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Multicriteria efficiency with arbitrary finite sets and cyclic preferences

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  • Peter C. Fishburn

Abstract

It is shown that when X is an arbitrary finite subset of an n‐factor product set and preference relations on each factor or criterion are assumed only to be asymmetric, efficient (undominated) points always exist in the set P of probability distributions on X when the preference relations are extended to probability distributions on the factors according to SSB utility theory. Thus, arbitrary finite structures and potentially cyclic preferences do not present a problem for the theory of efficiency under the convexification‐extension procedure.

Suggested Citation

  • Peter C. Fishburn, 1988. "Multicriteria efficiency with arbitrary finite sets and cyclic preferences," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 567-574, December.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:6:p:567-574
    DOI: 10.1002/1520-6750(198812)35:63.0.CO;2-D
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    References listed on IDEAS

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    1. Fishburn, P. C., 1984. "Dominance in SSB utility theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 130-148, October.
    2. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    3. Fishburn, P.C., 1984. "SSB Utility theory: an economic perspective," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 63-94, August.
    4. Loomes, Graham & Sugden, Robert, 1987. "Some implications of a more general form of regret theory," Journal of Economic Theory, Elsevier, vol. 41(2), pages 270-287, April.
    5. Slovic, Paul & Lichtenstein, Sarah, 1983. "Preference Reversals: A Broader Perspective," American Economic Review, American Economic Association, vol. 73(4), pages 596-605, September.
    6. P. C. Fishburn, 1984. "Probabilistic Social Choice Based on Simple Voting Comparisons," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(4), pages 683-692.
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