Chapter 1
Introduction: Five Breakthroughs in Decision and Risk Analysis

Louis Anthony (Tony) Cox, Jr.

Cox Associates, NextHealth Technologies,
University of Colorado-Denver, Denver, CO, USA

This book is about breakthroughs in decision and risk analysis-new ideas, methods, and computational techniques that enable people and groups to choose more successfully when the consequences of different choices matter, yet are uncertain. The twentieth century produced several such breakthroughs. Development of subjective expected utility (SEU) theory combined with Bayesian statistical inference as a model of ideal, rational decision-making was among the most prominent of these. Chapter 2 introduces SEU theory as a point of departure for the rest of the book. It also discusses more recent developments-including prospect theory and behavioral decision theory-that seek to bridge the gap between the demanding requirements of SEU theory and the capabilities of real people to improve their decision-making. Chapters 5 and 8 address practical techniques for improving risky decisions when there are multiple objectives and when SEU cannot easily be applied, either because of uncertainty about relevant values, causal models, probabilities, and consequences; or because of the large number and complexity of available choices.

Historical Development of Decision Analysis and Risk Analysis

Perhaps the most audacious breakthrough in twentieth-century decision analysis was the very idea that a single normative theory of decision-making could be applied to all of the varied risky decisions encountered in life. It may not be obvious what the following problems, discussed in ensuing chapters, have in common:

• Investment decisions: How should investors allocate funds across investment opportunities in a financial portfolio? (Chapter 3)
• Operations management decisions: How should a hospital emergency room be configured to make the flow of patients as easy and efficient as possible? How should an insurance company staff its claims-handling operations? (Chapter 3)
• Inventory management and retail decisions: How much of an expensive, perishable product should a business buy if demand for the product is uncertain? (Chapter 4)
• Trial evaluation and selection decisions: How much trial, testing, and comparative evaluation should be done before selecting one of a small number of costly alternatives with uncertain consequences, for example, in choosing among alternative new public policies, consumer or financial products, health care insurance plans, research and development (R&D) projects, job applicants, supply contracts, locations in which to drill for oil, or alternative drugs or treatments in a clinical trial? (Chapter 4)
• Adversarial risk management decisions: How should we model the preferences and likely actions of others, in order to make effective decisions ourselves in situations where both their choices and ours affect the outcomes? (Chapters 2, 5, 9, and 10)
• Regulatory decisions: When experimentation is unethical or impractical, how can historical data be used to estimate and compare the probable consequences that would be caused by alternative choices, such as revising versus maintaining currently permitted levels of air pollutants? (Chapter 6)
• Learning how to decide in uncertain environments: Suppose that not enough is known about a system or process to simulate its behavior. How can one use well-designed trial-and-error learning to quickly develop high-performance decision rules for deciding what to do in response to observations? (Chapters 4 and 7)
• Medical decision-making: How should one trade off the ordinary pleasures of life, such as consumption of sugar-sweetened drinks, against the health risks that they might create (e.g., risk of adult-onset diabetes)? More generally, how can and should individuals make decisions that affect their probable future health states in ways that may be difficult to clearly imagine, evaluate, or compare? (Chapter 8)

That the same basic ideas and techniques might be useful for decision-making in such very different domains is a profound insight that might once have excited incredulity among experts in these fields. It is now part of the canon of management science, widely taught in business schools and in many economics, statistics, and engineering programs.

Decision analysis views the "success" of a decision process in terms of the successes of the particular decisions that it leads to, given the information (usually incomplete and possibly incorrect or inconsistent) that is available when decisions must be made. The "success" of a single choice, in turn, can be assessed by several criteria. Does it minimize expected post-decision regret? Is it logically consistent with (or implied by) one's preferences for and beliefs about probable consequences? In hindsight, would one want to make the same choice again in the same situation, if given the same information? The giants of twentieth-century decision theory, including Frank Ramsey in the 1920s, John von Neumann in the 1940s, and Jimmy Savage in the 1950s, proved that, for perfectly rational people (homo economicus) satisfying certain mathematical axioms of coherence and consistency (i.e., complete and transitive preference orderings for outcomes and for probability distributions over outcomes), all of these criteria prescribe the same choices. All imply that a decision-maker should choose among risky prospects (including alternative acts, policies, or decision rules with uncertain consequences) as if she were maximizing subjective expected utility (SEU). Chapters 2 and 7 introduce SEU theory and some more recent alternatives. Decision-making processes and environments that encourage high-quality decisions as judged by one of these criteria will also promote the rest.

However, real people are not perfectly rational. As discussed in Chapter 2, homo economicus is a fiction. The prescriptions of decision theory are not necessarily easy to follow. Knowing that SEU theory, the long-reigning gold standard for rational decision-making, logically implies that one should act as if one had coherent (e.g., transitive) preferences, and clear subjective probabilities are cold comfort to people who find that they have neither. These principles and limitations of decision theory were well understood by 1957, when Duncan Luce and Howard Raiffa's masterful survey Games and Decisions explained and appraised much of what had been learned by decision theorists, and by game theorists for situations with multiple interacting decision-makers. Chapter 2 introduces both decision theory and game theory and discusses how they have been modified recently in light of insights from decision psychology and behavioral economics.

During the half-century after publication of Games and Decisions, a host of technical innovations followed in both decision analysis and game theory. Decision tree analysis (discussed in Chapters 8 and 10) was extended to include Monte Carlo simulation of uncertainties (see Chapter 3). Influence diagrams were introduced that could represent large decision problems far more compactly than decision trees, and sophisticated computer science algorithms were created to store and solve them efficiently. Methods of causal analysis and modeling were developed to help use data to create risk models that accurately predict the probable consequences of alternative actions (see Chapter 6). Markov decision processes for dynamic and adaptive decision-making were formulated, and algorithms were developed to adaptively and robustly optimize decision rules under uncertainty (see Chapter 7). SEU theory was generalized, e.g., to allow for robust optimization with ambiguity aversion when probabilities are not well known. Practical constructive approaches were created for structuring and eliciting probabilities and utilities, as discussed and illustrated in Chapters 5, 8, and 10.

These technical developments supported a firmly founded discipline of applied decision analysis, decision aids, and decision support consulting. The relatively new discipline of applied decision analysis, developed largely from the 1960s on, emphasized structuring of decision problems (especially, identifying and solving the right problem(s)); clearly separating beliefs about facts from values and preferences for outcomes; eliciting or constructing well-calibrated probabilities and coherent utilities; presenting decision recommendations, together with sensitivity and uncertainty analyses, in understandable ways that decision-makers find useful; assessing value of information and optimal timing of actions; and deliberate, careful learning from results, for both individuals and organizations. The 1976 publication of the landmark Decisions with Multiple Objectives: Preferences and Value Tradeoffs by Ralph Keeney and Howard Raiffa summarized much of the state of the art at the time, with emphasis on recently developed multiattribute value and utility theory and methods. These were designed to allow clearer thinking about decisions with multiple important consequence dimensions, such as costs, safety,...