Abstract. We present an alternative proof of the Gibbard
s
random dictatorship theorem with ex post Pareto optimality.
Gibbard(1977) showed that when the number of alternatives is finite and
larger than two, and individual preferences are linear (strict), a
strategy-proof decision scheme (a probabilistic analogue of a social
choice function or a voting rule) is a convex combination of decision
schemes which are, in his terms, either unilateral or duple. As a
corollary of this theorem (credited to H. Sonnenschein) he showed that
a decision scheme which is strategy-proof and satisfies ex post Pareto
optimality is randomly dictatorial. We call this corollary the
Gibbards random dictatorship theorem. We present a proof of this theorem which is direct and follows closely the original Gibbard
s
approach. Focusing attention to the case with ex post Pareto optimality
our proof is more simple and intuitive than the original Gibbard
s proof.
Received: 15 October 2001, Accepted: 23 May 2003, JEL Classification:
D71, D72
Yasuhito
Tanaka: The author is grateful to an anonymous referee and the
Associate editor of this journal for very helpful comments and
suggestions. And this research has been supported by a grant from the
Zengin Foundation for Studies on Economics and Finance in Japan.