Decision theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory and analytic philosophy concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome. There are three branches of decision theory: Normative decision theory: Concerned with the 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. Prescriptive decision theory: Concerned with describing observed behaviors through the use of conceptual models, under the assumption that those making the decisions are behaving under some consistent rules. Descriptive decision theory: Analyzes how individuals actually make the decisions that they do. Decision theory is a broad field from management sciences and is an interdisciplinary topic, studied by management scientists, medical researchers, mathematicians, data scientists, psychologists, biologists, social scientists, philosophers and computer scientists. Empirical applications of this theory are usually done with the help of statistical and discrete mathematical approaches from computer science. Normative and descriptive 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