IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00150064.html
   My bibliography  Save this paper

Information and capacities

Author

Listed:
  • Jean-Christophe Vergnaud

    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Most economists consider that the cases of negative information value that non-Bayesian decision makers seem to exhibit, clearly show that these models are not models representing rational behaviour. We consider this issue for Choquet Expected Utility maximizers in a simple framework, that is the problem of choosing on which event to bet. First, we find a necessary condition to prevent negative information vlaue that we call Separative Monotonicity. This is a weaker condition than Savage Sure thing Principle and it appears that necessity and possibility measures satisfy it and that we cand find conditioning rules such that the information value is always positive. In a second part, we question the way information value is usually measured and suggest that negative information values are merely resulting from an inadequate formula. Yet, we suggest to impose what appears as a weaker requirement, that is, the betting strategy should not be Statistically Dominated. We show for classical updating rules applied to belief functions that this requirement is violated. We consider a class of conditioning rules and exhibit a necessary and sufficient condition in order to satisfy the Statistical Dominance criterion in the case of belief functions.

Suggested Citation

  • Jean-Christophe Vergnaud, 2002. "Information and capacities," Post-Print halshs-00150064, HAL.
    • Handle: RePEc:hal:journl:halshs-00150064
    DOI: 10.1007/s00362-001-0089-0
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pascal Toquebeuf, 2013. "The value of information with neo-additive beliefs," Economics Bulletin, AccessEcon, vol. 33(3), pages 2402-2406.
    2. Jean-Philippe Lefort, 2006. "Comparison of experts in the non-additive case," Post-Print halshs-00130451, HAL.
    3. Jean-Philippe Lefort, 2006. "Comparison of experts in the non-additive case," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00130451, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    3. 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.
    4. 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.
    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. Pivato, Marcus & Vergopoulos, Vassili, 2020. "Subjective expected utility with imperfect perception," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 104-122.
    7. Pivato, Marcus & Vergopoulos, Vassili, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.
    8. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    9. Peter Wakker, 2011. "Jaffray’s ideas on ambiguity," Theory and Decision, Springer, vol. 71(1), pages 11-22, July.
    10. 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.
    11. 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.
    12. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:halshs-00150064. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.