Updating Probability: Tracking Statistics as Criterion

Bas C. Van Fraassen
San Francisco State University
Joseph Y. Halpern
Cornell University
ABSTRACT For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible posteriors. Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. _1_ Introduction _2_ Alternative Updating Policies _3_ Modelling the Situation for Normal Updating _4_ Tracking: A Criterion for Updating Policies _5_ Tracking: Precise Formulation and Relation to Convexity _6_ The Spanning Criterion _7_ Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria _8_ Policies that Violate the Spanning and Tracking Criteria Appendix Appendix
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/bjps/axv027
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 36,649
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

A Problem for Relative Information Minimizers in Probability Kinematics.Bas C. van Fraassen - 1981 - British Journal for the Philosophy of Science 32 (4):375-379.
Entropy and Uncertainty.Teddy Seidenfeld - 1986 - Philosophy of Science 53 (4):467-491.

View all 8 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Regular Updating.Alain Chateauneuf, Thibault Gajdos & Jean-Yves Jaffray - 2011 - Theory and Decision 71 (1):111-128.
A Rule For Updating Ambiguous Beliefs.Cesaltina Pacheco Pires - 2002 - Theory and Decision 53 (2):137-152.
Three Models of Sequential Belief Updating on Uncertain Evidence.James Hawthorne - 2004 - Journal of Philosophical Logic 33 (1):89-123.
A Probability Path.Sidney Resnick - 1998 - Birkhäuser Boston.
Conditional Probability and Dutch Books.Frank Doring - 2000 - Philosophy of Science 67 (3):391 - 409.
The Work of E. T. Jaynes on Probability, Statistics and Statistical Physics.D. A. Lavis & P. J. Milligan - 1985 - British Journal for the Philosophy of Science 36 (2):193-210.
Defeasible Conditionalization.Paul D. Thorn - 2014 - Journal of Philosophical Logic 43 (2-3):283-302.
Quantum Probability and Operational Statistics.Stanley Gudder - 1990 - Foundations of Physics 20 (5):499-527.


Added to PP index

Total downloads
57 ( #116,077 of 2,304,171 )

Recent downloads (6 months)
3 ( #202,140 of 2,304,171 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature