We give a direct and very short proof of the famous Gibbard-Satterthwaite theorem [Alan Gibbard (1977) and Mark Satterthwaite (1975)]. The proof is based on investigating the properties of one critical preference profile constructed from those alternatives that individuals are not decisive on....

We study necessary and sufficient conditions for a choice function to be rationalised in the following sense: there exists a complete asymmetric relation T (a tournament) such that for each feasible (finite) choice situation, the choice coincides with the uncovered set of T restricted to that...