A cardinal approach to straightforward probabilistic mechanisms (Q761227)

This paper extends Gibbard's theorem on the manipulation of schemes that mix voting with chance, to the domain of cardinal utilities. Let there be a finite set of voters N (at least two), and a finite set of alternative S (at least three). Each player i has a von Neumann-Morgenstern utility \(u_ i\) defined over S. A probabilistic mechanism is a map from the vector of reported utilities \((u'_ i)\) to the space of probability measures on S. Such a mechanism is straightforward if, for every player i, \(u_ i\) is a dominant strategy for expected utility maximization. The major result of the paper gives necessary and sufficient conditions for a probabilistic mechanism to be straightforward. The class of such mechanisms includes Gibbard's unilateral and duple mechanisms as special cases.