y and Ton Storcken

In spatial environments we consider social welfare functions satisfying Ar-row's requirements, i.e. weak Pareto and independence of irrelevant alterna-tives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2 N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional we estab-lish Arrow's impossibility theorem. Among others we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex