Abstract
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 l p -norm (for a fixed 1 ≤ p ≤ ∞ ). 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.
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