The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty.
Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour.
This representation theorem for expected utility assumes that preferences are defined over a set of bets where each option has a different yield.
Ramsey believed that we should always make decisions to receive the best-expected outcome according to our personal preferences.
[5] Ramsey shows that In the 1950s, Leonard Jimmie Savage, an American statistician, derived a framework for comprehending expected utility.
Savage's framework involved proving that expected utility could be used to make an optimal choice among several acts through seven axioms.
Savage concluded that people have neutral attitudes towards uncertainty and that observation is enough to predict the probabilities of uncertain events.
This theoretical model has been known for its clear and elegant structure and is considered by some researchers to be "the most brilliant axiomatic theory of utility ever developed."
For example, if someone says, "I got the job," this affirmation is not considered an outcome since the utility of the statement will be different for each person depending on intrinsic factors such as financial necessity or judgment about the company.
Additionally, the theorem ranks the outcome according to a utility function that reflects personal preferences.
The utility function It exhibits constant absolute risk aversion and, for this reason, is often avoided, although it has the advantage of offering substantial mathematical tractability when asset returns are normally distributed.
In the context of mean-variance analysis, variance is used as a risk measure for portfolio return; however, this is only valid if returns are normally distributed or otherwise jointly elliptically distributed,[12][13][14] or in the unlikely case in which the utility function has a quadratic form—however, David E. Bell proposed a measure of risk that follows naturally from a certain class of von Neumann–Morgenstern utility functions.
The St. Petersburg paradox presented by Nicolas Bernoulli illustrates that decision-making based on the expected value of monetary payoffs leads to absurd conclusions.
"Only a few participants were willing to pay a maximum of $25 to enter the game because many were risk averse and unwilling to bet on a very small possibility at a very high price.
[20] In the early days of the calculus of probability, classic utilitarians believed that the option with the greatest utility would produce more pleasure or happiness for the agent and, therefore, must be chosen.
[21] The main problem with the expected value theory is that there might not be a unique correct way to quantify utility or to identify the best trade-offs.
[3] The classic counter example to the expected value theory (where everyone makes the same "correct" choice) is the St. Petersburg Paradox.
[3] In empirical applications, several violations of expected utility theory are systematic, and these falsifications have deepened our understanding of how people decide.
The mathematical clarity of expected utility theory has helped scientists design experiments to test its adequacy and to distinguish systematic departures from its predictions.
This has led to the behavioral finance field, which has produced deviations from the expected utility theory to account for the empirical facts.
[24] According to the empirical results, there has been almost no recognition in decision theory of the distinction between the problem of justifying its theoretical claims regarding the properties of rational belief and desire.
One of the main reasons is that people's basic tastes and preferences for losses cannot be represented with utility as they change under different scenarios.
These deviations are described as "irrational" because they can depend on the way the problem is presented, not on the actual costs, rewards, or probabilities involved.
[26] Additionally, experiments have shown systematic violations and generalizations based on the results of Savage and von Neumann–Morgenstern.
This is demonstrated in the contrast of individual preferences under the insurance and lottery context, which shows the degree of indeterminacy of the expected utility theory.
Additionally, experiments have shown systematic violations and generalizations based on the results of Savage and von Neumann–Morgenstern.
Starting with studies such as Lichtenstein & Slovic (1971), it was discovered that subjects sometimes exhibit signs of preference reversals about 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).
[27] Many studies have examined this "preference reversal", from both an experimental (e.g., Plott & Grether, 1979)[28] and theoretical (e.g., Holt, 1986)[29] standpoint, indicating that this behavior can be brought into accordance with neoclassical economic theory under specific assumptions.
Three components in the psychology field are seen as crucial to developing a more accurate descriptive theory of decision under risks.