The proof of the Gibbard-Satterthwaite theorem revisited

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 voting rule is neutral. The simple arguments in the proofs may be especially useful in classroom situations.