Strategy Proofness, Pareto Optimality and Strictly Convex Norms.

A voting scheme assigns to each profile of alternatives chosen by "n" individuals a compromise alternative. Here the set of alternatives is represented by the Euclidean plane. The individual utilities for the compromise point are equal to the negatives of the distances of this point to the individually best points. These distances are measured by a given strictly convex norm, common to all agents. A voting scheme is strategy-proof, if voting for one's best point is an optimal strategy for all agents.