Expected utility hypothesis

The hypothesis that choices under uncertainty can be represented as maximizing the probability-weighted average of outcomes’ utility. It distinguishes preferences over outcomes from preferences over money or probability alone.

Utility: A numerical representation of how desirable an outcome is to an agent. Expected utility assigns values to outcomes before weighting them by probability.
Expected utility: The probability-weighted average of an outcome’s utility across a lottery’s possible results. This quantity is what the hypothesis says a chooser maximizes.
Prospect theory: A descriptive theory in which choices depend on reference points, loss aversion, and transformed probabilities. It explains patterns of risky choice that expected utility struggles to predict.
Decision theory: The study of how agents choose among actions under certainty, risk, or uncertainty. Expected utility is a central model within formal decision theory.
Daniel Bernoulli: An eighteenth-century mathematician who introduced diminishing marginal utility to explain choices involving risk. His analysis of the St. Petersburg paradox anticipated utility-weighted evaluation of uncertain outcomes.
Expected value: The probability-weighted average of the numerical outcomes of a random variable. It values outcomes directly, unlike expected utility, which first transforms them through preferences.
Utility function: A function assigning numerical values to outcomes to represent preferences. It translates each possible consequence into the values used in the calculation.
Allais paradox: A pair of lottery choices whose common preferences violate the independence axiom. The paradox demonstrates a systematic challenge to expected-utility predictions.
Expected utility of wealth: A model that evaluates risky prospects by applying a utility function to final wealth. It is the standard economic application for explaining choices over gambles and insurance.
St. Petersburg paradox: A lottery with infinite expected monetary value that most people would pay only a modest amount to play. It exposed the limits of evaluating risky choices by expected money alone.

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