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  1. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, vol. 4(1), pages 13-33.
  3. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  4. Orhan Erdem & M. Sanver, 2005. "Minimal monotonic extensions of scoring rules," Social Choice and Welfare, Springer, vol. 25(1), pages 31-42, October.
  5. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May.
  6. Eyal Baharad & Shmuel Nitzan, 2003. "The Borda rule, Condorcet consistency and Condorcet stability," Economic Theory, Springer, vol. 22(3), pages 685-688, October.
  7. Weber, James S, 1993. " An Elementary Proof of the Conditions for a Generalized Condorcet Paradox," Public Choice, Springer, vol. 77(2), pages 415-19, October.
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