 Integrability presents a serious challenge to the economic account of rationality. Nevertheless, the theory has substantial resources to meet this challenge. To illustrate, consider Neumann’s [2007] analysis of the famous example used by Anand [1993] and Sen [1993]. In this example, they consider an agent whom we shall call Freddie. Freddie is Liza’s guest for dinner and he has been offered a plate with three slices of cake on it. One slice is small, one medium, and one large. Freddie has two concerns: he wants the largest piece of cake available and he wants to conform to the social norm “never take the largest piece”. In Sen’s and Anand’s account, Freddie cannot integrate these two concerns into a preference because his choices violate a condition of contraction consistency which is necessary for transitivity. That is, from the pair (small slice, medium slice), Freddie chooses the small slice but from the triple (small slice, medium slice, large slice), Freddie chooses the medium slice. These choices, however, are inconsistent only under the description given. 