Open Research Index

Arrow's theorem via Fourier analysis

Joris Roos

Palomar Registrypalomar/PALOMAR-2026-09-01-000011Sep 1, 2026cs.DMscore 0

This is a formalization in Lean 4 of Arrow's theorem for three-candidate elections as stated in Ryan O'Donnell's book "Analysis of Boolean Functions", Sec. 2.5, with a single voting rule applied to every pairwise election. The theorem states that every unanimous voting rule that always admits a Condorcet winner must be a dictatorship, i.e. there must exist a voter that alone determines the outcome. Here voting rules are encoded by Boolean-valued functions on the Hamming cube. The proof follows the exposition given there, which is based on Gil Kalai's Fourier-analytic argument using the…

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