A decision maker may be concerned about the effects of his or her actions on other individuals. There may be altruistic or malevolent motives involved, but, since we prefer to think positively, we shall concentrate our attention on the prototypical higher-level, benevolent, executive decision maker. Let us refer to this individual decision maker simply as the “Decision Maker”—that person who wishes to incorporate the feelings, values, preferences, and Utilities of others into her own value assessments. She wants to make everyone happy but, alas, tradeoffs will have to be made. These concerns will be the subject matter of this chapter but before we delve into details, let us put this problem into a broader perspective: that of the group decision problem. We must be careful, however, since we believe there is no such thing as the group decision problem. We should talk in the plural about group decision problems.

From a descriptive point of view, as contrasted to a prescriptive point of view, most actions taken by decision makers, both private and public, can only be explained in terms of a panoply of various interacting forces and actions taken by many individuals acting through a mixture of motives. Just imagine how a bill gets through the U.S. Congress. This is truly a group effort.

If we wanted the title of this book merely to convey the subject matter, it would be some horrendously complicated concoction such as: “On Cardinal Utility Analysis with Multiple Conflicting Objectives: The Case of Individual Decision making Under Uncertainty from the Prescriptive Point of View—with Special Emphasis on Applications but with a Little Theory Thrown In for Spice.”

Our actual title, Decisions with Multiple Objectives: Preferences and Value Tradeoffs is longer than we think a title should ideally be, but, unfortunately, it is too short to prevent unjustified sales. Even in such a simple case, it is not so easy to balance among the conflicting objectives: convey the subject matter, minimize the length, and promote justified sales but prevent unjustified ones.

To an ever growing circle of people, “Decision Analysis” has carved out for itself a niche in the literature of operations research, Systems analysis, management sciences, decision and control, and cybernetics. Decision analysis looks at the paradigm in which an individual decision maker (or decision unit) contemplates a choice of action in an uncertain environment. The approach employs systematic analysis, with some number pushing, which helps the decision maker clarify in his own mind which course of action he should choose. In this sense, the approach is not descriptive, because most people do not attempt to think systematically about hard choices under uncertainty. It is also not normative since it is not an idealized theory designed for the superrational being with an all-powering intellect. It is, instead, a prescriptive approach designed for normally intelligent people who want to think hard and systematically about some important real problems.

Way back in the mid-seventies when we wrote Decisions with Multiple Objectives, our objectives were clear. We aspired to develop a sound, practical theory for analyzing decisions with multiple, competing objectives; to make this theory and framework of thought accessible to a diverse audience of scholars and practitioners of the art of decision analysis; and to promote applications of multiattribute analysis. Today, our objectives are exactly the same. In the intervening sixteen years, the theory most relevant to applications has been augmented a little and the application of the theory has greatly expanded.

Decision analysis is widely recognized as a sound prescriptive theory. When a decision involves multiple objectives – and this is almost always the case with important problems – multiattribute Utility theory forms the basic foundation for applying decision analysis. The theory explicitly addresses the value tradeoffs and uncertainties that are invariably at the center of multiple-objective decisions. The experience of numerous applications indicates that the theory available in 1976 is still the most relevant theory available today. The important addition since 1976 concerns value functions that address strength of preferences between pairs of consequences (see Dyer and Sarin, 1979; Bell and Raiffa, 1988).

The art of applying multiattribute Utility has expanded in many directions since 1976. Collectively, decision scientists know much more today about identifying and structuring objectives and about measuring their achievement in terms of objectives. We are more skilled at assessing Utility functions, and Computer programs greatly assist analyses and sensitivity analysis.

This chapter applies decision analysis to a large-scale public decision problem: selection of a strategy for developing the major airport facilities of the Mexico City metropolitan area. There are two purposes in discussing this study here. First, many of the techniques and procedures developed in earlier chapters of this book are utilized on a very important “typical” problem. Of course, it's typical of those one-of-a-kind Strategic decisions that always concern many atypical aspects. Second, although the analysis Stresses the value side of the multiattribute problem, it also deals with structuring the problem, aspects of modeling the possible impacts of various alternatives, and the larger framework within which the analysis occurred.

Many people contributed significantly to the study. It was done in the summer of 1971 for the Government of Mexico under the auspices of the Secretaria de Obras Publicas (Ministry of Public Works, SOP) and directed by F. J. Jauffred, Director of the Center for Computation and Statistics, and F. Dovali, Head of the Department of Airports. Richard de Newville of the Massachusetts Institute of Technology and we authors were consultants assisting SOP on the project. The total time spent by the consultants on the project was 50 man-days.

The general problem addressed can be stated simply. A decision maker must choose among several alternatives A1, A2, …, Am, each of which will eventually result in a consequence describable in terms of a Single attribute X. The decision maker does not know exactly what consequence will result from each of the various alternatives, but he can assign probabilities to the various possibilities that might result from any course of action. What should he do?

THE MOTIVATION FOR UTILITY THEORY

The power of the concept of Utility and the grounds for our interest in it is as follows. If an appropriate Utility is assigned to each possible consequence and the expected Utility of each alternative is calculated, then the best course of action is the alternative with the highest expected Utility. Different sets of axioms that imply the existence of Utilities with the property that expected Utility is an appropriate guide for consistent decision making are presented in von Neumann and Morgenstern (1947), Savage (1954), Luce and Raiffa (1957), Pratt, Raiffa, and Schlaifer (1965), and Fishburn (1970). The next subsection informally reviews the basic ideas of the theory.

Many complex decision problems involve multiple conflicting objectives. It is often true that no dominant alternative will exist that is better than all other alternatives in terms of all of these objectives. Perhaps some of the original alternatives can be eliminated from further consideration because they are dominated, but generally you simply cannot maximize several objectives simultaneously. You cannot maximize benefits and at the same time minimize costs; you cannot necessarily maximize yield and minimize risk; nor can you share a pie by giving the maximum amount to each child. The literature is replete with high-sounding rhetoric where an advocate cries out for doing “best” for everybody, in every possible way, in the shortest time, with the least inconvenience, and with the maximum security for all. Ah, for the simplicity of the romanticist's dream world!

THE MULTIATTRIBUTE VALUE PROBLEM

Our problem is one of value tradeoffs. In this chapter we see what can be done about systematically structuring such tradeoffs. In essence, the decision maker is faced with a problem of trading off the achievement of one objective against another objective. If there is no uncertainty in the problem, if we know the multiattribute consequence of each alternative, the essence of the issue is, “How much achievement on objective 1 is the decision maker willing to give up in order to improve achievement on objective 2 by some fixed amount?” If there is uncertainty in the problem, the tradeoff issue remains, but difficulties are compounded because it is not clear what the consequences of each of the alternatives will be.

In an uncertain world the responsible decision maker must balance judgments about uncertainties with his or her preferences for possible consequences or outcomes. It's not easy to do and, even though we all have a lot of practice, we are not very good at it. Here we suggest formal techniques that will be helpful in this decision-making process. We concentrate on formalizing the preference or value side of the problem rather than developing procedures for the assessments of uncertainties. This doesn't mean that we think modeling of the uncertainties is unimportant. However, we feel that many capable scholars have already dealt with the modeling aspects of the kind of problems we have in mind; our efforts on the value side of the problem are meant to complement theirs. So, let's assume that the assessments of uncertainties are given, and let's worry about how we, as decision makers, can make sense out of our conflicting values, objectives, or goals and arrive at a wise decision. As one of our associates expressed it, “the aim of the analysis is to get your head straightened out!”

We suggest—or prescribe—how a decision maker (perhaps you) should think systematically about identifying and structuring objectives, about making vexing value tradeoffs, and about balancing various risks. The following sketches of problems will set the stage.

We are dealing in this book with a nonvacuous problem: many difficult, real-world decision problems do involve multiple objectives. Consequently, many of the concepts we have introduced are relevant and must be applied in either a formal or informal analysis of the alternatives. If we choose to analyze multiple objectives and value or utility tradeoffs in a formal manner, then we immodestly believe that the ideas and procedures discussed in this book can often be of considerable use. This chapter and Chapter 8 support this contention by illustrating many cases where multiattribute preferences have been formalized. This chapter, in a variety of settings, focuses exclusively on the preference assessments themselves whereas Chapter 8, which concerns the site selection of an airport for Mexico City, presents a complete case including probability assessments, analysis of alternatives, interactions with the decision makers, and so on, as well as multiattribute preference assessments.

The applications discussed in this chapter cover the range of topics presented in Chapters 2-6. Section 7.1 discusses the generation of objectives and the specification of measures of effectiveness for an air pollution problem. Section 7.2 discusses the allocation of resources for an educational program and the value functions of the members of a local school board and other local education officials are formalized. Next, a five-attribute Utility function for response times of various fire trucks is assessed.

The consequences of a decision often do not all occur simultaneously. Thus a decision maker may have to consider his preferences for some consequence x at a time t1 and a consequence y at a time t2. This indicates the distinguishing characteristic of time preferences: the consequences accrue at two or more points in the future. A typical example is the stream of income and cash flow resulting from a long-term Investment. In this case it may be natural to divide time into discrete periods (e.g., months or quarters), and to use (x1, x2, …, xn) to indicate a time stream of consequences, where xi indicates the consequences in time period i. Alternatively, we may have a continuous stream of consequences, which we shall denote by x(·), where x(t) is the consequence at time t. For example, in consumption problems x(t) might represent a decision maker's rate of consumption at time t for each component of a commodity bundle. Because (1) many continuous-time problems can be reasonably formulated as discrete-time problems without oversimplifying the issues involved, and (2) the development of procedures for analyzing continuous-time problems are analogous to those for discrete ones, we emphasize the discrete-time problems in this chapter.

Two important features affecting time preferences are (1) the timing of the resolution of uncertainties and (2) the horizon to be used. Both of these considerations, discussed in Section 9.1, influence greatly the appropriateness of a given approach for specifying one's preferences.

This book is a collection of papers presented at a conference, “Decision Making: Descriptive, Normative, and Prescriptive Interactions,” held in Boston at the Harvard Business School during June 16–18, 1983. The conference was one of several celebrating the 75th anniversary of the Harvard Business School. It might equally have been held as a celebration of the renaissance of interest in the analysis of decision making under uncertainty that has occurred in recent years. Not since the early 1950s, in the aftermath of the pathbreaking work by von Neumann and Morgenstern, has so much intellectual enthusiasm been directed at the question of how people should, and do, behave when called upon to take action in the face of uncertainty.

When Amos Tversky visited Harvard in the spring of 1982, the three of us had long discussions about the philosophy behind the contribution made by various disciplines to research on decision making. It was clear that mathematicians (decision theorists) are interested in proposing rational procedures for decision making – how people should make decisions if they wish to obey certain fundamental laws of behavior. Psychologists are interested in how people do make decisions (whether or not rational) and in determining the extent to which their behavior is compatible with any rational model. They are also interested in learning the cognitive capacities and limitations of ordinary people to process the information required of them if they do not naturally behave rationally, but wish to.