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. Economics (from the Greek οίκος [oikos], house, and νομος [nomos], rule, hence household management) is a social science that studies the production, distribution, trade and consumption of goods and services. ... In [economics]], utility is a measure of the happiness or satisfaction gained consuming good and services. ... An agent is an autonomous entity with an ontological commitment and agenda of its own. ... // Relation between uncertainty, probability and risk In his seminal work Risk, Uncertainty, and Profit, Frank Knight (1921) established the important distinction between risk and uncertainty: … Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. ... In statistics, given a set of data, X = { x1, x2, ..., xn} and corresponding weights, W = { w1, w2, ..., wn} the weighted mean is calculated as Note that if all the weights are equal, the weighted mean is the same as the arithmetic mean. ... In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical... Probability theory is the mathematical study of probability. ...

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. Daniel Bernoulli Daniel Bernoulli (Groningen, February 9, 1700 – Basel, March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland. ... In probability theory and decision theory the St. ... John von Neumann in the 1940s. ... Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ... In linguistics, prescription is the laying down or prescribing of normative rules of the language. ... Decision theory is an interdisciplinary area of study, related to and of interest to practitioners in mathematics, statistics, economics, philosophy, management and psychology. ...

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 today instead of a 50% chance of $2 tomorrow, even though the expected value 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 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. Risk aversion is a concept in economics and finance theory explaining the behaviour of consumers and investors under uncertainty. ... Insurance, in law and economics, is a form of risk management primarily used to hedge against the risk of potential financial loss. ... A lottery is a popular form of gambling which involves the drawing of lots for a prize. ... In linguistics, prescription is the laying down or prescribing of normative rules for a language. ... The prospect theory was developed by Daniel Kahneman and Amos Tversky in 1979. ... Bank of Sweden Prize in Economic Sciences winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ...

Further readings

K.J. Arrow (1963) "Uncertainty and the Welfare Economics of Medical Care", American Economic Review, Vol. 53, p.941-73.