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Mixex: mixtures of multiattribute exponential utilities

Author: Tsetlin, Ilia ; Winkler, Robert L.INSEAD Area: Decision SciencesPublisher: Fontainebleau : INSEAD, 2008.Language: EnglishDescription: 24 p.Type of document: INSEAD Working Paper Online Access: Click here Abstract: 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, his or her utility function should be a weighted average (a mixture) of multi-attribute exponential utilities (mixex utility). In the singleattribute 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, with risk aversion with respect to any attribute decreasing as that attribute increases. Under certain restrictions, such risk aversion also decreases as any other attribute increases and a multivariate oneswitch 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. However, additive utility is only a limiting case that does not satisfy the spirit of preferring to combine good with bad. We present an illustration of fitting mixex utility to utility assessments in a capital investment example.
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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, his or her utility function should be a weighted average (a mixture) of multi-attribute exponential utilities (mixex utility). In the singleattribute 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, with risk aversion with respect to any attribute decreasing as that attribute increases. Under certain restrictions, such risk aversion also decreases as any other attribute increases and a multivariate oneswitch 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. However, additive utility is only a limiting case that does not satisfy the spirit of preferring to combine good with bad. We present an illustration of fitting mixex utility to utility assessments in a capital investment example.

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