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Measurability Is Not About Information

Dubra, Juan and Echenique, Federico (2001) Measurability Is Not About Information. Cowles Foundation Discussion Paper, 1296. Yale University , New Haven, CT. https://resolver.caltech.edu/CaltechAUTHORS:20160321-140546406

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Abstract

We comment on the relation between models of information based on signals/partitions, and those based on σ-algebras. We show that more informative signals need not generate finer σ-algebras, hence that Blackwell's theorem fails if information is modeled as σ-algebras. The reason is that the σ-algebra generated by a partition does not contain all the events that can be known from the information provided by the signal. We also show that there is a non-conventional σ-algebra that can be associated to a signal which does preserve its information content. Further, expectations and conditional expectations may depend on the choice of σ-algebra that is associated to a signal. We provide a simple characterization of when the model is robust to changes in the σ-algebras.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://cowles.yale.edu/sites/default/files/files/pub/d12/d1296.pdfPublisherCowles Foundation discussion paper
http://resolver.caltech.edu/CaltechAUTHORS:20101004-103515138Related ItemJournal article
ORCID:
AuthorORCID
Echenique, Federico0000-0002-1567-6770
Alternate Title:Information is not about measurability
Additional Information:March 19, 2001. We are grateful to David Blackwell, Don Brown, David Levine, Jim Pitman, Maxwell Stinchcombe, Tarun Sabarwal, Bill Sudderth, Sergio Turner, Bill Zame, and seminar participants at UCLA and Yale for comments. We thank Catherine Huafei Yan, Ernesto Mordecki, Malempati Rao, and Srinivasa Varadhan for their kind attention to our questions.
Subject Keywords:Blackwell's Theorem, measurability, models of information, partitions, information preserving σ-algebras.
Series Name:Cowles Foundation Discussion Paper
Issue or Number:1296
Classification Code:JEL C60, C70, G12
Record Number:CaltechAUTHORS:20160321-140546406
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160321-140546406
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65551
Collection:CaltechAUTHORS
Deposited By: Susan Vite
Deposited On:23 Mar 2016 22:55
Last Modified:26 Nov 2019 11:15

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