Information about Expected Utility
The expected utility hypothesis is the hypothesis in economics that the utility of an 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. To determine utility according to this method, the decision maker must rank their preferences according to the outcomes of various decision options. According to the theory, if someone prefers A to B and B to C, then weights for the weighted average must exist such that she is indifferent between receiving B outright and gambling-- with the specified weights-- between A and C.
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.) Von Neumann and Morgenstern published this in their Theory of Games and Economic Behavior in 1944. It is important because it was developed shortly after the Hicks-Allen “ordinal revolution” of the 1930's, and it revived the idea of cardinal utility in economic theory. Economics has not resolved whether (and in what cases) utility is cardinal or ordinal.
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 $3, even though the expected value of the latter is more. People may be risk-averse or risk-loving depending on the amounts involved and on whether the gamble relates to becoming better off or worse off; this is a possible explanation for why the same person may buy both an insurance policy and a lottery ticket. However, expected utility as a descriptive model of decisions under risk has in recent years been replaced by more sophisticated variants that take irrational deviations from the expected utility model into account; compare Prospect theory and the general article on Behavioral finance.
The concept of risk-aversion comes into play in many gambling scenarios, such as poker strategy. A risk-neutral stance is generally the best strategy under normal conditions, as it attempts to maximize the expected value of each bet. However, there are situations where different strategies will be more beneficial. For example, many experts advocate a risk-averse strategy in the early stages of a poker tournament, when there are still many players left. As the tournament advances, a more risk-neutral or even risk-loving strategy becomes the more optimal play, especially as more players are eliminated. This change in strategy is due to the difference between expected value and expected utility. See M-ratio for more information on this concept as it relates to poker theory.
Preference Reversals over Uncertain Outcomes: Starting with studies such as Lichtenstein & Slovic (1971), it was discovered that subjects sometimes exhibit signs of preference reversals with regards to their certainty equivalents of different lotteries. Specifically, when eliciting certainty equivalents, subjects tend to value "p bets" (lotteries with a high chance of winning a low prize) lower than "$ bets" (lotteries with a small chance of winning a large prize). When subjects are asked which lotteries they prefer in direct comparison, however, they frequently prefer the "p bets" over "$ bets." Many studies have examined this "preference reversal," from both an experimental (e.g., Plott & Grether, 1979) and theoretical (e.g., Holt, 1986) standpoint, indicating that this behavior can be brought into accordance with neoclassical economic theory under certain assumptions.
The weighted mean, or weighted average, of a non-empty list of data
with corresponding non-negative weights
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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.) Von Neumann and Morgenstern published this in their Theory of Games and Economic Behavior in 1944. It is important because it was developed shortly after the Hicks-Allen “ordinal revolution” of the 1930's, and it revived the idea of cardinal utility in economic theory. Economics has not resolved whether (and in what cases) utility is cardinal or ordinal.
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 $3, even though the expected value of the latter is more. People may be risk-averse or risk-loving depending on the amounts involved and on whether the gamble relates to becoming better off or worse off; this is a possible explanation for why the same person may buy both an insurance policy and a lottery ticket. However, expected utility as a descriptive model of decisions under risk has in recent years been replaced by more sophisticated variants that take irrational deviations from the expected utility model into account; compare Prospect theory and the general article on Behavioral finance.
The concept of risk-aversion comes into play in many gambling scenarios, such as poker strategy. A risk-neutral stance is generally the best strategy under normal conditions, as it attempts to maximize the expected value of each bet. However, there are situations where different strategies will be more beneficial. For example, many experts advocate a risk-averse strategy in the early stages of a poker tournament, when there are still many players left. As the tournament advances, a more risk-neutral or even risk-loving strategy becomes the more optimal play, especially as more players are eliminated. This change in strategy is due to the difference between expected value and expected utility. See M-ratio for more information on this concept as it relates to poker theory.
