Collective Rationality and Social Choice

Arrow’s impossibility theorem states that if a collective choice rule satisfies unrestricted domain, weak Pareto, independence of irrelevant alternatives, and collective rationality, then there exists a dictator. Among others, Arrow’s postulate of collective rationality is controversial. We propose a new axiom for a collective choice rule, decisiveness coherence, which is weaker than collective rationality. It is shown that given the Arrovian axioms other than collective rationality, a dictatorship arises if and only if decisiveness coherence is satisfied. Moreover, we demonstrate that there exists a dictatorial collective choice rule that does not satisfy collective rationality but satisfies the other Arrovian axioms. JEL classification D71