Decision theory (or the theory of choice not to be confused with choice theory) is the study of an agent’s choices. Decision theory can be broken into two branches: normative one, which analyzes the outcomes of decisions or determines the optimal decisions given constraints and assumptions, and descriptive one, which analyzes how agents actually make the decisions they do.
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, positive or descriptive decision theory is concerned with describing observed behaviors often 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 (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). The prescriptions or predictions about behavior that positive decision theory produces 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.
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A general criticism of this theory based on a fixed universe of possibilities is that it considers the “known unknowns”, not the “unknown unknowns”: it focuses on expected variations, not on unforeseen events, which some argue have outsized impact and must be considered – significant events may be “outside model”. This line of argument, called the ludic fallacy, is that there are inevitable imperfections in modeling the real world by particular models, and that unquestioning reliance on models blinds one to their limits.