Strategy-proofness and single-plateaued preferences

Abstract

In the framework of the provision of one pure public good, we obtain a characterization of the class of strategy-proof voting schemes on single-plateaued preferences over a convex and closed subset of the real line (the set of feasible levels of the public good). Moulin [8] completely characterizes strategy-proof voting schemes on single-peaked preferences as the family of minmax rules. We obtain the result that any strategy-proof voting scheme on the domain of single-plateaued preferences can be viewed as a two-stage procedure. First, we choose a Moulin's minmax rule. Then, in the tie-breaking stage, we select one representative alternative from each voter's plateau using a strategy-proof scheme with respect to the other voters. The final choice is obtained by applying the minmax rule to the representative best alternatives. Similarly, we can also characterize the subclass of strategy-proof social choice functions satisfying uncompromisingness.