A Tutorial Introduction to Decision Theory

A Tutorial Introduction to Decision Theory

11 Pages · 2006 · 2.25 MB · English

decision theory is available from many sources, most notably Applied Statistical Decision Theory. Boston, Mass.: Graduate School of Business, Harvard Uni-

A Tutorial Introduction to Decision Theory free download

IEEE TRANSACTIONS ON SYSTEMS SCIENCE AND CY13ERNETICS, VOL. SSC-4, NO. 3, SEPTEMLIER 1968 A Tutorial Introduction to Decision Theory D. WARNER NORTH Abstract-Decision theory provides a rational framework for choosing between alternative courses of action when the conse- quences resulting from this choice are imperfectly known. Two streams of thought serve as the foundations: utility theory and the inductive use of probability theory. The intent of this paper is to provide a tutorial introduction to this increasingly important area of systems science. The foundations are developed on an axiomatic basis, and a simple example, the "anni- versary problem," is used to illustrate decision theory. The concept of the value of information is developed and demonstrated. At times mathematical rigor has been subordinated to provide a clear and readily accessible exposition of the fundamental assumptions and concepts of decision theory. A sampling of the many elegant and rigorous treatments of decision theory is provided among the references. INTRODUCTION THE NECESSITY of makinig decisions in the face of uncertainty is an integral part of our lives. We must act without knowing the consequeinces that will result from the action. This uncomfortable situation is partic- ularly acute for the systems engineer or manager who must make far-reaching decisions oIn complex issues in a rapidly changing technological environment. Uncertainty appears as the dominant consideration in many systems problems as well as in decisions that we face in our personal lives. To deal with these problems oii a rational basis, we must develop a theoretical structure for decisiotn making that includes uncertainity. Confronting uncertainty is Inot easy-. We naturally try to avoid it; sometimes we even pretend it does not exist. Our primitive ancestors sought to avoid it by consulting soothsayers and oracles who would "reveal" the uncertain future. The methods have changed: astrology and the reading of sheep entrails are somewhat out of fashion to- day, but predictions of the future still abound. Much current scientific effort goes into forecasting future eco- nomic and technological developments. If these predictions are assumed to be completely accurate, the uncertainty in many systems decisions is eliminated. The outcome result- ing from a possible course of action may then be presumed to be known. Decision making becomes an optimization problem, and techniques such as mathematical program- ming may be used to obtain a solution. Such problems may be quite difficult to solve, but this difficulty should Manuscript received M\ay 8, 1968. An earlier version of this paper was presented at the IEEE Systems Science and Cybernetics Con- ference, Washington, D.C., October 17, 1966. This research was sup- ported in part by the Graduate Cooperative Fellowship Program of the National Science Foundation at Stanford University, Stanford, Calif. The author is with the Systems Sciences Area, Stanford Research Institute, MTenlo Park, Calif. 94025. not obscure the fact that they represent the limiting case of perfect predictions. It is often tempting to assume perfect predictions, but in so doing we may be eliminatinig the most important features of the problem.' We should like to include in the analysis not just the predictions themselves, but also a measure of the confidence we have in these predictions. A formal theory of decision making must take uncertainty as its departure point and regard precise knowledge of outcomes as a limiting special case. Before we begin our exposition, we will clarify our point of view. We shall take the enginieering rather than the purely sc ientific viewpoint. We are not observing the way people make decisions; rather we are participanits in the decision-making process. Our concerin is in actually making a decision, i.e., making a choice between

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