Constructing Multiattribute Utility Functions for Decision Analysis
Abstract
A fundamental step in decision analysis is the accurate representation of the decision maker's preferences. When the decision situation is deterministic, each alternative leads to a single prospect (consequence). A prospect may be characterized by one or more attributes, such as health state and wealth. A value function that ranks the prospects is sufficient to rank order the decision alternatives in deterministic decision problems. When uncertainty is present, each alternative may result in a number of possible prospects, each characterized by a number of attributes. A von Neumann–Morgenstern utility function, defined over the domain of the attributes, is then required for each prospect we face. The best decision alternative is the one with the highest expected utility. This chapter surveys a variety of methods for constructing multiattribute utility functions. These methods include (i) using a deterministic value function and a one-dimensional utility function over value, (ii) using a general expansion theorem for multiattribute utility functions, (iii) using an independence assumption and a utility diagram to simplify the assessment of the conditional utility functions, (iv) using an attribute dominance condition to reduce the number of assessments, (v) using a utility copula to incorporate dependence using single-attribute assessments, (vi) deriving the functional form by asserting the number of preference switches that may occur for lotteries defined on a subset of the attributes, and (vii) characterizing preferences using functional equations to derive the functional form.
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