Expected utility hypothesis

The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour.

The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e., the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is ${\displaystyle U(p)=\sum u(x_{k})p_{k}}$ where ${\displaystyle p_{k}}$ is the probability that outcome indexed by ${\displaystyle k}$ with payoff ${\displaystyle x_{k}}$ is realized, and function u expresses the utility of each respective payoff.^[1] Graphically the curvature of the u function captures the agent's risk attitude.

For example, imagine you’re offered a choice between receiving $50 for sure, or flipping a coin to win $100 if heads, and nothing if tails. Although both options have the same average payoff ($50), many people choose the guaranteed $50 because they value the certainty of the smaller reward more than the possibility of a larger one, reflecting risk-averse preferences.

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).

Although the expected utility hypothesis is a commonly accepted assumption in theories underlying economic modeling, it has frequently been found to be inconsistent with the empirical results of experimental psychology. Psychologists and economists have been developing new theories to explain these inconsistencies for many years.^[2] These include prospect theory, rank-dependent expected utility and cumulative prospect theory, and bounded rationality.