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ABSTRACTThis paper considers the modeling of decision‐making problems under uncertainty, indicating current gaps in knowledge and promising research directions. Technical details are omitted, and no attempt is made to review past work since excellent recent reviews are available. The discussion of research topics is divided into four categories: model formulation, modeling uncertainty, modeling preferences, and modeling competitive and group decisions. The primary focus is normative, although descriptive work that can be valuable from a normative perspective is included. The suggested research directions cover the entire spectrum from theory to application.Subject Areas: Decision Analysis, Statistical Decision Theory, and Game Theory.

Targets are used quite often as a management tool, and it has been argued that thinking in terms of targets may be more natural than thinking in terms of utilities. The standard expected-utility framework with a single attribute (such as money) and nondecreasing, bounded utility is equivalent to a target-oriented setting. A utility function, properly scaled, can be expressed as a cumulative distribution function (cdf) and related to the probability of meeting a target value. We consider whether the equivalence of the two approaches extends to the case of multiattribute utility. Our analysis shows that a multiattribute utility function cannot always be expressed in the form of a cumulative distribution function and, furthermore, cannot always be expressed in the form of a target-oriented utility function. However, in each case equivalence does hold for certain well-known classes of utility functions. In general, our results imply that although interpreting utility as a cdf and thinking about achieving targets works fine in the case of a single attribute, this approach should be used with caution in the multiattribute case, with cdf representations requiring more caution than target-oriented representations.

Averaging forecasts from several experts has been shown to lead to improved forecasting accuracy and reduced risk of bad forecasts. Similarly, it is accepted knowledge in decision analysis that an expert can benefit from using more than one assessment method to look at a situation from different viewpoints. In this paper, we investigate gains in accuracy in assessing correlations by averaging different assessments from a single expert and/or from multiple experts. Adding experts and adding methods can both improve accuracy, with diminishing returns to extra experts or methods. The gains are generally much greater from adding experts than from adding methods, and restricting the set of experts to those who do particularly well individually leads to the greatest improvements in the averaged assessments. The variability of assessment accuracy decreases considerably as the number of experts or methods increases, implying a large risk reduction. We discuss conditions under which the general pattern of results obtained here might be expected to be similar or different in other situations with multiple experts and/or multiple methods.

This paper concerns the combination of experts' probability distributions in risk analysis, discussing a variety of combination methods and attempting to highlight the important conceptual and practical issues to be considered in designing a combination process in practice. The role of experts is important because their judgments can provide valuable information, particularly in view of the limited availability of "hard data" regarding many important uncertainties in risk analysis. Because uncertainties are represented in terms of probability distributions in probabilistic risk analysis (PRA), we consider expert information in terms of probability distributions. The motivation for the use of multiple experts is simply the desire to obtain as much information as possible. Combining experts' probability distributions summarizes the accumulated information for risk analysts and decision‐makers. Procedures for combining probability distributions are often compartmentalized as mathematical aggregation methods or behavioral approaches, and we discuss both categories. However, an overall aggregation process could involve both mathematical and behavioral aspects, and no single process is best in all circumstances. An understanding of the pros and cons of different methods and the key issues to consider is valuable in the design of acombination process for a specific PRA. The output, a "combined probabilitydistribution," can ideally be viewed as representing a summary of the current state of expert opinion regarding the uncertainty of interest.