Brief proofs of Arrovian impossibility theorems

Since Kenneth Arrow showed the general possibility theorem, a number of social choice theorists have provided alternative proofs of it. In a recent article, Geanakoplos (Econ Theory 26:211-215, 2005) has constructed a new proof of the theorem. The present article provides alternative proofs of various Arrovian impossibility results from the 1960s to the 1970s by utilizing Geanakoplos's method. We prove semi-order impossibility theorems, the quasi-transitive veto theorem, the quasi-transitive dictatorship theorem, the triple acyclic veto theorem, and the impossibility theorem without the Pareto principle.