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

Author

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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. repec:hal:journl:halshs-00625706 is not listed on IDEAS
    3. Jean-Christophe Vergnaud, 2002. "Information and capacities," Statistical Papers, Springer, vol. 43(1), pages 111-125, January.
    4. repec:hal:journl:halshs-00186905 is not listed on IDEAS
    5. 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.
    6. repec:hal:journl:halshs-00664715 is not listed on IDEAS
    7. 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.
    8. 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.
    9. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    10. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    11. Peter Wakker, 2011. "Jaffray’s ideas on ambiguity," Theory and Decision, Springer, vol. 71(1), pages 11-22, July.
    12. 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.

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