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Arrow's impossibility theorem (general finite version)

Arthur Freitas Ramos

Palomar Registrypalomar/PALOMAR-2026-09-25-000024Sep 25, 2026math.LOscore 0

Formalizes Arrow's impossibility theorem for finitely many voters and finitely many alternatives (at least three): every social welfare function satisfying unanimity and independence of irrelevant alternatives is dictatorial. The proof follows the classical decisive-coalition argument: field expansion (a coalition decisive for one pair is decisive for every pair) and group contraction (a decisive coalition with at least two voters contains a smaller decisive coalition), iterated down to a singleton dictator. This is a reusable formalization artifact, not a claim of new mathematics.

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