IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v43y2002i1p111-125.html
   My bibliography  Save this article

Information and capacities

Author

Listed:
  • Jean-Christophe Vergnaud

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Jean-Christophe Vergnaud, 2002. "Information and capacities," Statistical Papers, Springer, vol. 43(1), pages 111-125, January.
    • Handle: RePEc:spr:stpapr:v:43:y:2002:i:1:p:111-125
    DOI: 10.1007/s00362-001-0089-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-001-0089-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-001-0089-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

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

    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. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    2. 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.
    3. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    4. Peter Wakker, 2011. "Jaffray’s ideas on ambiguity," Theory and Decision, Springer, vol. 71(1), pages 11-22, July.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.
    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:spr:stpapr:v:43:y:2002:i:1:p:111-125. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.