 Although societies are very different from individuals, they have mechanisms to evaluate alternatives and make choices, and their evaluations and choices may be rational or irrational. It is not, however, obvious, what principles of rationality should govern the choices and evaluations of society. Transitivity is one plausible condition. It seems that a society that chooses X when faced with the alternatives X or Y, Y when faced with the alternatives Y or Z and Z when faced with the alternatives X or Z either has had a change of heart or is choosing irrationally. Yet, purported irrationalities such as these can easily arise from standard mechanisms that aim to link social choices and individual preferences. Suppose there are three individuals in the society. Individual One ranks the alternatives X, Y, Z. Individual Two ranks them Y, Z, X. Individual Three ranks them Z, X, Y. If decisions are made by pairwise majority voting, X will be chosen from the pair (X, Y), Y will be chosen from (Y, Z), and Z will be chosen from (X, Z). Clearly this is unsettling, but are possible cycles in social choices irrational?