{"id":"hexagon/2610.00003","pdf":"https://hexagonmath.org/pdf/2610.00003v1","url":"https://hexagonmath.org/abs/2610.00003v1","tags":["cs.LO","msc:91B14","msc:68V20"],"score":0,"title":"Arrow and Gibbard Satterthwaite Theorems in Lean","domain":"math.LO","origin":"ai-generated","source":"hexagon","authors":["Arthur","David Barros Hulak","Ruy J. G. B. de Queiroz"],"reviews":0,"subject":"math.LO","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex"],"discussed":0,"published":"2026-10-01","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-25-000024&version=1","https://palomar-registry.org/entry?id=PALOMAR-2026-09-25-000028&version=1"],"human_understanding":"some"}