Invariant multiattribute utility functions
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We present a method to characterize the preferences of a decision maker in decisions with multiple attributes. The approach modifies the outcomes of a multivariate lottery with a multivariate transformation and observes the change in the decision maker’s certain equivalent. If the certain equivalent follows this multivariate transformation, we refer to this situation as multiattribute transformation invariance, and we derive the functional form of the utility function. We then show that any additive or multiplicative utility function that is formed of continuous and strictly monotonic utility functions of the individual attributes must satisfy transformation invariance with a multivariate transformation. This result provides a new interpretation for multiattribute utility functions with mutual utility independence as well as a necessary and sufficient condition that must be satisfied when assuming these widely used functional forms. We work through several examples to illustrate the approach.
KeywordsInvariance Zero-switch Risk aversion Utility independence Multiattribute utility
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- Abbas, A. E., Aczél, J., & Chudziak, J. (2008). Invariance of multiattribute utility functions under shift transformations. Results in Mathematics. doi: 10.1007/s00025-007-0266-0.
- Aczél J. (1966) Lectures on functional equations and their applications. Academic Press, NYGoogle Scholar
- Arrow, K. J. (1965). The theory of risk aversion. Lecture 2 in aspects of the theory of risk-bearing. Helsinki: Yrjo Jahnssonin Saatio.Google Scholar
- Howard, R.A. (1967). Value of information lotteries. IEEE Transactions on Systems Science and Cybernetics, SCC-3(1), 24–60.Google Scholar
- Keeney R.L., Raiffa H. (1976) Decisions with multiple objectives: preferences and value tradeoffs. John Wiley and Sons, Inc., New YorkGoogle Scholar
- Pfanzagl, J. (1959). A general theory of measurement applications to utility, Naval Research Logistic Quarterly, 6, 283–294.Google Scholar
- Raiffa H. (1968) Decision analysis. Addison-Wesley, Reading, MAGoogle Scholar
- von Neumann J., Morgenstern O. (1947) Theory of games and economic behavior. Princeton University Press, Princeton, NJGoogle Scholar