 Suppose, in addition, that we demand that the collective preference satisfy the Pareto criterion. That is, if each individual in society prefers policy p to policy q, then society collectively must prefer p to q. Unfortunately, Seidenfeld, Kadane, and Schervish [1989] have proven that, if at least two individuals both rank two consequences differently and assess the likelihoods of two states of the world differently, then society cannot simultaneously satisfy the Pareto criterion and the demands of aggregate rationality.