Rational Decision Making

Rational decision making is choosing among alternatives in a way that "properly" accords with the preferences and beliefs of an individual decision maker or those of a group making a joint decision. The subject has been developed in decision theory (Luce and Raiffa 1957; see RATIONAL CHOICE THEORY), decision analysis (Raiffa 1968), GAME THEORY (von Neumann and Morgenstern 1953), political theory (Muller 1989), psychology (Kahneman, Slovic, and TVERSKY 1982; see DECISION-MAKING), and economics (Debreu 1959; Henderson and Quandt 1980; see ECONOMICS AND COGNITIVE SCIENCE), in which it is the primary activity of homo economicus, "rational economic man." The term refers to a variety of notions, with each conception of alternatives and proper accord with preferences and beliefs yielding a "rationality" criterion. At its most abstract, the subject concerns unanalyzed alternatives (choices, decisions) and preferences reflecting the desirability of the alternatives and rationality criteria such as maximal desirability of chosen alternatives with respect to the preference ranking. More concretely, one views the alternatives as actions in the world, and determines preferences among alternative actions from preference rankings of possible states of the world and beliefs or probability judgments about what states obtain as outcomes of different actions, as in the maximal expected utility criterion of decision theory and economics. UTILITY THEORY and the FOUNDATIONS OF PROBABILITY theory provide a base for its developments. Somewhat unrelated, but common, senses of the term refer to making decisions through reasoning (Baron 1985), especially reasoning satisfying conditions of logical consistency and deductive completeness (see DEDUCTIVE REASONING; LOGIC) or probabilistic soundness (see PROBABILISTIC REASONING). The basic elements of the theory were set in place by Bernoulli (1738), Bentham (1823), Pareto (1927), Ramsey (1926), de Finetti (1937), VON NEUMANN and Morgenstern (1953), and Savage (1972). Texts by Raiffa (1968), Keeney and Raiffa (1976), and Jeffrey (1983) offer good introductions.

The theory of rational choice begins by considering a set of alternatives facing the decision maker(s). Analysts of particular decision situations normally consider only a restricted set of abstract alternatives that capture the important or interesting differences among the alternatives. This often proves necessary because, particularly in problems of what to do, the full range of possible actions exceeds comprehension. The field of decision analysis (Raiffa 1968) addresses how to make such modeling choices and provides useful techniques and guidelines. Recent work on BAYESIAN NETWORKS (Pearl 1988) provides additional modeling techniques. These models and their associated inference mechanisms form the basis for a wide variety of successful KNOWLEDGE-BASED SYSTEMS (Wellman, Breese, and Goldman 1992).

The theory next considers a binary relation of preference among these alternatives. The notation x y means that alternative y is at least as desirable as alternative x, read as y is weakly preferred to x; "weakly" because x y permits x and y to be equally desirable. Decision analysis also provides a number of techniques for assessing or identifying the preferences of decision makers. Preference assessment may lead to reconsideration of the model of alternatives when the alternatives aggregate together things differing along some dimension on which preference depends.

Decision theory requires the weak preference relation to be a complete preorder, that is, reflexive (x x), transitive (x y and y z imply x z), and relating every pair of alternatives (either x y or y x). These requirements provide a formalization in accord with ordinary intuitions about simple decision situations in which one can readily distinguish different amounts, more is better, and one can always tell which is more. Various theoretical arguments have also been made in support of these requirements; for example, if someone's preferences lack these properties, one may construct a wager against him he is sure to lose.

Given a complete preordering of alternatives, decision theory requires choosing maximally desirable alternatives, that is, alternatives x such that y x for all alternatives y. There may be one, many, or no such maxima. Maximally preferred alternatives always exist within finite sets of alternatives. Preferences that linearly order the alternatives ensure that maxima are unique when they exist.

