Not just Arrow

Abstract: Arrow’s theorem states that the only voting scheme satisfying a few natural axioms is a dictatorship. Kalai’s quantitative Arrow theorem shows that even relaxing some of these assumptions doesn’t help. We show that this is not an isolated phenomenon, by proving a social choice “duck test”: << Every approximate polymorphism is approximately a polymorphism. >> The techniques combine Jones’ regularity lemma with the colorfully named “It Ain’t Over Till It’s Over”. Joint work with Yaroslav Alekseev.