Strategy-Proofness and 'Median Voters'

Abstract

We consider the problem of choosing a level of the public good for an economy in which agents have continuous and single-peaked preferences (Black, 1948). We show that a solution satisfying strategy-proofness and continuity if and only if it is an augmented median-voter solution. An augmented median-voter solution is described in terms of 2^n parameters (which satisfy an anti-monotonicity condition) as follows: n+1 of them are selected according to an increasing order of the peaks; the outcome is the median of these n+1 parameters and the n peaks. This result establishes a formal connection between strategy-proofness and a generalized notion of median voter. (Similar median formulas were used by Moulin (1980) to describe smaller classes of solutions.) We provide an interpretation of these 2^n parameters in terms of the following properties: anonymity, voter sovereignty, unanimity, and Pareto efficiency.

JEL Classification: D7, D8