Strategy-proofness and “median voters”

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 2n parameters (which satisfy an antimonotonicity 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 2n parameters in terms of the following properties: anonymity, voter sovereignty, unanimity, and Pareto efficiency.