# Expected utility hypothesis

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Outline

The **expected utility hypothesis** is the hypothesis in economics that the utility of an agent facing uncertainty is calculated by considering utility in each possible state and constructing a weighted average. The weights are the agent's estimate of the probability of each state. The expected utility is thus an expectation in terms of probability theory.

Daniel Bernoulli (1738) gave the earliest known written statement of this hypothesis as a way to resolve the St. Petersburg Paradox. In the expected utility theorem, v. Neumann and Morgenstern proved that any "normal" preference relation over a finite set of states can be written as an expected utility. (Therefore, it is also called **von-Neumann Morgenstern utility**.) For this reason, the expected utility is considered to be the best prescriptive theory for decisions under risk.

A related concept is the **certainty equivalent** of a gamble. The more risk-averse a person is, the more he will be prepared to pay to eliminate risk, for example accepting $1 instead of a 50% chance of $3, even though the expected value of the latter is more. People may be risk-averse or risk-loving depending on the amounts involved and on whether the gamble relates to becoming better off or worse off; this is a possible explanation for why people may buy an insurance policy and a lottery ticket on the same day. However, expected utility as a descriptive model of decisions under risk has in recent years been replaced by more sophisticated variants that take irrational deviations from the expected utility model into account; compare Prospect theory and the general article on Behavioral finance.

## Further readingEdit

P.Anand (1993) "Foundations of Rational Choice Under Risk", Oxford, Oxford University Press.
K.J. Arrow (1963) "Uncertainty and the Welfare Economics of Medical Care", *American Economic Review*, Vol. 53, p.941-73.

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