Journal of Philosophical Logic

, Volume 33, Issue 1, pp 89–123 | Cite as

Three Models of Sequential Belief Updating on Uncertain Evidence

  • James Hawthorne


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.

Bayesian updating Jeffrey conditionalization probability kinematics probabilistic logic uncertain evidence 


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  1. Diaconis, P. and Zabell, S. L., 1982: Updating subjective probability, J. Amer. Statist. Assoc. 77, 822-830.Google Scholar
  2. Doring, F., 1999: Why Bayesian psychology is incomplete, Philos. Sci. 66, S379-S389.Google Scholar
  3. Field, H., 1978: A note on Jeffrey conditionalization, Philos. Sci. 45, 361-367.Google Scholar
  4. Garber, D., 1980: Discussion: Field and Jeffrey conditionalization, Philos. Sci. 47, 142-145.Google Scholar
  5. Good, I. J., 1950: Probability and the Weighing of Evidence, Charles Griffin, London.Google Scholar
  6. Jeffrey, R. C., 1965: The Logic of Decision, McGraw-Hill, New York (2nd edn 1983). University of Chicago Press, Chicago.Google Scholar
  7. 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.Google Scholar
  8. Jeffrey, R. C., 1987: Alias Smith and Jones: The testimony of the senses, Erkenntnis 26, 391-399. Reprinted in (Jeffrey, 1992).Google Scholar
  9. 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).Google Scholar
  10. Jeffrey, R. C., 1992: Probability and the Art of Judgment, Cambridge University Press, Cambridge.Google Scholar
  11. Jeffrey, R. and Hendrickson, M., 1989: Probabilizing pathology, Proc. Aristotelian Soc. 89, 211-225.Google Scholar
  12. Lange, M., 2000: Is Jeffrey conditionalization defective in virtue of being non-commutative? Remarks on the sameness of sensory experience, Synthese 123, 393-403.Google Scholar
  13. Levi, I., 1967: Probability kinematics, British J. Philos. Sci. 18, 197-209.Google Scholar
  14. Wagner, C. G., 2002: Probability kinematics and commutativity, Philos. Sci. 69, 266-278.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • James Hawthorne
    • 1
  1. 1.Department of PhilosophyUniversity of OklahomaNormanU.S.A

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