This paper provides three short proofs of the classical Gibbard–Satterthwaite theorem. The theorem is first proved in the case with only two voters. The general case follows then from an induction argument over the number of voters. The proof of the theorem is further simplified when the...

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 lp-norm (for a fixed 1=p=[infinity]). When the policy space...