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The implementation of social choice functions via social choice correspondences: A general formulation and a limit result

Arunava Sen
Social Choice and Welfare
Vol. 12, No. 3 (June 1995), pp. 277-292
Published by: Springer
Stable URL: http://www.jstor.org/stable/41106133
Page Count: 16
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The implementation of social choice functions via social choice correspondences: A general formulation and a limit result
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Abstract

A corollary of Maskin's characterization theorem for Nash implemen table social choice correspondences is that only trivial social choice functions can be implemented. This paper explores the consequences of implementing non-trivial social choice functions by extending them minimally to social choice correspondences which are implementable. The concept of asymptotic monotonicity is introduced. The main result states that it is not possible to find social choice rules satisfying a mild condition on its range, which is asymptotically monotonic. The implication of this result is that the multiplicity of equilibria problem which is at the heart of Nash implementation theory persists even in the limit as the number of individuals in society tends to infinity. This is true even though the opportunities for an individual to manipulate the outcome disappears in the limit.

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