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Equivalences and Continuity in Multivalent Preference Structures

Author

Listed:
  • Peter H. Farquhar

    (University of California, Davis, California)

  • Peter C. Fishburn

    (Bell Telephone Laboratories, Inc., Murray Hill, New Jersey)

Abstract

In assessing multiattribute utility functions, the valence approach partitions the elements of each attribute into equivalence classes. Since attribute interactions are reflected by these equivalence classes, the functional forms of the utility representations are kept simple. This paper establishes equivalence relations for multivalent forms of additive independence, utility independence, and fractional independence, which lead to several new representation theorems. We show also that some simple partitions are not possible multivalent structures when the utility function is continuous. These results should simplify the assessment of utility functions when the attributes are interdependent.

Suggested Citation

  • Peter H. Farquhar & Peter C. Fishburn, 1981. "Equivalences and Continuity in Multivalent Preference Structures," Operations Research, INFORMS, vol. 29(2), pages 282-293, April.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:2:p:282-293
    DOI: 10.1287/opre.29.2.282
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    Cited by:

    1. Peter P. Wakker & Sylvia J. T. Jansen & Anne M. Stiggelbout, 2004. "Anchor Levels as a New Tool for the Theory and Measurement of Multiattribute Utility," Decision Analysis, INFORMS, vol. 1(4), pages 217-234, December.

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