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

M. Ali Khan, Haomiao Yu and Zhixiang Zhang

Economics Letters, 2025, vol. 247, issue C

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.

Keywords: Experiment; Information structure; Sufficiency; More-informativeness; Infinite state space (search for similar items in EconPapers)
JEL-codes: C6 D5 D8 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016517652400630X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:247:y:2025:i:c:s016517652400630x

DOI: 10.1016/j.econlet.2024.112146

Access Statistics for this article

Economics Letters is currently edited by Economics Letters Editorial Office

More articles in Economics Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().