Why Fair Ranking Rules Collide

Four voters keep the same A-versus-B preferences, but a points rule reverses the group ranking. This original example introduces the specific requirements in Arrow's impossibility theorem. We enumerate every unanimous, pairwise-independent strict ranking rule for two and three voters with three options. Only rules that copy a fixed voter survive every ballot profile. These finite illustrations are not a general proof, and the theorem does not say every voting method is equally good. CHAPTERS 00:00 The ranking flips 01:44 Which requirements collide? 04:22 The two-voter rule factory 05:54 Every three-voter rule 06:53 Why majority can cycle 08:06 What the theorem does and does not say 09:38 Choose the requirements first SOURCES Arrow (1950): https://doi.org/10.1086/256963 Mossel (2009): https://arxiv.org/abs/0901.4727 Maskin (2014): https://nrs.harvard.edu/URN-3:HUL.INS... All graphics and finite examples are original Oddly Certain work. Two independent exact verifiers check the rule census. Oddly Certain creates original animated explanations of paradoxes, probability, logic and counterintuitive systems. #ArrowsTheorem #VotingTheory #OddlyCertain