From Condorcet’s paradox to Arrow: yet another simple proof of the impossibility theorem

Abstract Condorcet exposed a limitation of majority-based pairwise comparison by showing that, for specific preference profiles over three alternatives, it leads to a contradiction. Arrow’s theorem is often introduced as a generalization of this finding. A novel formulation of the proof is presented that strictly adheres to this logic, establishing that for any non-dictatorial social choice rule, a contradiction-generating preference profile always exists and can be identified using a straightforward procedure.