Expected utility

Expected utility is a decision rule that evaluates an option by averaging the utilities of its possible outcomes, weighted by their probabilities. It recommends choosing the available option with the highest expected utility.

Utility function: A function assigning numerical values to outcomes to represent their desirability for a decision-maker. Expected utility averages these values across possible outcomes.
Prospect theory: A descriptive theory in which people evaluate gains and losses relative to a reference point and weight probabilities nonlinearly. It accounts for choice patterns that systematically depart from expected utility.
Decision theory: The mathematical study of how agents choose among actions under certainty, risk, or uncertainty. Expected utility is one rule within the broader study of choice.
Expected utility hypothesis: The claim that agents choose as if they maximize expected utility when facing risky alternatives. It applies the decision rule as a model of economic behavior.
Expected value: The probability-weighted average of the numerical outcomes of a random variable. It averages outcomes directly, whereas expected utility averages their desirability.
Allais paradox: A pair of lottery choices whose commonly observed pattern violates the independence axiom. It demonstrates a direct conflict between observed preferences and standard expected utility.
Probability theory: The mathematical framework for representing uncertainty and calculating probabilities of events. Its probabilities supply the weights used in expected-utility calculations.
Insurance: A contract that transfers specified financial risks from a policyholder to an insurer in exchange for payment. Expected utility helps explain why risk-averse people may buy insurance despite its cost.
Von Neumann–Morgenstern utility theorem: A theorem showing that preferences satisfying specified axioms over lotteries can be represented by maximizing expected utility. It explains when a preference ordering can be represented by this rule.
Ellsberg paradox: A set of choices showing that people often prefer known risks to ambiguous prospects with unknown probabilities. It challenges expected-utility models that assign precise probabilities to ambiguous events.

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