David E. Bell

Regret in Decision Making under Uncertainty

Evidence exists that people do not always make decisions involving uncertain monetary rewards as if they were maximizing expected utility of final assets. Explanations for this behavior postulate that the cognitive demands of consistency to such a theory are too great. However, situations exist in which more than mental shortcuts are involved and these anomalies raise questions about expected utility theory as a guide to behavior. This paper explores the possibility that expected utility theory appears to fail because the single outcome descriptor—money—is not sufficient. After making a decision under uncertainty, a person may discover, on learning the relevant outcomes, that another alternative would have been preferable. This knowledge may impart a sense of loss, or regret. The decision maker who is prepared to tradeoff financial return in order to avoid regret will exhibit some of the behavioral paradoxes of decision theory. By explicitly incorporating regret, expected utility theory not only becomes a better descriptive predictor but also may become a more convincing guide for prescribing behavior to decision makers.

Disappointment in Decision Making Under Uncertainty

Decision analysis requires that two equally desirable consequences should have the same utility and vice versa. Most analyses of financial decision making presume that two consequences with the same dollar outcome will be equally preferred However, winning the top prize of

Conflicting objectives in decisions

10,000 in a lottery may leave one much happier than receiving

A Market Share Theorem

10,000 as the lowest prize in a lottery. This paper explores the implications of disappointment, a psychological reaction caused by comparing the actual outcome of a lottery to ones prior expectations, for decision making under uncertainty. Explicit recognition that decision makers may be paying a premium to avoid potential disappointment provides an interpretation for some known behavioral paradoxes, and suggests that decision makers may be sensitive to the manner in which a lottery is resolved. The concept of disappointment is integrated into utility theory in a prescriptive model.

Decision Making: DESCRIPTIVE, NORMATIVE, AND PRESCRIPTIVE INTERACTIONS IN DECISION MAKING

This book deals with quantitative approaches in making decisions when conflicting objectives are present. This problem is central to many applications of decision analysis, policy analysis, operational research, etc. in a wide range of fields, for example, business, economics, engineering, psychology, and planning. The book surveys different approaches to the same problem area and each approach is discussed in considerable detail so that the coverage of the book is both broad and deep. The problem of conflicting objectives is of paramount importance, both in planned and market economies, and this book represents a cross-cultural mixture of approaches from many countries to the same class of problem.

High‐dimensional coexistence based on individual variation: a synthesis of evidence

Many marketing models use variants of the relationship: Market share equals marketing effort divided by total marketing effort. Replacing marketing effort with its resulting “attraction,” the relationship is derived from the assumptions: (1) attraction is nonnegative, (2) equal attractions imply equal shares, and (3) a seller’s share is affected the same if the attraction of any other seller increases a fixed amount.

Sequential Testing in Product Development

The focus of our attention is the individual decision maker facing a choice involving uncertainty about outcomes. We will consider how people do make decisions, how “rational” people should make decisions, and how we might help less rational people, who nevertheless aspire to rationality, to do better. When we speak of nonrational people, we do not mean those with diminished capacities; we refer instead to normal people who have not given thought to the process of decision making or, even if they have, are unable, cognitively, to implement the desired process. Our decision makers are not economic automatons; they make mistakes, have remorse, suffer anxieties, and cannot make up their minds. We start with a premise, not that people have well thought out preferences, but that they may be viewed as having divided minds with different aspirations, that decision making, even for the individual, is an act of compromise among the different selves. For our purposes we shall augment the usual dichotomy that distinguishes between the normative and descriptive sides (the “ought” and the “is”) of decision making, by adding a third component: the prescriptive side. We do this because much of our concern in this paper addresses the question: “How can real people – as opposed to imaginary, idealized, super-rational people without psyches – make better choices in a way that does not do violence to their deep cognitive concerns?” And we find that much that we have to say on these matters does not fit conveniently into the usual normative or descriptive niches.

A Convergent Duality Theory for Integer Programming

High biodiversity of forests is not predicted by traditional models, and evidence for trade-offs those models require is limited. High-dimensional regulation (e.g., N factors to regulate N species) has long been recognized as a possible alternative explanation, but it has not be been seriously pursued, because only a few limiting resources are evident for trees, and analysis of multiple interactions is challenging. We develop a hierarchical model that allows us to synthesize data from long-term, experimental, data sets with processes that control growth, maturation, fecundity, and survival. We allow for uncertainty at all stages and variation among 26 000 individuals and over time, including 268 000 tree years, for dozens of tree species. We estimate population-level parameters that apply at the species level and the interactions among latent states, i.e., the demographic rates for each individual, every year. The former show that the traditional trade-offs used to explain diversity are not present. Demographic rates overlap among species, and they do not show trends consistent with maintenance of diversity by simple mechanisms (negative correlations and limiting similarity). However, estimates of latent states at the level of individuals and years demonstrate that species partition environmental variation. Correlations between responses to variation in time are high for individuals of the same species, but not for individuals of different species. We demonstrate that these relationships are pervasive, providing strong evidence that high- dimensional regulation is critical for biodiversity regulation.

A Utility Function for Time Streams Having Inter-Period Dependencies

A fundamental problem in managing product development is the optimal timing, frequency, and fidelity of sequential testing activities that are carried out to evaluate novel product concepts and designs. In this paper, we develop a mathematical model that treats testing as an activity that generates information about technical and customer-need related problems. An analysis of the model results in several important findings. First, optimal testing strategies need to balance the tension between several variables, including the increasing cost of redesign, the cost of a test as function of fidelity, and the correlation between sequential tests. Second, a simple form of our model results in an EOQ-like result: The optimal number of tests called the Economic Testing Frequency or ETF is the square root of the ratio of avoidable cost and the cost of a test. Third, the relationship between sequential tests can have an impact on optimal testing strategies. If sequential tests are increasing refinements of one another, managers should invest their budgets in a few high-fidelity tests, whereas if the tests identify problems independently of one another it may be more effective if developers carry out a higher number of lower-fidelity tests. Using examples, the implications for managerial practice are discussed and suggestions for further research undertakings are provided.

Strong One-Switch Utility

We present a constructive procedure for generating a finite sequence of increasingly stronger dual problems to a given integer programming problem. The last dual problem in the sequence yields an optimal solution to the integer programming problem. We show that this dual problem approximates the convex hull of the feasible integer solutions in a neighborhood of the optimal solution it finds. The theory is applicable to any bounded integer programming problem with rational data.