Three models of sequential belief updating on uncertain evidence

Journal of Philosophical Logic 33 (1):89-123 (2004)
James Hawthorne
University of Oklahoma
Jeffrey updating is a natural extension of Bayesian updating to cases where the evidence is uncertain. But, the resulting degrees of belief appear to be sensitive to the order in which the uncertain evidence is acquired, a rather un-Bayesian looking effect. This order dependence results from the way in which basic Jeffrey updating is usually extended to sequences of updates. The usual extension seems very natural, but there are other plausible ways to extend Bayesian updating that maintain order-independence. I will explore three models of sequential updating, the usual extension and two alternatives. I will show that the alternative updating schemes derive from extensions of the usual rigidity requirement, which is at the heart of Jeffrey updating. Finally, I will establish necessary and sufficient conditions for order-independent updating, and show that extended rigidity is closely related to these conditions
Keywords Bayesian updating  Jeffrey conditionalization  probability kinematics  probabilistic logic  uncertain evidence
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DOI 10.1023/B:LOGI.0000019237.02534.71
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References found in this work BETA

The Logic of Decision.Richard Jeffrey - 1965 - University of Chicago Press.
Probability and the Art of Judgment.Richard Jeffrey - 1992 - Cambridge University Press.
Probability Kinematics and Commutativity.Carl G. Wagner - 2002 - Philosophy of Science 69 (2):266-278.
A Note on Jeffrey Conditionalization.Hartry Field - 1978 - Philosophy of Science 45 (3):361-367.

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