It has been suggested that Neumann-Morgenstern utility be merged into this article or section. (Discuss)

It has been suggested that this article or section be merged into utility. (Discuss)

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. Image File history File links Please see the file description page for further information. ... It has been suggested that this article or section be merged into Expected utility hypothesis. ... Wikipedia does not have an article with this exact name. ... In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained. ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ... In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained. ... This article or section does not adequately cite its references or sources. ... 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 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 as the outcome of the random trial when identical odds are... Probability theory is a branch of mathematics concerned with analysis of random phenomena. ...

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.) Daniel Bernoulli Daniel Bernoulli (Groningen, February 8, 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 (Hungarian Margittai Neumann János Lajos) (born December 28, 1903 in Budapest, Austria-Hungary; died February 8, 1957 in Washington D.C., United States) was a Hungarian-born American mathematician who made contributions to quantum physics, functional analysis, set theory, topology, economics, computer science, numerical analysis, hydrodynamics... 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. ...

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 the same person may buy both an insurance policy and a lottery ticket. 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 a contingent 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. ... Prospect theory was developed by Daniel Kahneman and Amos Tversky in 1979 as a psychologically realistic alternative to expected utility theory. ... Economics Nobel Laureate Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ...

Further reading

• Bernoulli, D (1954) "Exposition of a New Theory on the Measurement of Risk" (original: 1738), "Econometrica" 22:23-36.
• Schoemaker PJH (1982) "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations", "Journal of Economic Literature", 20:529-563.
• P.Anand (1993) "Foundations of Rational Choice Under Risk", Oxford, Oxford University Press. ISBN 0198233035
• K.J. Arrow (1963) "Uncertainty and the Welfare Economics of Medical Care", American Economic Review, Vol. 53, p.941-73.
• Scott Plous (1993) "The psychology of judgment and decision making", Chapter 7 (specifically) and 8,9,10, (to show paradoxes to the theory).