IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v85y2018i1d10.1007_s11238-017-9639-3.html
   My bibliography  Save this article

Weighted averaging, Jeffrey conditioning and invariance

Author

Listed:
  • Denis Bonnay

    (Université Paris-Ouest Nanterre and IHPST)

  • Mikaël Cozic

    (Université Paris-Est Créteil (EA LIS), IUF and IHPST)

Abstract

Jeffrey conditioning tells an agent how to update her priors so as to grant a given probability to a particular event. Weighted averaging tells an agent how to update her priors on the basis of testimonial evidence, by changing to a weighted arithmetic mean of her priors and another agent’s priors. We show that, in their respective settings, these two seemingly so different updating rules are axiomatized by essentially the same invariance condition. As a by-product, this sheds new light on the question how weighted averaging should be extended to deal with cases when the other agent reveals only parts of her probability distribution. The combination of weighted averaging (for the events whose probability the other agent reveals) and Jeffrey conditioning (for the events whose probability the other agent does not reveal) is a comprehensive updating rule to deal with such cases, which is again axiomatized by invariance under embedding. We conclude that, even though one may dislike Jeffrey conditioning or weighted averaging, the two make a natural pair when a policy for partial testimonial evidence is needed.

Suggested Citation

  • Denis Bonnay & Mikaël Cozic, 2018. "Weighted averaging, Jeffrey conditioning and invariance," Theory and Decision, Springer, vol. 85(1), pages 21-39, July.
    • Handle: RePEc:kap:theord:v:85:y:2018:i:1:d:10.1007_s11238-017-9639-3
    DOI: 10.1007/s11238-017-9639-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-017-9639-3
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-017-9639-3?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Dietrich, Franz & List, Christian & Bradley, Richard, 2016. "Belief revision generalized: A joint characterization of Bayes' and Jeffrey's rules," Journal of Economic Theory, Elsevier, vol. 162(C), pages 352-371.
    2. repec:hal:pseose:halshs-01249635 is not listed on IDEAS
    3. Dietrich, Franz & List, Christian & Bradley, Richard, 2016. "Belief revision generalized: A joint characterization of Bayes' and Jeffrey's rules," Journal of Economic Theory, Elsevier, vol. 162(C), pages 352-371.
    Full references (including those not matched with items on IDEAS)

    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. Franz Dietrich & Wlodek Rabinowicz, 2018. "Introduction to the special issue “Beliefs in Groups” of Theory and Decision," Theory and Decision, Springer, vol. 85(1), pages 1-4, July.
    2. Hill, Brian, 2022. "Updating confidence in beliefs," Journal of Economic Theory, Elsevier, vol. 199(C).

    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:kap:theord:v:85:y:2018:i:1:d:10.1007_s11238-017-9639-3. 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.