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MERGING OF OPINIONS AND PROBABILITY KINEMATICS

Published online by Cambridge University Press:  17 November 2015

SIMON M. HUTTEGGER
SIMON M. HUTTEGGER*
Affiliation:
Department of Logic and Philosophy of Science, University of California at Irvine
*
*DEPARTMENT OF LOGIC AND PHILOSOPHY OF SCIENCE UNIVERSITY OF CALIFORNIA, IRVINE SOCIAL SCIENCE PLAZA A IRVINE, CA-92697, USA E-mail: shuttegg@uci.edu
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Abstract

We explore the question of whether sustained rational disagreement is possible from a broadly Bayesian perspective. The setting is one where agents update on the same information, with special consideration being given to the case of uncertain information. The classical merging of opinions theorem of Blackwell and Dubins shows when updated beliefs come and stay closer for Bayesian conditioning. We extend this result to a type of Jeffrey conditioning where agents update on evidence that is uncertain but solid (hard Jeffrey shifts). However, merging of beliefs does not generally hold for Jeffrey conditioning on evidence that is fluid (soft Jeffrey shifts, Field shifts). Several theorems on the asymptotic behavior of subjective probabilities are proven. Taken together they show that while a consensus nearly always emerges in important special cases, sustained rational disagreement can be expected in many other situations.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 4 , December 2015 , pp. 611 - 648
Copyright
Copyright © Association for Symbolic Logic 2015 

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