Von Neumann and Morgenstern proved the expected utility theorem, which says that when a rational agent chooses between different "gambles" (probability distributions over outcomes), the utility of such a gamble can always be seen as the expected utility of the gamble's outcome.
Humans, of course, are a different story.
By Stuart Armstrong:
- Extreme risks: when not to use expected utility
- Expected utility without the independence axiom
- Money pumping: the axiomatic approach
- In conclusion: in the land beyond money pumps lie extreme events