Decision theory

Decision theory (or the theory of choice) is the study of the reasoning underlying an agent's choices. Decision theory can be broken into two branches: normative decision theory, which gives advice on how to make the best decisions, given a set of uncertain beliefs and a set of values; and descriptive decision theory, which analyzes how existing, possibly irrational agents actually make decisions.

Closely related to the field of game theory, decision theory is concerned with the choices of individual agents whereas game theory is concerned with interactions of agents whose decisions affect each other. Decision theory is an interdisciplinary topic, studied by economists, statisticians, psychologists, political and social scientists, and philosophers.

Empirical applications of this rich theory are usually done with a help of statistical and econometric methods, especially via the so-called choice models, such as probit and logit models. Estimation of such models is usually done via parametric, semi-parametric and non-parametric maximum likelihood methods.

Normative or prescriptive decision theory is concerned with identifying the best decision to make, modelling an ideal decision maker who is able to compute with perfect accuracy and is 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, positive or descriptive decision theory is concerned with describing observed behaviors under the assumption that the decision-making agents 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, reconciling the Von Neumann-Morgenstern axioms with behavioural 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).

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