---
title: "Decision theory"
chunk: 1/2
source: "https://en.wikipedia.org/wiki/Decision_theory"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:56:30.080120+00:00"
instance: "kb-cron"
---

Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability to model how individuals would behave rationally under uncertainty. It differs from the cognitive and behavioral sciences in that it is mainly prescriptive and concerned with identifying optimal decisions for a rational agent, rather than describing how people actually make decisions. Despite this, the field is important to the study of real human behavior by social scientists, as it lays the foundations to mathematically model and analyze individuals in fields such as sociology, economics, criminology, cognitive science, moral philosophy and political science.

== History ==

The roots of decision theory lie in probability theory, developed by Blaise Pascal and Pierre de Fermat in the 17th century, which was later refined by others like Christiaan Huygens. These developments provided a framework for understanding risk and uncertainty, which are central to decision-making.
In the 18th century, Daniel Bernoulli introduced the concept of "expected utility" in the context of gambling, which was later formalized by John von Neumann and Oskar Morgenstern in the 1940s. Their work on Game Theory and Expected Utility Theory helped establish a rational basis for decision-making under uncertainty.
After World War II, decision theory expanded into economics, particularly with the work of economists like Milton Friedman and others, who applied it to market behavior and consumer choice theory. This era also saw the development of Bayesian decision theory, which incorporates Bayesian probability into decision-making models.
By the late 20th century, scholars like Daniel Kahneman and Amos Tversky challenged the assumptions of rational decision-making. Their work in behavioral economics highlighted cognitive biases and heuristics that influence real-world decisions, leading to the development of prospect theory, which modified expected utility theory by accounting for psychological factors.

== Branches ==
Normative decision theory is concerned with identification of optimal decisions where optimality is often determined by considering an ideal decision maker who is able to calculate with perfect accuracy and is in some sense fully rational. The practical application of this prescriptive approach (how people ought to make decisions) is called decision analysis and is aimed at finding tools, methodologies, and software (decision support systems) to help people make better decisions.
In contrast, descriptive decision theory is concerned with describing observed behaviors often under the assumption that those making decisions are behaving under some consistent rules. These rules may, for instance, have a procedural framework (e.g. Amos Tversky's elimination by aspects model) or an axiomatic framework (e.g. stochastic transitivity axioms), reconciling the Von Neumann-Morgenstern axioms with behavioral violations of the expected utility hypothesis, or they may explicitly give a functional form for time-inconsistent utility functions (e.g. Laibson's quasi-hyperbolic discounting).
Prescriptive decision theory is concerned with predictions about behavior that positive decision theory produces to allow for further tests of the kind of decision-making that occurs in practice. In recent decades, there has also been increasing interest in "behavioral decision theory", contributing to a re-evaluation of what useful decision-making requires.

== Types of decisions ==

=== Choice under uncertainty ===

The area of choice under uncertainty represents the heart of decision theory. Known from the 17th century (Blaise Pascal invoked it in his famous wager, which is contained in his Pensées, published in 1670), the idea of expected value is that, when faced with a number of actions, each of which could give rise to more than one possible outcome with different probabilities, the rational procedure is to identify all possible outcomes, determine their values (positive or negative) and the probabilities that will result from each course of action, and multiply the two to give an "expected value", or the average expectation for an outcome; the action to be chosen should be the one that gives rise to the highest total expected value. In 1738, Daniel Bernoulli published an influential paper entitled Exposition of a New Theory on the Measurement of Risk, in which he uses the St. Petersburg paradox to show that expected value theory must be normatively wrong. He gives an example in which a Dutch merchant is trying to decide whether to insure a cargo being sent from Amsterdam to St. Petersburg in winter. In his solution, he defines a utility function and computes expected utility rather than expected financial value.
In the 20th century, interest was reignited by Abraham Wald's 1939 paper pointing out that the two central procedures of sampling-distribution-based statistical-theory, namely hypothesis testing and parameter estimation, are special cases of the general decision problem. Wald's paper renewed and synthesized many concepts of statistical theory, including loss functions, risk functions, admissible decision rules, antecedent distributions, Bayesian procedures, and minimax procedures. The phrase "decision theory" itself was used in 1950 by E. L. Lehmann.
The revival of subjective probability theory, from the work of Frank Ramsey, Bruno de Finetti, Leonard Savage and others, extended the scope of expected utility theory to situations where subjective probabilities can be used. At the time, von Neumann and Morgenstern's theory of expected utility proved that expected utility maximization followed from basic postulates about rational behavior.
The work of Maurice Allais and Daniel Ellsberg showed that human behavior has systematic and sometimes important departures from expected-utility maximization (Allais paradox and Ellsberg paradox). The prospect theory of Daniel Kahneman and Amos Tversky renewed the empirical study of economic behavior with less emphasis on rationality presuppositions. It describes a way by which people make decisions when all of the outcomes carry a risk. Kahneman and Tversky found three regularities – in actual human decision-making, "losses loom larger than gains"; people focus more on changes in their utility-states than they focus on absolute utilities; and the estimation of subjective probabilities is severely biased by anchoring.

=== Intertemporal choice ===