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Decomposition of Utility Functions on Subsets of Product Sets

Author

Listed:
  • François Sainfort

    (University of Wisconsin, Madison, Wisconsin)

  • Jean M. Deichtmann

    (University of Wisconsin, Madison, Wisconsin)

Abstract

The standard decomposition theorem for additive and multiplicative utility functions (Pollak [Pollak, R. O. 1967. Additive von Neumann-Morgenstern utility functions. Econometrica 35 485–494.], Keeney [Keeney, R. L. 1974. Multiplicative utility functions. Opns. Res. 22 22–34.]) assumes that the outcome set is a whole product set. In this paper this assumption is relaxed, and the question of whether or not a natural revision of this theorem necessarily holds is investigated. This paper proves that two additional conditions are needed for the decomposition theorem to hold in the context where the outcome set is a subset of a Cartesian product. It is argued that these two new conditions are satisfied by a large family of subsets corresponding to significant real-world problems. Further research avenues are suggested including a generalization of this new decomposition result to nonexpected utility theories.

Suggested Citation

  • François Sainfort & Jean M. Deichtmann, 1996. "Decomposition of Utility Functions on Subsets of Product Sets," Operations Research, INFORMS, vol. 44(4), pages 609-616, August.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:4:p:609-616
    DOI: 10.1287/opre.44.4.609
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    Cited by:

    1. Onur Şeref & J. Paul Brooks & Bernice Huang & Stephen S. Fong, 2017. "Enumeration and Cartesian Product Decomposition of Alternate Optimal Fluxes in Cellular Metabolism," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 197-210, May.
    2. He, Ying & Huang, Rui-Hua, 2008. "Risk attributes theory: Decision making under risk," European Journal of Operational Research, Elsevier, vol. 186(1), pages 243-260, April.

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