Arrow and Gibbard-Satterthwaite revisited. Extended domains and shorter proofs

This short note offers some insights on Arrow's theorem for social choice functions and the Gibbard-Satterthwaite theorem on the manipulatibility of voting schemes. At no cost in complexity, it extends these results by exploring the possibility that indifferences be admissible for some pairs of alternatives and not for others: the latter theorem is shown to apply under a larger class of domain conditions than the first. At the same time, the proposed proofs for the celebrated theorems (in their extended versions) are of independent interest, being much shorter and more transparent than previous proofs for the standard versions.