Summary: A social choice correspondence is Arrovian if it satisfies Arrow's choice axiom and independence of infeasible alternatives. For any such correspondence there is a large fraction of the population whose preferences are irrelevant to the social decision in a large fraction of situations. We consider the case of a finite outcome set, and also an outcome set of positive but finite Lebesgue measure (in some Euclidean space). An unrestricted individual preference domain is assumed. The agenda domain assumption allows for a finite lower bound, possibly greater than 2, on the size of a feasible set.