Abstract
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.
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References
Diaconis, P. and Zabell, S. L., 1982: Updating subjective probability, J. Amer. Statist. Assoc. 77, 822-830.
Doring, F., 1999: Why Bayesian psychology is incomplete, Philos. Sci. 66, S379-S389.
Field, H., 1978: A note on Jeffrey conditionalization, Philos. Sci. 45, 361-367.
Garber, D., 1980: Discussion: Field and Jeffrey conditionalization, Philos. Sci. 47, 142-145.
Good, I. J., 1950: Probability and the Weighing of Evidence, Charles Griffin, London.
Jeffrey, R. C., 1965: The Logic of Decision, McGraw-Hill, New York (2nd edn 1983). University of Chicago Press, Chicago.
Jeffrey, R. C., 1975: Carnap's empiricism, in G. Maxwell and R. M. Anderson, Jr. (eds.), Minnesota Studies in Philosophy of Science, Vol. 6, University of Minnesota Press, Minneapolis, pp. 37-49.
Jeffrey, R. C., 1987: Alias Smith and Jones: The testimony of the senses, Erkenntnis 26, 391-399. Reprinted in (Jeffrey, 1992).
Jeffrey, R. C., 1988: Conditioning, kinematics, and exchangeability, in B. Skyrms and W. L. Harper (eds.), Causation, Chance, and Credence, Vol. 1, Kluwer, Dordrecht, pp. 221-255. Reprinted in (Jeffrey, 1992).
Jeffrey, R. C., 1992: Probability and the Art of Judgment, Cambridge University Press, Cambridge.
Jeffrey, R. and Hendrickson, M., 1989: Probabilizing pathology, Proc. Aristotelian Soc. 89, 211-225.
Lange, M., 2000: Is Jeffrey conditionalization defective in virtue of being non-commutative? Remarks on the sameness of sensory experience, Synthese 123, 393-403.
Levi, I., 1967: Probability kinematics, British J. Philos. Sci. 18, 197-209.
Wagner, C. G., 2002: Probability kinematics and commutativity, Philos. Sci. 69, 266-278.
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Hawthorne, J. Three Models of Sequential Belief Updating on Uncertain Evidence. Journal of Philosophical Logic 33, 89–123 (2004). https://doi.org/10.1023/B:LOGI.0000019237.02534.71
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DOI: https://doi.org/10.1023/B:LOGI.0000019237.02534.71