Expected utility theory (EUT), formalized by von Neumann and Morgenstern (1944), is the standard normative model of rational choice under risk. It prescribes that a rational decision maker should choose the option that maximizes expected utility — the sum of each outcome's utility (subjective value) weighted by its probability. The theory is derived from axioms (completeness, transitivity, independence, continuity) that define rational preferences.
The Theory
EUT improves on expected value theory by replacing objective monetary values with subjective utilities, accommodating risk aversion through a concave utility function (diminishing marginal utility of wealth). A risk-averse agent prefers a sure $50 to a 50-50 gamble for $100 because the utility of the first $50 exceeds the additional utility of the second $50. EUT has been the foundation of economic theory, financial modeling, and game theory for decades.
Violations and Alternatives
Systematic violations of EUT have been extensively documented. The Allais paradox (1953) showed that people's choices violate the independence axiom. The Ellsberg paradox (1961) showed aversion to ambiguity (unknown probabilities) beyond what EUT can explain. Preference reversals demonstrate intransitive choices. These violations motivated alternative theories: prospect theory, rank-dependent utility theory, regret theory, and support theory, each relaxing different axioms of EUT while maintaining a formal decision-theoretic framework.
Despite its descriptive failures, EUT remains the benchmark for rational decision making. Departures from EUT are defined as biases or irrationalities precisely because EUT provides the normative standard. Whether this is appropriate — whether EUT truly captures what it means to be rational given human cognitive constraints — is debated between the heuristics-and-biases tradition (which treats EUT violations as errors) and the ecological rationality tradition (which argues that EUT is not the right standard for bounded agents in uncertain environments).