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**Expected utility** is the expected value of a utility function.

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.

- 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