A+Behavioral+Model+of+Rational+Choice

A Behavioral Model of Rational Choice Herbert A. Simon The Quarterly Journal of Economics, Vol. 69, No. 1. (Feb., 1955), pp. 99-118. Stable URL: http://links.jstor.org/sici?sici=0033-5533%28195502%2969%3A1%3C99%3AABMORC%3E2.0.CO%3B2-A The Quarterly Journal of Economics is currently published by The MIT Press. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/mitpress.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Thu Nov 29 09:15:18 2007 A BEHAVIORAL MODEL OF RATIONAL CHOICE Introduction, 99. -I. Some general features of rational choice, 100. - 11. The essential simplifications, 103. -111. Existence and uniqueness of solu- tions, 111. - IV. Further comments on dynamics, 113. -V. Conclusion, 114. - Appendix, 115. Traditional economic theory postulates an "economic man," who, in the course of being "economic" is also "rational." This man is assumed to have knowledge of the relevant aspects of his environ- ment which, if not absolutely complete, is a t least impressively clear and voluminous. He is assumed also to have a well-organized and stable system of preferences, and a skill in computation that enables him to calculate, for the alternative courses of action that are avail- able to him, which of these will permit him to reach the highest attainable point on his preference scale. Recent developments in economics, and particularly in the theory of the business firm, have raised great doubts as to whether this schematized model of economic man provides a suitable foundation on which to erect a theory -whether it be a theory of how firms do behave, or of how they "should" rationally behave. I t is not the purpose of this paper to discuss these doubts, or to determine whether they are justified. Rather, I shall assume that the concept of "eco- nomic man" (and, I might add, of his brother "administrative man") is in need of fairly drastic revision, and shall put forth some sugges- tions as to the direction the revision might take. Broadly stated, the task is to replace the global rationality of economic man with a kind of rational behavior that is compatible with the access to information and the computational capacitiesthat are actually possessed by organisms, including man, in the kinds of environments in which such organisms exist. One is tempted to turn * The ideas embodied in this paper were initially developed in a series of discussions with Herbert Bohnert, Norman Dalkey, Gerald Thompson, and Robert Wolfson during the summer of 1952. These collaborators deserve a large share of the credit for whatever merit this approach to rational choice may possess. A first draft of this paper was prepared in my capacity as a consultant to the RAND Corporation. It has been developed further (including the Appen- dix) in work with the Cowles Commission for Research in Economics on L'Decision Making Under Uncertainty," under contract with the Office of Naval Research, and has been completed with the aid of a grant from the Ford Foundation. 99 100 QUARTERLY JOURNAL OF ECONOMICS to the literature of psychology for the answer. Psychologists have certainly been concerned with rational behavior, particularly in their interest in learning phenomena. But the distance is so great between our present psychological knowledge of the learning and choice processes and the kinds of knowledge needed for economic and administrative theory that a marking stone placed halfway between might help travellers from both directions to keep to their courses. Lacking the kinds of empirical knowledge of the decisional processes that will be required for a definitive theory, the hard facts of the actual world can, a t the present stage, enter the theory only in a relatively unsystematic and unrigorous way. But none of us is completely innocent of acquaintance with the gross characteristics of human choice, or of the broad features of the environment in which this choice takes place. I shall feel free to call on this common experience as a source of the hypotheses needed for the theory about the nature of man and his world. The problem can be approached initially either by inquiring into the properties of the choosing organism, or by inquiring into the environment of choice. In this paper, I shall take the former approach. I propose, in a sequel, to deal with the characteristics of the environ- ment and the interrelations of environment and organism. The present paper, then, attempts to include explicitly some of the properties of the choosing organism as elements in defining what is meant by rational behavior in specific situations and in selecting a rational behavior in' terms of such a definition. In part, this involves making more explicit what is already implicit in some of the recent work on the problem - that the state of information mayas well be regarded as a characteristic of the decision-maker as a characteristic of his environment. In part, it involves some new considerations - in particular taking into account the simplifications the choosing organism may deliberately introduce into its model of the situation in order to bring the model within the range of its computing capacity. I. SOME GENERAL FEATURES CHOICEOF RATIONAL The "flavor" of various models of rational choice stems primarily from the specific kinds of assumptions that are introduced as to the '(givens" or constraints within which rational adaptation must take place. Among the common constraints -which are not themselves the objects of rational calculation -are (1) the set of alternatives open to choice, (2) the relationships that determine the pay-offs ("satisfactions," "goal attainment") as a function of the alternative that is chosen, and (3) the preference-orderings among pay-offs. The A BEHA'1710RdL JIODEL OF RATIOSAL CHOICE 101 selection of particular constraints and the rejection of others for incorporation in the model of rational behavior involves implicit assumptions as to what variables the rational organism "controls" - and hence can "optimize" as a means to rational adaptation -and what variables it must take as fixed. I t also involves assumptions as to the