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 thar a solution satisfying strategy-proofness a nd continuity if and only if it is an augmented median-voter solution. An augmented median-voter solution is described in terms of 2'' param eters (which satisfy an anti-monotonicity condition) as follows: n + 1 of them are selected according to an increasing order of the peaks; t he outcome is the median of these n + 1 parameters and the,1 peaks. Th is result establishes a formal connection between strategy-proofness a nd a generalized notion of median voter. (Similar median formulas were used by Moulin (1980) to describe smaller classes of solutions.) We p rovide an interpretation of these 2'' parameters in terms of the follo wing properties: anonymity, voter sovereignty, unanimity, and Pareto e fficiency.