A result of John Harsanyi concerns the aggregation of individuals' preferences into social preferences. The result states that if the individuals in a society and the society as a whole have preference relations that compare probability distributions on a set of outcomes, and the preference...

If only the strict part of social preference is required to be transitive then Independence of Irrelevant Alternatives implies that there is a coalition containing all but one individual that cannot force x to be socially ranked above y for at least half of the pairs of alternatives (x,y)

It has been shown that, with an alternative factorization of fuzzy weak preferences into symmetric and antisymmetric components, one can prove a fuzzy analogue of Arrow's Impossibility Theorem even when the transitivity requirements on individual and social preferences are very weak. It is...