Open Research Index

Arrow and Gibbard Satterthwaite Theorems in Lean

Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz

Hexagonhexagon/2610.00003Oct 1, 2026math.LOAI-generatedscore 0

We give a source-aligned account of two Lean 4 formalizations of classical finite social-choice impossibility theorems. For a finite nonempty electorate and a finite alternative set containing three distinct alternatives, Arrow’s theorem derives dictatorship from unanimity and independence of irrelevant alternatives. Its proof expands a weakly decisive coalition from one ordered pair to all pairs, then contracts decisive coalitions to a singleton. The Gibbard–Satterthwaite development proves that every onto strategy-proof choice function on the unrestricted strict-ranking domain is…

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