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Bayesian updating rules and AGM belief revision

Basu, Pathikrit (2019) Bayesian updating rules and AGM belief revision. Journal of Economic Theory, 179 . pp. 455-475. ISSN 0022-0531. http://resolver.caltech.edu/CaltechAUTHORS:20181126-113807729

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Abstract

We interpret the problem of updating beliefs as a choice problem (selecting a posterior from a set of admissible posteriors) with a reference point (prior). We use AGM belief revision to define the support of admissible posteriors after arrival of information, which applies also to zero probability events. We study two classes of updating rules for probabilities: 1) “lexicographic” updating rules where posteriors are given by a lexicographic probability system 2) “minimum distance” updating rules which select the posterior closest to the prior by some metric. We show that an updating rule is lexicographic if and only if it is Bayesian, AGM-consistent and satisfies a weak form of path independence. While not all lexicographic updating rules have a minimum distance representation, we study a sub-class of lexicographic rules, which we call “support-dependent” rules, which admit a minimum distance representation. Finally, we apply our approach to the problem of updating preferences.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jet.2018.11.005DOIArticle
Additional Information:© 2018 Published by Elsevier Inc. Received 25 February 2018, Revised 19 November 2018, Accepted 22 November 2018, Available online 26 November 2018. I am deeply grateful to Kalyan Chatterjee, Edward Green, Neil Wallace, Stephen Simpson, Giacomo Bonnano, Ariel Rubinstein, Arunava Sen, Vijay Krishna, Debasis Mishra, Federico Echenique, Yuval Salant, Willemien Kets, Ryan Fang and Bruno Salcedo for discussions, comments and suggestions.
Subject Keywords:Bayesian updating; AGM belief revision; Information processing; Lexicographic updating
Classification Code:JEL classification: D01; D80; D81; D83
Record Number:CaltechAUTHORS:20181126-113807729
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181126-113807729
Official Citation:Pathikrit Basu, Bayesian updating rules and AGM belief revision, Journal of Economic Theory, Volume 179, 2019, Pages 455-475, ISSN 0022-0531, https://doi.org/10.1016/j.jet.2018.11.005. (http://www.sciencedirect.com/science/article/pii/S002205311830680X)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91168
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Nov 2018 21:44
Last Modified:03 Dec 2018 23:19

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