IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v247y2025ics016517652400630x.html
   My bibliography  Save this article

A simple proof of Blackwell’s theorem on the comparison of experiments for a general state space

Author

Listed:
  • Khan, M. Ali
  • Yu, Haomiao
  • Zhang, Zhixiang

Abstract

This paper offers, for a general state space, a simple proof of the equivalence between Blackwell sufficiency and the Bohnenblust–Shapley–Sherman criterion of more-informativeness. The proof relies on nothing more than the finite intersection property of compact sets. While several proofs exist for finite state spaces, infinite spaces, as necessitated in applications with continuous distributions, is explored by Boll (1955), Amershi (1988) (but for a finite-dimensional action set), and reviewed in LeCam’s foundational rubric for the subject. We offer two examples to show the fragility of Boll’s definition of the second criterion, and the necessity of his assumption of absolute continuity.

Suggested Citation

  • Khan, M. Ali & Yu, Haomiao & Zhang, Zhixiang, 2025. "A simple proof of Blackwell’s theorem on the comparison of experiments for a general state space," Economics Letters, Elsevier, vol. 247(C).
    • Handle: RePEc:eee:ecolet:v:247:y:2025:i:c:s016517652400630x
    DOI: 10.1016/j.econlet.2024.112146
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016517652400630X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2024.112146?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.

    More about this item

    Keywords

    Experiment; Information structure; Sufficiency; More-informativeness; Infinite state space;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    Statistics

    Access and download statistics

    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:eee:ecolet:v:247:y:2025:i:c:s016517652400630x. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.