An applied branch of decision theory. Decision analysis offers individuals and organizations a methodology for making decisions; it also offers techniques for modeling decision problems mathematically and finding optimal decisions numerically. Decision models have the capacity for accepting and quantifying human subjective inputs: judgments of experts and preferences of decision-makers. Implementation of models can take the form of simple paper-and-pencil procedures or sophisticated computer programs known as decision aids or decision systems.
The methodology is rooted in postulates of rationality—a set of properties which preferences of rational individuals must satisfy. One such property is transitivity: if an individual prefers action a to action b and action b to action c, he or she should prefer a to c. From the rationality postulates, principles of decision-making are derived mathematically. The principles prescribe how decisions ought to be made, if one wishes to be rational. In that sense, decision analysis is normative.
The methodology is broad and must always be adapted to the problem at hand. An illustrative adaptation to a class of problems known as decision-making under uncertainty (or risk) is outlined in the illustration and consists of seven steps:
The problem is structured by identifying feasible actions, one of which must be decided upon; possible events, one of which occurs thereafter; and outcomes, each of which results from a combination of decision and event. Problem structuring can be facilitated by displays such as decision trees and decision matrices.
At the time of decision-making, the event that will actually occur cannot be predicted perfectly. The degree of certainty about the occurrence of an event, given all information at hand, is quantified in terms of the probability of the event.
Preferences are personal: the same outcome may elicit different degrees of desirability from different individuals. The subjective value that a decision-maker attaches to an outcome is quantified and termed the utility of outcome.
The preceding steps conform to the principle of decomposition: probabilities of events and utilities of outcomes must be measured independently of one another. They are next combined in a criterion for evaluating decisions. The utility of a decision is defined as the expected utility of the outcome. The optimal, or the most preferred, decision is one with the maximum utility.
The probability encodes the current state of information about a possible event. Often, additional information can be acquired in the hope of reducing the uncertainty. The monetary value of such information is computed before purchase and compared with the cost of information. Thus, one can determine whether or not acquiring information is economically rational.
The source of information may be a real-world experiment, a laboratory test, a mathematical model, or the knowledge of an expert. The informativeness of the source is described in terms of a probabilistic relation between information and event. This relation, known as the likelihood function, makes it possible to revise the prior probability of the event and to obtain a posterior probability of the event, conditional on additional information. The revision is carried out via Bayes' rule.
Given the additional information, prior probabilities can be replaced by posterior probabilities, and the analysis can be repeated from step 4 onward. Steps 4–6 may be cycled many times, until the cost of additional information exceeds its value, at which moment the optimal decision is implemented.
A methodology of decision analysis.
Measurement of probability and utility functions is guided by principles of decision theory, statistical estimation procedures, and empirical laws provided by behavioral decision theory—a branch of cognitive psychology. See also Cognition; Decision theory.
