Another direct proof for the Gibbard-Satterthwaite Theorem

We prove the following result which is equivalent to the Gibbard-Satterthwaite Theorem: when there are at least 3 alternatives, for any unanimous and strategy-proof social choice function, at any given profile if an individual's top ranked alternative differs from the social choice, then she can not change the social choice at that profile by changing her ranking. Hence, proving it yields a new proof for the Gibbard-Satterthwaite Theorem.

► This paper provides a new proof for the Gibbard-Satterthwaite Theorem. ► We prove it in two steps. ► We modify the notion of option set and show that these are singletons for some of the individuals.