IEEE TRANSACTIONS ON SYSTEMS SCIENCE AND CY13ERNETICS, VOL.
3, SEPTEMLIER 1968
to Decision Theory
D. WARNER NORTH
Abstract-Decision theory provides a rational framework for
choosing between alternative courses of action when the consequences 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 "anniversary 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.
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 particularly 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
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 today, but predictions of the future still abound. Much current scientific effort goes into forecasting future economic and technological developments. If these predictions are assumed to be completely accurate, the uncertainty in
many systems decisions is eliminated. The outcome resulting from a possible course of action may then be presumed to be known. Decision making becomes an optimization
problem, and techniques such as mathematical programming 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 Conference, 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 alternative ways
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