Unequivocal majority and Maskin-monotonicity |
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Authors: | Pablo Amorós |
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Institution: | 1.Departamento de Teoría e Historia Económica,Universidad de Málaga,Malaga,Spain |
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Abstract: | The unequivocal majority of a social choice rule is a number of agents such that whenever at least this many agents agree
on the top alternative, then this alternative (and only this) is chosen. The smaller the unequivocal majority is, the closer
it is to the standard (and accepted) majority concept. The question is how small can the unequivocal majority be and still
permit the Nash-implementability of the social choice rule; i.e., its Maskin-monotonicity. We show that the smallest unequivocal
majority compatible with Maskin-monotonicity is
n-
ë \fracn-1m
û{n-\left\lfloor \frac{n-1}{m} \right\rfloor} , where n ≥ 3 is the number of agents and m ≥ 3 is the number of alternatives. This value is equal to the minimal number required for a majority to ensure the non-existence
of cycles in pairwise comparisons. Our result has a twofold implication: (1) there is no Condorcet consistent social choice
rule satisfying Maskin-monotonicity and (2) a social choice rule satisfies k-Condorcet consistency and Maskin-monotonicity if and only if
k 3 n-
ë \fracn-1m
û{k\geq n-\left\lfloor \frac{n-1}{m}\right\rfloor}. |
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Keywords: | |
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