The rationality requirements of decision theory on preferences and choices constitute an ideal rarely observed but useful nonetheless (see Kahneman, Slovic, and Tversky 1982; DECISION MAKING, ECONOMICS AND COGNITIVE SCIENCE, JUDGMENT HEURISTICS). In practice, people apparently violate reflexivity (to the extent that they distinguish alternative statements of the same alternative), transitivity (comparisons based on aggregating subcomparisons may conflict), and completeness (having to adopt preferences among things never before considered). Indeed, human preferences change over time and through reasoning and action, which renders somewhat moot the usual requirements on instantaneous preferences. People also seem to not optimize their choices in the required way, more often seeming to choose alternatives that are not optimal but are nevertheless good enough. These "satisficing" (Simon 1955), rather than optimizing, decisions constitute a principal focus in the study of BOUNDED RATIONALITY, the rationality exhibited by agents of limited abilities (Horvitz 1987; Russell 1991; Simon 1982). Satisficing forms the basis of much of the study of PROBLEM SOLVING in artificial intelligence; indeed, NEWELL (1982: 102) identifies the method of problem solving via goals as the foundational (but weak) rationality criterion of the field ("If an agent has knowledge that one of its actions will lead to one of its goals, then the agent will select that action"). Such "heuristic" rationality lacks the coherence of the decision-theoretic notion because it downplays or ignores issues of comparison among alternative actions that all lead to a desired goal, as well as comparisons among independent goals. In spite of the failure of humans to live up to the requirements of ideal rationality, the ideal serves as a useful approximation, one that supports predictions, in economics and other fields, of surprisingly wide applicability (Becker 1976; Stigler and Becker 1977).

Though the notions of preference and optimal choice have qualitative foundations, most practical treatments of decision theory represent preference orders by means of numerical utility functions. We say that a function U that assigns numbers to alternatives represents the relation just in case U(x)U(y) whenever x y. Note that if a utility function represents a preference relation, then any monotone-increasing transform of the function represents the relation as well, and that such transformation does not change the set of maximally preferred alternatives. Such functions are called ordinal utility functions, as the numerical values only indicate order, not magnitude (so that U(x) = 2 U(y) does not mean that x is twice as desirable as y).

To formalize choosing among actions that may yield different outcomes with differing likelihoods, the theory moves beyond maximization of preferability of abstract alternatives to the criterion of maximizing expected utility, which derives preferences among alternatives from preference orderings of the possible outcomes together with beliefs or expectations that indicate the probability of different consequences. Let denote the set of possible outcomes or consequences of choices. The theory supposes that the beliefs of the agent determine a probability measure Pr, where Pr (|x) is the probability that outcome w obtains as a result of taking action x. The theory further supposes a preference relation over outcomes. If we choose a numerical function U over outcomes to represent this preference relation, then the expected utility Û(x) of alternative x denotes the total utility of the consequences of x, weighting the utility of each outcome by its probability, that is

Equation 1

Because the utilities of outcomes are added together in this definition, this utility function is called a cardinal utility function, indicating magnitude as well as order. We then define x y to hold just in case Û(x) Û(y). Constructing preferences over actions to represent comparisons of expected utility in this way transforms the abstract rational choice criterion into one of maximizing the expected utility of actions.

The identification of rational choice under UNCERTAINTY with maximization of expected utility also admits criticism (Machina 1987). Milnor (1954) examined a number of reasonable properties one might require of rational decisions, and proved no decision method satisfied all of them. In practice, the reasonability of the expected utility criterion depends critically on whether the modeler has incorporated all aspects of the decision into the utility function, for example, the decision maker's attitudes toward risk.

The theory of rational choice may be developed in axiomatic fashion from the axioms above, in which philosophical justifications are given for each of the axioms. The complementary "revealed preference" approach uses the axioms instead as an analytical tool for interpreting actions. This approach, pioneered by Ramsey (1926) and de Finetti (1937) and developed into a useful mathematical and practical method by von Neumann (von Neumann and Morgenstern 1953) and Savage (1972), uses real or hypothesized sets of actions (or only observed actions in the case of Davidson, Suppes, and Siegel 1957) to construct probability and utility functions that would give rise to the set of actions.

When decisions are to be made by a group rather than an individual, the above model is applied to describing both the group members and the group decision. The focus in group decision making is the process by which the beliefs and preferences of the group determine the beliefs and preferences of the group as a whole. Traditional methods for making these determinations, such as voting, suffer various problems, notably yielding intransitive group preferences. Arrow (1963) proved that there is no way, in general, to achieve group preferences satisfying the rationality criteria except by designating some group member as a "dictator," and using that member's preferences as those of the group. May (1954), Black (1963), and others proved good methods exist in a number of special cases (Sen 1977). When all preferences are well behaved and concern exchanges of economic goods in markets, the theory of general equilibrium (Arrow and Hahn 1971; Debreu 1959) proves the existence of optimal group decisions about allocations of these goods. Game theory considers more refined rationality criteria appropriate to multiagent settings in which decision makers interact. Artificial markets (Wellman 1993) and negotiation techniques based on game theory (Rosenschein and Zlotkin 1994) now form the basis for a number of techniques in MULTIAGENT SYSTEMS.

