On the manipulation of social choice correspondences |
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Authors: | Carmelo Rodríguez-Álvarez |
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Institution: | (1) Departamento de Economía, Universidad Carlos III de Madrid, Calle Madrid 126, 28903 Getafe, Spain;(2) Departamento de Teoría e Historia Económica, Universidad de Málaga, Plaza El Ejido, 29071 Málaga, Spain |
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Abstract: | Duggan and Schwartz (Soc Choice and Welfare 17: 85–93, 2000) have proposed a generalization of the Gibbard–Satterthwaite Theorem to multivalued social choice rules.
They show that only dictatorial rules are strategy-proof and satisfy citizens sovereignty and residual resoluteness. Citizens sovereignty requires that each alternative is chosen at some preference profile. Residual resoluteness compels
the election to be single-valued when the preferences of the voters are “similar”. We propose an alternative proof to the
Duggan and Schwartz’s Theorem. Our proof highlights the crucial role of residual resoluteness. In addition, we prove that
every strategy-proof and onto social choice correspondence concentrates the social decision power in the hands of an arbitrary group of voters. Finally,
we show that this result still holds in a more general framework in which voters report their preferences over sets of alternatives. |
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