Money Pump with Foresight

I describe in section 1 how cyclical preferences can arise. In section 2, I relate preference to judgments of choiceworthiness and distinguish between two kinds of preference cycles, vicious and benign. In section 3, I run through the standard money pump in order to show, in section 4, how this pump can be stopped by foresight, using backward induction. A new money pump that *cannot* be stopped by foresight is presented in section 5. This pump works even for agents with benign cyclical preferences. What makes it work is persistency on the part of the would-be exploiter. In section 6, I compare this pump to a diachronic Dutch book that can be set up against someone whose probability assignments violate Reflection. Even in this case, the book only works if the bookie is assumed to be persistent. I use this comparison between preference cyclicity and violations of Reflection in order to question whether exploitability must be seen as a proof of irrationality. Finally, in section 7, I consider resolute choice as an alternative to the backward-induction procedure. While a resolute chooser cannot be exploited, I argue that resoluteness is not required by rationality. The argument is based on a suggestion that rationality, when it comes to actions, is a local rather than a global requirement.