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

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  • 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
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    References listed on IDEAS

    as
    1. Khan, M. Ali & Yu, Haomiao & Zhang, Zhixiang, 2024. "On comparisons of information structures with infinite states," Journal of Economic Theory, Elsevier, vol. 218(C).
    2. Bielinska-Kwapisz, Agnieszka, 2003. "Sufficiency in Blackwell's theorem," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 21-25, August.
    3. Cremer, Jacques, 1982. "A simple proof of Blackwell's "comparison of experiments" theorem," Journal of Economic Theory, Elsevier, vol. 27(2), pages 439-443, August.
    4. de Oliveira, Henrique, 2018. "Blackwell's informativeness theorem using diagrams," Games and Economic Behavior, Elsevier, vol. 109(C), pages 126-131.
    Full references (including those not matched with items on IDEAS)

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    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

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