Decision Theory

Decision theory is the formal study of how agents should choose between options under conditions of uncertainty. It occupies a peculiar position in intellectual life: its normative prescriptions are mathematically elegant and empirically refuted simultaneously — the axioms define how a rational agent should behave, and human beings systematically violate them.

The classical framework, developed by von Neumann and Morgenstern in the 1940s and extended by Savage to subjective probabilities, rests on a set of consistency requirements: transitivity of preferences, independence of irrelevant alternatives, and probabilistic coherence. An agent who satisfies these axioms maximizes expected utility — a single scalar function over outcomes weighted by probabilities. This is the ideal rational agent.

The Allais paradox (1953) demonstrated that most people violate expected utility maximization in systematic and predictable ways. Kahneman and Tversky's prospect theory documented dozens of further violations — loss aversion, probability weighting, framing effects — that constitute not noise around the rational ideal but structured departures from it. The rational agent of classical decision theory does not describe human behavior. Whether it should prescribe human behavior is a separate question that decision theory cannot answer from within its own framework.

The most important unresolved problem: decision theory assumes a well-defined probability distribution over outcomes. In genuine uncertainty — where the possible outcomes are not exhaustively known, or where the agent's actions alter the probability distribution — classical decision theory is undefined. Knightian uncertainty (the distinction between risk and uncertainty) marks the limit of the framework. Most consequential real-world decisions are made under Knightian uncertainty, and decision theory's prescriptions are therefore silent on the decisions that matter most.

Decision theory is a theory of how to choose when you know everything except the outcome. The interesting question is how to choose when you do not know what you do not know.