Expected utility
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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.
Arrow (1963) attributes to Daniel Bernoulli (1738) the earliest known written statement of this hypothesis. 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.
A related concept is the certainty equivalent of a gamble. The more risk-averse a person is, the more they will be prepared to pay to eliminate risk, for example accepting $1 today instead of a 50% chance of $2 tomorrow, even though the expected utility is the same. 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 why people may buy an insurance policy and a lottery ticket on the same day.
Further readings
K.J. Arrow (1963) "Uncertainty and the Welfare Economics of Medical Care", American Economic Review, Vol. 53, p.941-73.