STRATEGY-PROOFNESS ON EUCLIDEAN SPACES

In this paper we characterize strategy-proof voting schemes on Euclide an spaces. A voting scheme is strategy-proof whenever it is optimal fo r every agent to report his best alternative. Here the individual pref erences underlying these best choices are separable and quadratic. It turns out that a voting scheme is strategy-proof if and only if (alpha ) its range is a closed Cartesian subset of Euclidean space, (beta) th e outcomes are at a minimal distance to the outcome under a specific c oordinatewise veto voting scheme, and (gamma) it satisfies some monoto nicity properties. Neither continuity nor decomposability is implied b y strategy-proofness, but these are satisfied if we additionally impos e Pareto-optimality or unanimity.