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