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Subjective expected utility

 

 
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Subjective expected utility is a method in decision theory
Decision theory

Decision theory in mathematics and statistics is concerned with identifying the values, uncertainty and other issues relevant in a given decision making and the resulting optimal decision....
 in the presence of risk
Risk

Risk is a concept that denotes the precise probability of specific eventualities. Technically, the notion of risk is independent from the notion of value and, as such, eventualities may have both beneficial and adverse consequences....
, originally put forward by L. J. Savage in 1954 . It combines two distinct subjective concepts: a personal utility
Utility

In economics, utility is a measure of the relative satisfaction from, or desirability of, consumption of various goods and services. 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....
 function and a personal probability
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
 analysis based on Bayesian probability
Bayesian probability

Bayesian probability interprets the concept of probability as 'a measure of a state of knowledge' , and not as a frequentist . Broadly speaking, there are two views on Bayesian probability that interpret the 'state of knowledge' concept in different ways....
 theory.

Savage proved that, if you adhere to axioms of rationality, if you believe an uncertain event has possible outcomes each with a utility to you of then your choices can be explained as arising from a function in which you believe that there is a subjective probability of each outcome is , and your subjective expected utility is the expected value
Expected value

In probability theory and statistics, the expected value of a random variable is the Lebesgue integral of the random variable with respect to its probability measure....
 of the utility, You may be able to make a decision which changes the possible outcomes to in which case your subjective expected utility will become Which decision you prefer depends on which subjective expected utility is higher.






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Subjective expected utility is a method in decision theory
Decision theory

Decision theory in mathematics and statistics is concerned with identifying the values, uncertainty and other issues relevant in a given decision making and the resulting optimal decision....
 in the presence of risk
Risk

Risk is a concept that denotes the precise probability of specific eventualities. Technically, the notion of risk is independent from the notion of value and, as such, eventualities may have both beneficial and adverse consequences....
, originally put forward by L. J. Savage in 1954 . It combines two distinct subjective concepts: a personal utility
Utility

In economics, utility is a measure of the relative satisfaction from, or desirability of, consumption of various goods and services. 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....
 function and a personal probability
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
 analysis based on Bayesian probability
Bayesian probability

Bayesian probability interprets the concept of probability as 'a measure of a state of knowledge' , and not as a frequentist . Broadly speaking, there are two views on Bayesian probability that interpret the 'state of knowledge' concept in different ways....
 theory.

Savage proved that, if you adhere to axioms of rationality, if you believe an uncertain event has possible outcomes each with a utility to you of then your choices can be explained as arising from a function in which you believe that there is a subjective probability of each outcome is , and your subjective expected utility is the expected value
Expected value

In probability theory and statistics, the expected value of a random variable is the Lebesgue integral of the random variable with respect to its probability measure....
 of the utility, You may be able to make a decision which changes the possible outcomes to in which case your subjective expected utility will become Which decision you prefer depends on which subjective expected utility is higher. Different people may make different decisions because they may have different utility functions or different beliefs about the probabilities of different outcomes.

Savage assumed that it was possible to take convex combinations of decisions and that preferences would be preserved. So if you prefer to and to then you will prefer to , for .

Experiments have shown that many individuals do not behave in a manner consistent with subjective expected utility, most prominently Allais
Allais paradox

The Allais paradox is a choice problem designed by Maurice Allais to show an inconsistency of actual observed choices with the predictions of expected utility theory....
 (1953) and Ellsberg
Ellsberg paradox

The Ellsberg paradox is a paradox in decision theory and experimental economics in which people's choices violate the expected utility hypothesis....
 (1961) . Savage's response was not that this showed a flaw in his method, rather that applying his method allowed individuals to improve their decision making.

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