# decision theory

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decision theory
the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome.
[1960-65]

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In statistics and related subfields of philosophy, the theory and method of formulating and solving general decision problems.

Such a problem is specified by a set of possible states of the environment or possible initial conditions; a set of available experiments and a set of possible outcomes for each experiment, giving information about the state of affairs preparatory to making a decision; a set of available acts depending on the experiments made and their consequences; and a set of possible consequences of the acts, in which each possible act assigns to each possible initial state some particular consequence. The problem is dealt with by assessing probabilities of consequences conditional on different choices of experiments and acts and by assigning a utility function to the set of consequences according to some scheme of value or preference of the decision maker. An optimal solution consists of an optimal decision function, which assigns to each possible experiment an optimal act that maximizes the utility, or value, and a choice of an optimal experiment. See also cost-benefit analysis, game theory.

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in statistics, a set of quantitative methods for reaching optimal decisions. A solvable decision problem must be capable of being tightly formulated in terms of initial conditions and choices or courses of action, with their consequences. In general, such consequences are not known with certainty but are expressed as a set of probabilistic outcomes. Each outcome is assigned a “utility” value based on the preferences of the decision maker. An optimal decision, following the logic of the theory, is one that maximizes the expected utility. Thus, the ideal of decision theory is to make choices rational by reducing them to a kind of routine calculation.

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Universalium. 2010.

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