character of the variables that are fixed. For example, by making different assumptions about the amount of information the organism has with respect to the relations bet~veen alternatives and pay-offs, optimization might involve selection of a certain maximum, of an expected value, or a minimax. Another way of characterizing the givens and the behavior variables is to say that the latter refer to the organism itself, the former to its environment. But if Tve adopt this vie~vpoint, \T-e must be prepared to accept the possibility that what n-e call "the environ- ment" may lie, in part, ~vithin the skin of the biological organism. That is, some of the constraints that must be taken as givens in an optimization problem may be physiological and psychological limita- tions of the organism (biologically defined) itself For example, the maximum speed a t ~i-hich an organism can move establishes a bound- ary on the set of its available behavior alternatives. Similarly, limits on computational capacity may be important constraints enter- ing into the definition of rational choice under particular circum- stances. We shall explore possible Tvays of formulating the process of rational choice in situations where Ire wish to take explicit account of the "internal" as well as the "external" constraints that define the problem of rationality for the organism. Whether our interests lie in the normative or in the descriptive aspects of rational choice, the construction of models of this kind should prove instructive. Because of the psychological limits of the organism (particularly with respect to computational and predictive ability), actual human rationality-strivi~~g can a t best be an extremely crude and simplified approximation to the kind of global rationality that is implied, for example, by game-theoretical models. While the approximations that organisms employ may not be the best -even at the levels of computational complexity they are able to handle - it is probable that a great deal can be learned about possible mecha- nisms from an examination of the schemes of approximation that are actually employed by human and other organisms. In describing the proposed model, we shall begin with elements it has in common with the more global models, and then proceed to introduce simplifying assumptions and (what is the same thing) approximating procedures. 102 QUARTERLY JOURNAL OF ECONOMICS 1.1 Primitive Terms and Definitions Models of rational behavior -both the global kinds usually constructed, and the more limited kinds to be discussed here - generally require some or all of the following elements: 1. A set of behavior alternatives (alternatives of choice or deci- sion). In a mathematical model, these can be represented by a point set, A. 2. The subset of behavior alternatives that the organism "considers" or "perceives." That is, the organism may make its choice within a set of alternatives more limited than the whole range objectively available to it. The "considered" subset can be represented by a point set A, with 1 included in A (AcA). 3. The possible future states of afairs, or outcomes of choice, represented by a point set, S. (For the moment it is not necessary to distinguish between actual and perceived outcomes.) 4. A "pay-o$" function, representing the "value" or "utility" placed by the organism upon each of the possible outcomes of choice. The pay-off may be represented by a real function, V(s) defined for all elements, s, of S. For many purposes there is needed only an ordering relation on pairs of elements of S- i.e., a relation that states that sl is preferred to sz or vice versa -but to avoid unneces- sary complications in the present discussion, we will assume that a cardinal utility, V(s), has been defined. 5. Information as to which outcomes in S will actually occur if a particular alternative, a, in A (or in A) is chosen. This information may be incomplete - that is, there may be more than one possible outcome, s, for each behavior alternative, a. We represent the information, then, by a mapping of each element, a, in A upon a subset, 8, -the set of outcomes that may ensue if a is the chosen behavior alternative. 6. Information as to the probability that a particular outcome wilt ensue if a particular behavior alternative is chosen. This is a more precise kind of information than that postulated in (5), for it asso- ciates with each element, s, in the set S,, a probability, P,(s) -the probability that s will occur if a is chosen. The probability P,(s) is a, real, non-negative function with 2 P,(s) = 1. Sa Attention is directed to the threefold distinction drawn by the definitions among the set of behavior alternatives, A, the set of out- comes or future states of affairs, S, and the pay-off, V. In the ordi- nary representation of a game, in reduced form, by its pay-off matrix, the set S corresponds to the cells of the matrix, the set A to the A BEHAVIORAL MODEL OF RATIONAL CHOICE 103 strategies of the first player, and the function V to the values in the cells. The set S, is then the set of cells in the ath row. By keeping in mind this interpretation, the reader may compare the present formu- lation with "classical" game theory. 1.2 "Classical" Concepts of Rationality With these elements, we can define procedures of rational choice corresponding to the ordinary game-theoretical and probabilistic models.' A. Max-min Rule. Assume that whatever alternative is chosen, the worst possible outcome will ensue - the smallest V(s) for s in S, will be realized. Then select that alternative, a, for which this worst pay-off is as large as possible. A V(&) = Min V(s) = Max Min V(s) seSd arA saSa Instead of the maximum with respect to the set, A, of actual alternatives, we can substitute the maximum with respect to the set, A, of "considered" alternatives. The probability distribution of outcomes, (6) does not play any role in the max-min rule. B. Probabilistic Rule. Maximize the expected value of V(s) for the (assumed known) probability distribution, P,(s). A V(&) = 2 V(s)Pd(s) = Max Z V(s)P,(s) seSa atA arSa C. Certainty Rule. Given the information that each a in A (or in A) maps upon a specified s, in S, select the behavior alternative whose outcome has the largest pay-off. A V(b) = V(Sa) = Max V(S,) aaA If we examine closely the "classical" concepts of rationality out- lined above, we see immediately what severe demands they make upon the choosing organism. The organism must be able to attach definite pay-offs (or a t least a definite range of pay-offs) to each possible out- come. This, of course, involves also the ability to specify the exact nature of the outcomes -there is no room in the scheme for "unan- ticipated consequences." The pay-offs must be completely ordered - 1. See Kenneth J. Arrow, "Alternative Approaches to the Theory of Choice in Risk-Taking Situations," Econometrics, XIX, 404-37 (Oct. 1951). 