Arrow's theorem proves that no voting procedure can meet certain conditions of both fairness and logic. In this note, Grant Hayden explores the ramifications of the theorem for qualitative vote dilution. After describing Arrow's argument, Mr. Hayden considers four democratic voting procedures...

Introduction -- Elementary Logic -- Sets, Relations, Functions -- Binary Relations -- Social Choice Theoretic Framework and Arrow Impossibility Theorem -- Some Important Value-Judgments, Rules and Theorems -- Implications of Weakening of Some of Arrow Conditions -- The Method of Majority...

Consider a setting in which individual strict preferences need to be aggregated into a social strict preference relation. For two alternatives and an odd number of agents, it follows from May’s Theorem that the majority aggregation rule is the only one satisfying anonymity, neutrality, and...

Politicians, CEOs and various other types of dictators make social choices that influence both their own and others' welfare. When a dictator's preferred alternative differs from recipients', it is unclear which preferences they aggregate and how they determine this set of admissible...