{"id":"palomar/PALOMAR-2026-09-25-000024","url":"https://github.com/Arthur742Ramos/arrow-impossibility-lean/tree/4f405d27d0b244574bbee5d3d79bae0c66bda16e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-25-000024-v1.json","repo":"https://github.com/Arthur742Ramos/arrow-impossibility-lean","tags":["math.LO","cs.GT","msc:91B14","social-choice","lean-formalization","arrow-theorem","game-theory"],"score":0,"title":"Arrow's impossibility theorem (general finite version)","trust":"high","domain":"math.LO","source":"palomar","authors":["Arthur Freitas Ramos"],"reviews":0,"subject":"math.LO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"formalizes":[{"title":"A Difficulty in the Concept of Social Welfare","identifier":"https://doi.org/10.1086/256963","relationship":"formalizes"}]}