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From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again

Mu, Xiaosheng and Pomatto, Luciano and Strack, Philipp and Tamuz, Omer (2021) From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again. Econometrica, 89 (1). pp. 475-506. ISSN 1468-0262. https://resolver.caltech.edu/CaltechAUTHORS:20200124-080643011

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Abstract

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Rényi divergences.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.3982/ECTA17548DOIArticle
http://arxiv.org/abs/1906.02838arXivDiscussion Paper
ORCID:
AuthorORCID
Mu, Xiaosheng0000-0002-2868-5182
Pomatto, Luciano0000-0002-4331-8436
Tamuz, Omer0000-0002-0111-0418
Alternate Title:Laws of large numbers for stochastic orders, Blackwell dominance in large samples
Additional Information:© 2021 The Econometric Society. Manuscript received 5 August, 2019; final version accepted 4 September, 2020; available online 11 September, 2020. We are grateful to the coeditor and three referees for their comments and suggestions. In addition, we would like to thank Kim Border, Laura Doval, Federico Echenique, Tobias Fritz, Drew Fudenberg, George Mailath, Massimo Marinacci, Margaret Meyer, Marco Ottaviani, and Peter Norman Sørensen for helpful discussions. Xiaosheng Mu acknowledges the hospitality of Columbia University and the Cowles Foundation at Yale University, which hosted him during parts of this research. Philipp Strack was supported by a Sloan research fellowship. Omer Tamuz was supported by a grant from the Simons Foundation (#419427), a Sloan research fellowship, and a BSF award (#2018397).
Funders:
Funding AgencyGrant Number
Cowles Foundation for Research in EconomicsUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Simons Foundation419427
Binational Science Foundation (USA-Israel)2018397
Subject Keywords:Comparison of experiments, stochastic dominance, divergences
Issue or Number:1
Record Number:CaltechAUTHORS:20200124-080643011
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200124-080643011
Official Citation:Mu, X., Pomatto, L., Strack, P. and Tamuz, O. (2021), From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again. Econometrica, 89: 475-506. https://doi.org/10.3982/ECTA17548
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100882
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Jan 2020 20:14
Last Modified:12 Feb 2021 23:32

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