 Could an agent really have intransitive preferences? Work in experimental and theoretical economics (see, for example, Tversky 1969) suggests that intransitive preferences exist and may be quite common. Consideration of the following situation might help make it clear how intransitive preferences can arise (whether or not they are rational). Suppose Jay can accept one of three jobs: job A is very stimulating but low-paying; job B is somewhat stimulating and pays decently; job C is not stimulating but pays very well. Given this situation, one can imagine Jay having the following preferences: He prefers job A over job B because the difference between having a low-paying job and a decently-paying job is not significant enough to make Jay want to pass up a very stimulating job. Similarly, he prefers job B over job C because the difference between having a decently-paying job and a high-paying job is not significant enough to make Jay want to pass up a stimulating job. But he prefers job C over job A because the difference between having a high-paying job and a low-paying job is significant enough to make Jay want to pass up even a very stimulating job.