Plott’s analysis reveals a subtlety. The full strength of SO is not needed to secure path independence of choice. It is sufficient that social preference is a (complete and) quasi-transitive relation, having a strict component that is transitive but an indifference component that, perhaps, is not transitive. Sen (1969: Theorem V) demonstrated the compatibility of this weaker requirement with all of Arrow’s other conditions, but noted that the aggregation function he came up with would not generally be found attractive. Its unattractiveness was no accident. Allan Gibbard showed that the only social welfare functions made available by allowing intransitivity of social indifference, while keeping Arrow’s other requirements in place, are what he called liberum veto oligarchies (Gibbard 1969, 2014). There has in every case to be some group of individuals, the oligarchs, such that the society always strictly prefers one alternative to another if all of the oligarchs strictly prefer it, but never does so if that would go against the strict preference of any oligarch.[5] A dictatorship, in Arrow’s sense, is a liberum veto oligarchy of one. Relaxing SO by limiting the transitivity requirement to strict social preferences therefore does not seem a promising way of securing, in spite of Arrow’s theorem, the existence of acceptable social welfare functions. 