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 co