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The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the outcome is unknown. The theory recommends which option rational individuals should choose in a complex situation, based on their risk appetite and preferences.

The expected utility of an agent's decision is probability-weighted average utility derived from each possible outcome. For example, if an agent derives 0 utils from 0 apples, 2 utils from one apple, and 3 utils from two apples, his expected utility for a 50-50 gamble between zero apples and two is .5u(0 apples) + .5u(2 apples) = .5(0 utils) + .5(3 utils) = 1.5 utils. Under the expected utility hypothesis, the consumer would prefer 1 apple (giving him 2 utils) to the gamble between zero and two.

Standard utility functions represent ordinal preferences. The expected utility hypothesis imposes limitations on the utility function and makes utility cardinal (though still not comparable across individuals). In the example above, any function such that u(0) < (1) < u(2) would represent the same preferences; we could specify u(0)= 0, u(1) = 2, and u(2) = 40, for example. Under the expected utility hypothesis, setting u(2) = 3 requires if the agent is indifferent between one apple with certainty and a gamble with a 1/3 probability of no apple and a 2/3 probability of two apples, the utility of two apples must be set to u(2) = 2. This is because it requires that (1/3)u(0) + (2/3)u(2) = u(1), and 2 = (1/3)(0) + (2/3)(3).

Although the expected utility hypothesis is standard in economic modelling, it has been found to be violated in psychology experiments. For many years, psychologists and economic theorists have been developing new theories to explain these deficiencies. These include prospect theory, rank-dependent expected utility and cumulative prospect theory, and bounded rationality.

Limits of the Expected Value Theory[edit]
In the early days of the calculus of probability, classic utilitarians believed that the option which has the greatest utility will produce more pleasure or happiness for the agent and therefore must be chosen. The main problem with the expected value theor y is that there might not be a correct way to quantify utility or to identify the best trade-offs. For example, some of the trade-offs may be intangible or qualitative. Rather than monetary incentives, other desirable ends can also be included in utility such as pleasure, knowledge, friendship, etc. Originally the total utility of the consumer was the sum of independent utilities of the goods. However, the expected value theory was dropped as it was considered too static and deterministic. The classical counter example to the expected value theory (where everyone makes the same "correct" choice) is the St. Petersburg Paradox. This paradox questioned if marginal utilities should be ranked differently as it proved that a “correct decision” for one person is not necessarily right for another person.