Preference Reversals over Uncertain Outcomes: Starting with studies such as Lichtenstein & Slovic (1971), it was discovered that subjects sometimes exhibit signs of preference reversals with regards to their certainty equivalents of different lotteries. Specifically, when eliciting certainty equivalents, subjects tend to value "p bets" (lotteries with a high chance of winning a low prize) lower than "$ bets" (lotteries with a small chance of winning a large prize). When subjects are asked which lotteries they prefer in direct comparison, however, they frequently prefer the "p bets" over "$ bets." Many studies have examined this "preference reversal," from both an experimental (e.g., Plott & Grether, 1979) and theoretical (e.g., Holt, 1986) standpoint, indicating that this behavior can be brought into accordance with neoclassical economic theory under certain assumptions.
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).
Economics is the social science that studies the production, distribution, and consumption of goods and services. The term economics comes from the Greek for oikos (house) and nomos (custom or law), hence "rules of the house(hold).
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In economics, utility is a measure of the relative satisfaction or desiredness from consumption of goods. Given this measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one's utility.
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Uncertainty is a term used in subtly different ways in a number of fields, including philosophy, statistics, economics, finance, insurance, psychology, engineering and science.
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- See weight function for the continuous case.
The weighted mean, or weighted average, of a non-empty list of data
with corresponding non-negative weights
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expected value (or mathematical expectation, or mean) of a discrete random variable is the sum of the probability of each possible outcome of the experiment multiplied by the outcome value (or payoff).
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Probability theory is the branch of mathematics concerned with analysis of random phenomena.[1] The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities
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In economics, utility is a measure of the relative satisfaction or desiredness from consumption of goods. Given this measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one's utility.
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Daniel Bernoulli (February 8, 1700 – March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland where he died. A member of a talented family of mathematicians, physicists and philosophers, he is particularly remembered for his
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John von Neumann
John von Neumann in the 1940s
Born November 28 1903
Budapest, Austria-Hungary
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John von Neumann in the 1940s
Born November 28 1903
Budapest, Austria-Hungary
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Oskar Morgenstern
Oskar Morgenstern
Born January 24 1902
Görlitz, Germany
Died July 26 1977 (aged 75)
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Oskar Morgenstern
Born January 24 1902
Görlitz, Germany
Died July 26 1977 (aged 75)
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Theory of Games and Economic Behavior
60th anniversary edition, 2004
Author John von Neumann, Oskar Morgenstern
Country United States
Language English
Subject(s)
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60th anniversary edition, 2004
Author John von Neumann, Oskar Morgenstern
Country United States
Language English
Subject(s)
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cardinal numbers, or cardinals for short, are a generalized kind of number used to denote the size of a set, known as its cardinality. For finite sets the cardinality is given by a natural number, being simply the number of elements in the set.
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ordinal, ordinal number, and transfinite ordinal number refer to a type of number introduced by Georg Cantor in 1897, to accommodate infinite sequences and to classify sets with certain kinds of order structures on them.
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Risk aversion is a concept in economics, finance, and psychology related to the behaviour of consumers and investors under uncertainty. Risk aversion is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but
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lottery is a popular form of gambling which involves the drawing of lots for a prize. Some governments outlaw it, while others endorse it to the extent of organizing a national lottery. It is common to find some degree of regulation of lottery by governments.
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In linguistics, prescription can refer both to the codification and the enforcement of rules governing how a language is to be used. These rules can cover such topics as standards for spelling and grammar or syntax; or rules for what is deemed socially or politically correct.
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Prospect theory is a theory that describes decisions between alternatives that involve risk, i.e. alternatives with uncertain outcomes, where the probabilities are known. The model is descriptive: it tries to model real-life choices, rather than optimal decisions.
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Behavioral finance and behavioral economics are closely related fields which apply scientific research on human and social cognitive and emotional biases to better understand economic decisions and how they affect market prices, returns and the allocation of resources.
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expected value (or mathematical expectation, or mean) of a discrete random variable is the sum of the probability of each possible outcome of the experiment multiplied by the outcome value (or payoff).
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In no-limit or pot limit poker, a player's M-ratio (also called "M number" or just "M") is a measure of the health of his chip stack as a function of the cost to play each round.
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