 He claimed that, for a substantial proportion of agents, one would find that \(P_{1}\succ P_{2}\) and \(P_{4}\succ P_{3}\) (call these the “Allais preferences”). However, on the assumptions that (i) the subjects’ degrees of belief align themselves with the objective probabilities given and (ii) the outcomes can be adequately characterised entirely in terms of the associated changes in level of wealth, such a combination of preferences runs contrary to Independence. More specifically, it runs counter to the special case of the principle, according to which the substitution of a common “consequence”, i.e., lottery, in a pair of mixtures leave the order of preference unchanged: