MANAGEMENT SCIENCE informs ® Vol. 50, No. 5, May 2004, pp. 561–574 doi 10.1287/mnsc.1040.0243 issn 0025-1909 eissn 1526-5501 04 5005 0561 © 2004 INFORMS Anniversary Article Decision Analysis in Management Science James E. Smith Fuqua School of Business, Duke University, Durham, North Carolina 27708, [email protected] Detlof von Winterfeldt School of Policy, Planning, and Development, University of Southern California, Los Angeles, California 90089, [email protected] s part of the 50th anniversary of Management Science, the journal is publishing articles that reflect on the Apast, present, and future of the various subfields the journal represents. In this article, we consider decision analysis research as it has appeared in Management Science. After reviewing the foundations of decision analysis and the history of the journal’s decision analysis department, we review a number of key developments in decision analysis research that have appeared in Management Science and offer some comments on the current state of the field. Key words: decision analysis; probability assessment; utility theory; game theory 1. Introduction for 12% of the papers in Management Science and Management Science (MS) has played a distinguished 17% of the “most-cited” papers (those receiving 50 and distinctive role in the development of decision or more cites). However, given the interdisciplinary analysis. As part of Management Science, the deci- nature of the field, it is difficult to draw sharp bound- sion analysis department has focused on papers that aries and determine precisely what counts as “deci- consider the use of scientific methods to improve sion analysis.” the understanding or practice of managerial decision Following Bell et al. (1988), we can distinguish making. The current departmental statement reads as among three different perspectives in the study of follows: decision making. In the normative perspective, the focus is on rational choice and normative models The decision analysis department publishes articles are built on basic assumptions (or axioms) that peo- that create, extend, or unify scientific knowledge per- ple consider as providing logical guidance for their taining to decision analysis and decision making. We seek papers that describe concepts and techniques for decisions. In the domain of decision making under modeling decisions as well as behaviorally oriented risk or uncertainty, the expected utility model of von papers that explain or evaluate decisions or judgments. Neumann and Morgenstern (1944) and the subjec- Papers may develop new theory or methodology, tive expected utility model of Savage (1954) are the address problems of implementation, present empiri- dominant normative models of rational choice. In the cal studies of choice behavior or decision modeling, domain of judgments and beliefs, probability theory synthesize existing ideas, or describe innovative appli- and Bayesian statistics, in particular, provide the nor- cations. In all cases, the papers must be based on sound mative foundation. decision-theoretic and/or psychological principles The descriptive perspective focuses on how real peo- Decision settings may consist of any combination ple actually think and behave. Descriptive studies of certainty or uncertainty; competitive or noncom- may develop mathematical models of behavior, but petitive situations; individuals, groups, or markets; such models are judged by the extent to which their and applications may include managerial decisions in business or government. predictions correspond to the actual choices people make. One of the most prominent descriptive models According to Hopp’s counts (Hopp 2004MS),1 Man- of decision making under uncertainty is the Prospect agement Science has published 590 decision analysis Theory model of Kahneman and Tversky (1979), later papers in the period from 1954 to 2003, accounting refined in Tversky and Kahneman (1992). This model captures many of the ways in which people deviate 1 We highlight papers that have appeared in Management Science by from the normative ideal of the expected utility model including “MS” after the publication year in the in-text citation. in a reasonably parsimonious form. 561 Smith and von Winterfeldt: Decision Analysis in Management Science 562 Management Science 50(5), pp. 561–574, © 2004 INFORMS The prescriptive perspective focuses on helping peo- and Bayes (1763). Bernoulli was concerned with the ple make better decisions by using normative models, fact that people generally do not follow the expected but with awareness of the limitations and descriptive value model when choosing among gambles, in par- realities of human judgment. For example, we might ticular when buying insurance. He proposed the build a mathematical model to help a firm decide expected utility model with a logarithmic utility func- whether to undertake a particular R&D project. Such tion to explain these deviations from the expected a model may not include all of the uncertainties, value model. Bayes was interested in the revision competitive effects, and sources of value that one of probability based on observations and proposed might expect a fully “rational” individual or firm an updating procedure that is now known as Bayes to consider. It would likely include approximations Theorem. and short cuts that make the model easier to formu- Ramsey (1931) recognized that the notions of prob- late, assess, and solve. Descriptive research on deci- ability and utility are intrinsically intertwined and sion making would help the analysts understand, showed that subjective probabilities and utilities for example, which model inputs (e.g., probabilities can be inferred from preferences among gambles. or utilities) can be reliably assessed and how these Ramsey’s essays did not have much influence when inputs might be biased. Prescriptive models are evalu- they were published but they are now much appre- ated pragmatically: Do the decision makers find them ciated: INFORMS’s Decision Analysis Society awards helpful? Or, what is more difficult to ascertain, do the Ramsey Medal to recognize and honor lifetime they help people make better decisions? contributions to the field. DeFinetti (1937) followed a Decision analysis is primarily a prescriptive disci- similar path by developing a system of assumptions pline, built on normative and descriptive foundations. about preferences among gambles that allowed him to In our review of decision analysis in Management derive subjective probabilities for events. His interest Science, we emphasize its prescriptive role, but we was primarily in the representations of beliefs as sub- also discuss normative and descriptive developments jective probabilities, not in the derivation of utilities. that have advanced prescriptive methodologies and The publication of the Theory of Games and Economic applications. We begin in §2 with the early history of Behavior by von Neumann and Morgenstern (1944) decision analysis into the late 1960s when the deci- attracted a great deal of attention and was a major sion analysis department at Management Science was milestone in the history of decision analysis and eco- created. In §3, we discuss the history of the decision nomics. While the primary purpose of von Neumann analysis department at Management Science, describ- and Morgenstern’s book was to lay the foundation ing the editorial structure from 1970 to the present for the study of games, it also established the founda- and reviewing the number of decision analysis arti- tion for decision analysis in the process. Specifically, cles published. In §4, we discuss some of the decision in an appendix to the second edition of the book (pub- analysis research that has been published in Manage- lished in 1947) von Neumann and Morgenstern pro- ment Science, focusing on developments in probabil- vided an axiomatization of the expected utility model, ity assessment (§4.1), utility assessment (§4.2), and in showing that a cardinal utility function could be cre- game theory (§4.3). In our discussion of the devel- ated from preferences among gambles. Their analy- opments of the field, we highlight specific develop- sis took the probabilities in the decision problem as ments that have appeared in Management Science but given and their axioms led to the conclusion that deci- do not strive to discuss all of the decision analysis sion makers should make decisions to maximize their research that has appeared in the journal or decision expected utility. The decision-making framework of analysis research published elsewhere. Our goal is to von Neumann and Morgenstern is now referred to as give a flavor of the decision analysis research that has the expected utility (EU) model. appeared in Management Science in its first 50 years In The Foundations of Statistics (Savage 1954), Savage and some of the debates that have influenced the extended von Neumann and Morgenstern’s expected field. In §5, we conclude and look ahead. utility model to consider cases in which the prob- abilities are not given. While Savage was greatly 2. The Early History of Decision influenced by the work of von Neumann and Analysis2 Morgenstern, his background was in statistics rather The normative foundations of decision analysis can than economics, and his goal was to provide a foun- be traced back at least as far as Bernoulli (1738) dation for a “a theory of probability based on the per- sonalistic view of probability derived mainly from the work of DeFinetti (1937)” (Savage 1954, p. 5). Savage 2 More complete discussions