In spatial environments we consider social welfare functions satisfying arrow’s requirements, i.e. Weak pareto and independence of irrelevant alternatives. Individual preferences measure distances between alternatives according to the lplp-norm (for a fixed 1=p=81=p=8). When the policy space is multi-dimensional and the set of alternatives has a non-empty and connected interior and its boundary has no tails, any quasi-transitive welfare function must be oligarchic. As a corollary we obtain that for transitive welfare functions weak pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty and connected interior and its boundary has no tails.