Chapter 3

Constructing Multiattribute Utility Functions for Decision Analysis

Ali E. Abbas
Department of Industrial and Enterprise Systems Engineering, College of Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61820, aliabbas@uiuc.edu

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 hen 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.

Key words: utility theory, multiple attributes, dependence, invariance, functional equations, graph-based methods

Download Chapter 3 - Password-protected content.

The 2010 volume of the TutORials in Operations Research series will be available to people who have registered for the 2010 INFORMS Annual Meeting. All INFORMS members will be able to access TutORials after January 1, 2011. Printed TutORials books from this and previous years can also be ordered here, along with CDs from 2005 to 2009.

For login instructions click here.

________________________________________________

Citation Information:

Abbas, E. A. 2010. Constructing multiattribute utility functions for decision analysis. J. J. Hasenbein, ed. TutORials in Operations Research, , Vol. 7. INFORMS, Hanover, MD, pp. 62–98.