-- Jon Doyle

References and Further Readings

Arrow, K. J. (1963). Social Choice and Individual Values. 2nd ed. New Haven: Yale University Press.

Arrow, K. J., and F. H. Hahn. (1971). General Competitive Analysis. Amsterdam: Elsevier.

Baron, J. (1985). Rationality and Intelligence. Cambridge: Cambridge University Press.

Becker, G. S. (1976). The Economic Approach to Human Behavior. Chicago: University of Chicago Press.

Bentham, J. (1823). Principles of Morals and Legislation. Oxford: Oxford University Press.

Bernoulli, D. (1738). Specimen theoriae novae de mensura sortis. Comentarii academiae scientarium imperialis Petropolitanae, vol. 5 for 1730 and 1731, pp. 175-192.

Black, D. (1963). The Theory of Committees and Elections. Cambridge: Cambridge University Press.

de Finetti, B. (1937). La prévision: Ses lois logiques, ses sources subjectives. Annales de l'Institut Henri Poincaré 7.

Davidson, D., P. Suppes, and S. Siegel. (1957). Decision Making: An Experimental Approach. Stanford, CA: Stanford University Press.

Debreu, G. (1959). Theory of Value: An Axiomatic Analysis of Economic Equlibrium. New York: Wiley.

Henderson, J. M., and R. E. Quandt. (1980). Microeconomic Theory: A Mathematical Approach. 3rd ed. New York: McGraw-Hill.

Horvitz, E. J. (1987). Reasoning about beliefs and actions under computational resource constraints. Proceedings of the Third AAAI Workshop on Uncertainty in Artificial Intelligence. Menlo Park, CA: AAAI Press.

Jeffrey, R. C. (1983). The Logic of Decision. 2nd ed. Chicago: University of Chicago Press.

Kahneman, D., P. Slovic, and A. Tversky, Eds. (1982). Judgment under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press.

Keeney, R. L., and H. Raiffa. (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs. New York: Wiley.

Luce, R. D., and H. Raiffa. (1957). Games and Decisions. New York: Wiley.

Machina, M. J. (1987). Choice under uncertainty: Problems solved and unsolved. Journal of Economic Perspectives 1(1):121-154.

May, K. O. (1954). Intransitivity, utility, and the aggregation of preference patterns. Econometrica 22:1-13.

Milnor, J. (1954). Games against nature. In R. M. Thrall, C. H. Coombs, and R. L. Davis, Eds., Decision Processes. New York: Wiley, pp. 49-59.

Mueller, D. C. (1989). Public Choice 2. 2nd ed. Cambridge: Cambridge University Press.

Newell, A. (1982). The knowledge level. Artificial Intelligence 18(1):87-127.

Pareto, V. (1927). Manuel d'economie politique, deuxième édition. Paris: M. Giard.

Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA: Morgan Kaufmann.

Raiffa, H. (1968). Decision Analysis: Introductory Lectures on Choices Under Uncertainty. Reading, MA: Addison-Wesley.

Ramsey, F. P. (1964). Truth and probability. In H. E. Kyburg, Jr. and H. E. Smokler, Eds., Studies in Subjective Probability. New York: Wiley. Originally published 1926.

Rosenschein, J. S., and G. Zlotkin. (1994). Rules of Encounter: Designing Conventions for Automated Negotiation among Computers. Cambridge, MA: MIT Press.

Russell, S. J. (1991). Do the Right Thing: Studies in Limited Rationality. Cambridge, MA: MIT Press.

Savage, L. J. (1972). The Foundations of Statistics. 2nd ed. New York: Dover Publications.

Sen, A. (1977). Social choice theory: A re-examination. Econometrica 45:53-89.

Simon, H. A. (1955). A behavioral model of rational choice. Quarterly Journal of Economics 69:99-118.

Simon, H. A. (1982). Models of Bounded Rationality: Behavioral Economics and Business Organization, vol. 2. Cambridge, MA: MIT Press.

Stigler, G. J., and G. S. Becker. (1977). De gustibus non est disputandum. American Economic Review 67:76-90.

von Neumann, J., and O. Morgenstern. (1953). Theory of Games and Economic Behavior. 3rd ed. Princeton, NJ: Princeton University Press.

Wellman, M. P. (1993). A market-oriented programming environment and its application to distributed multicommodity flow problems. Journal of Artificial Intelligence Research 1:1-23.

Wellman, M. P., J. S. Breese, and R. P. Goldman. (1992). From knowledge bases to decision models. The Knowledge Engineer ing Review 7(1):35-53.