Politics, Philosophy & Economics, Volume 21, Issue 4, Page 347-371, November 2022. We sometimes have to choose between options that are seemingly incomparable insofar as they seem to be neither better than, worse than, nor equal to each other. This often happens when the available options are quite different from one another. For instance, consider a choice between prioritizing either criminal justice reform or healthcare reform as a public policy goal. Even after the relevant details of the goals and possible (...) reforms are filled in, it is plausible that neither goal is better than, worse than, nor equal to the other. Such seemingly incomparable options present a problem for rational choice since it is unclear how an agent might rationally choose between them. What we need are some principles to help govern rational choice when faced with seemingly incomparable options. I here present three such principles. While each principle is individually compelling, I show that they are jointly incompatible. I then argue that the correct response to this inconsistent triad is to reject the principle that rationally censures performing a sequence of choices one knows will result in a suboptimal outcome. The upshot is that when seeming incomparability is involved, an agent can money pump themselves without being less rational for it. (shrink)