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Decision Analysis Under States-Additive SSB Preferences

Author

Listed:
  • Irving H. Lavalle

    (Tulane University, New Orleans, Louisiana)

  • Peter C. Fishburn

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

Abstract

We survey Fishburn's skew-symmetric bilinear (SSB) theory of risky choice under nonlinear and potentially nontransitive preferences and apply the states-additive special case in the context of decision analysis, showing that tractable characterizations of optimal choices are obtainable via linear programming once the decision has been expressed in normal (i.e., tabular) form. If preferences are transitive, they are also linear and representable by von Neumann-Morgenstern utility, in which case optimal choices may be obtained by the familiar recursion analysis of the extensive (i.e., tree) form.

Suggested Citation

  • Irving H. Lavalle & Peter C. Fishburn, 1987. "Decision Analysis Under States-Additive SSB Preferences," Operations Research, INFORMS, vol. 35(5), pages 722-735, October.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:5:p:722-735
    DOI: 10.1287/opre.35.5.722
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    Cited by:

    1. Matteo Brunelli & Bice Cavallo, 2020. "Incoherence measures and relations between coherence conditions for pairwise comparisons," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 613-635, December.
    2. Denis Bouyssou & Marc Pirlot, 2008. "On some ordinal models for decision making under uncertainty," Annals of Operations Research, Springer, vol. 163(1), pages 19-48, October.
    3. Bouyssou, Denis & Pirlot, Marc, 2004. "A note on Wakker's Cardinal Coordinate Independence," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 11-22, July.

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