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Decision Making with Belief Functions: Compatibility and Incompatibility with the Sure-Thing Principle

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  • Jaffray, Jean-Yves
  • Wakker, Peter

Abstract

This article studies situations in which information is ambiguous and only part of it can be probably. It is shown that the information can be modeled through belief functions if and only if the nonprobabilizable information is subject to the principle of complete ignorance. Next the representability of decisions by belief functions on outcomes is justified by means of a neutrality axiom. The natural weakening of Savage's sure-thing principle to unambiguous events is examined and its implications for decision making are identified. Copyright 1993 by Kluwer Academic Publishers

Suggested Citation

  • Jaffray, Jean-Yves & Wakker, Peter, 1993. "Decision Making with Belief Functions: Compatibility and Incompatibility with the Sure-Thing Principle," Journal of Risk and Uncertainty, Springer, vol. 7(3), pages 255-271, December.
    • Handle: RePEc:kap:jrisku:v:7:y:1993:i:3:p:255-71
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    Citations

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    Cited by:

    1. Miranda, Pedro & Grabisch, Michel & Gil, Pedro, 2006. "Dominance of capacities by k-additive belief functions," European Journal of Operational Research, Elsevier, vol. 175(2), pages 912-930, December.
    2. Jean-Christophe Vergnaud, 2002. "Information and capacities," Statistical Papers, Springer, vol. 43(1), pages 111-125, January.
    3. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    4. Pivato, Marcus & Vergopoulos, Vassili, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.
    5. Ying He, 2021. "Revisiting Ellsberg’s and Machina’s Paradoxes: A Two-Stage Evaluation Model Under Ambiguity," Management Science, INFORMS, vol. 67(11), pages 6897-6914, November.
    6. Michèle Cohen & Alain Chateauneuf & Eric Danan & Thibault Gajdos & Raphaël Giraud & Meglena Jeleva & Fabrice Philippe & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2011. "Tribute to Jean-Yves Jaffray July 22, 1939 - February 26, 2009," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00664715, HAL.
    7. Michèle Cohen & Alain Chateauneuf & Eric Danan & Thibault Gajdos & Raphaël Giraud & Meglena Jeleva & Fabrice Philippe & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2011. "Tribute to Jean-Yves Jaffray," Theory and Decision, Springer, vol. 71(1), pages 1-10, July.
    8. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
    9. Luca Rigotti & Matthew Ryan & Rhema Vaithianathan, 2011. "Optimism and firm formation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 1-38, January.
    10. Pivato, Marcus & Vergopoulos, Vassili, 2020. "Subjective expected utility with imperfect perception," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 104-122.
    11. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    12. Peter Wakker, 2011. "Jaffray’s ideas on ambiguity," Theory and Decision, Springer, vol. 71(1), pages 11-22, July.
    13. Dominiak, Adam & Eichberger, Jürgen, 2021. "Games in context: Equilibrium under ambiguity for belief functions," Games and Economic Behavior, Elsevier, vol. 128(C), pages 125-159.

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