 Utilities (desirabilities) of outcomes, their probabilities, and rational preferences are all intimately linked. The Port Royal Logic (Arnauld, 1662) showed how utilities and probabilities together determine rational preferences; de Finetti’s betting analysis derives probabilities from utilities and rational preferences; von Neumann and Morgenstern (1944) derive utilities from probabilities and rational preferences. And most remarkably, Ramsey (1926) (and later, Savage 1954 and Jeffrey 1966) derives both probabilities and utilities from rational preferences alone.