104 QUARTERLY JOURNAL OF ECONOMICS it must always be possible to specify, in a consistent way, that one outcome is better than, as good as, or worse than any other. And, if the certainty or probabilistic rules are employed, either the out- comes of particular alternatives must be known with certainty, or a t least it must be possible to attach definite probabilities to outcomes. My first empirical proposition is that there is a complete lack of evidence that, in actual human choice situations of any complexity, these computations can be, or are in fact, performed. The intro- spective evidence is certainly clear enough, but we cannot, of course, rule out the possibility that the unconscious is a better decision-maker than the conscious. Nevertheless, in the absence of evidence that the classical concepts do describe the decision-making process, i t seems reasonable to examine the possibility that the actual process is quite different from the ones the rules describe. Our procedure will be to introduce some modifications that appear (on the basis of casual empiricism) to correspond to observed behavior processes in humans, and that lead to substantial computa- tional simplifications in the making of a choice. There is no implica- tion that human beings use all of these modifications and simplifica- tions all the time. Nor is this the place to attempt the formidable empirical task of determining the extent to which, and the circum- stances under which humans actually employ these simplifications. The point is rather that these are procedures which appear often to be employed by human beings in complex choice situations to find an approximate model of manageable proportions. 2.1 "Simple" Pay-o$ Functions One route to simplification is to assume that V(s) necessarily assumes one of two values, (1,0), or of three values, (1,0, -I), for all s in S. Depending on the circumstances, we might want to interpret these values, as (a) (satisfactory or unsatisfactory), or (b) (win, draw or lose). As an example of (b), let S represent the possible positions in a chess game a t White's 20th move. Then a ($1) position is one in which White possesses a strategy leading to a win whatever Black does. A (0) position is one in which White can enforce a draw, but not a win. A ( - 1) position is one in which Black car1 force a win. As an example of (a) let S represent possible prices for a house an individual is selling. He may regard $15,000 as an '(acceptable" price, anything over this amount as ('satisfactory," anything less a s "unsatisfactory." In .psychological theory we would fix the boundary a t the "aspiration level" ; in economic theory we would fix the bound- A BEHAVIORAL MODEL OF RATIONAL CHOICE 105 ary a t the price which evokes indifference between selling and not selling (an opportunity cost concept). The objection may be raised that, although $16,000 and $25,000 are both "very satisfactory" prices for the house, a rational individual would prefer to sell a t the higher price, and hence, that the simple pay-off function is an inadequate representation of the choice situa- tion. The objection may be answered in several different ways, each answer corresponding to a class of situations in which the simple function might be appropriate. First, the individual may not be confronted simultaneously with I I FIGURE I a number of buyers offering to purchase the house a t different prices, but may receive a sequence of offers, and may have to decide to accept or reject each one before he receives the next. (Or, more generally, he may receive a sequence of pairs or triplets or n-tuples of offers, and may have to decide whether to accept the highest of an n-tuple before the next n-tuple is received.) Then, if the elements S correspond to n-tuples of offers, V( s )would be 1whenever the highest offer in the n-tuple exceeded the "acceptance price" the seller had determined upon a t that time. We can then raise the further ques- tion of what would be a rational process for determining the accept- ance price.2 2. See the Appendix. It might be remarked here that the simple risk fuac- tion, introduced by Wald to bring problems in statistical decision theory within the bounds of computability, is anexample of a simple pay-off function as that term is defined here. 106 QUARTERLY JOURNAL OF ECONOMICS Second, even if there were a more general pay-off function, W(s), capable of assuming more than two different values, the simplified V(s) might be a satisfactory approximation to W(s) . Suppose, for example, that there were some way of introducing a cardinal utility function, defined over S, say U(s). Suppose further that U(W) is a monotonic increasing function with a strongly negative second deriva- tive (decreasing marginal utility). Then V(s) = V { W(s) } might be the approximation as shown on page 107. When a simple V(s), assuming only the values (+ 1,O) is admis- sible, under the circumstances just discussed or under other circum- stances, then a (fourth) rational decision-process could be defined as follows: D. (i) Search for a set of possible outcomes (a subset, Sfin S) such that the pay-off is satisfactory (V(s) = 1) for all these possible outcomes (for all s in 8'). o (ii) Search for a behavior alternative (an a in A) whose possible outcomes all are in S' (such that a maps upon a set, S,, that is con- tained in s ' ) .