Two Brief Proofs of Arrow's Impossibility Theorem
The ﬁrst proof shows that Arrow’s axioms guarantee neutrality: every social choice must be made in exactly the same way, which quickly leads to dictatorship. The second proof clariﬁes the last step, and also conﬁrms the intimate connection between Arrow’s Impossibility Theorem and the Condorcet triple. The second proof shows that a doubly pivotal agent must be a dictator; the Condorcet triple guarantees the existence of a doubly pivotal agent. Neutrality guarantees the existence of a (symmetrically) doubly pivotal agent.
Geanakoplos, John, "Two Brief Proofs of Arrow's Impossibility Theorem" (1996). Cowles Foundation Discussion Papers. 1366.