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Multiattribute Utility Satisfying a Preference for Combining Good with Bad

INSEAD, Singapore 138676, Singapore
Fuqua School of Business, Duke University, Durham, North Carolina 27708
ilia.tsetlin{at}insead.edu
rwinkler{at}duke.edu

An important challenge in multiattribute decision analysis is the choice of an appropriate functional form for the utility function. We show that if a decision maker prefers more of any attribute to less and prefers to combine good lotteries with bad, as opposed to combining good with good and bad with bad, her utility function should be a weighted average (a mixture) of multiattribute exponential utilities ("mixex utility"). In the single-attribute case, mixex utility satisfies properties typically thought to be desirable and encompasses most utility functions commonly used in decision analysis. In the multiattribute case, mixex utility implies aversion to any multivariate risk. Risk aversion with respect to any attribute decreases as that attribute increases. Under certain restrictions, such risk aversion also decreases as any other attribute increases, and a multivariate one-switch property is satisfied. One of the strengths of mixex utility is its ability to represent cases where utility independence does not hold, but mixex utility can be consistent with mutual utility independence and take on a multilinear form. An example illustrates the fitting of mixex utility to preference assessments.

Key Words: multiattribute utility; combining good with bad; mixex utility; risk aversion; multivariate one-switch property; sumex utility; multivariate Laplace transform
History: Received: November 17, 2008; accepted: August 2, 2009.