Conditioning, Kinematics, and Exchangeability

  • Richard Jeffrey
Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS, volume 41)


The change (“conditioning”) from prior P to posterior Q = P( |E) is appropriate only if it changes no probabilities conditionally on E. Under similar conditions a generalization of conditioning (“probability kinematics”) is appropriate when Q(E) < 1. That generalization is pretty nearly equivalent to ordinary conditioning on the extraordinary proposition that Q(E) has a certain value. Whether or not generalized conditioning is sensitive to the order in which successive changes are made depends on how the changes are set, e.g., by probabilities, or by ratios of probabilities. In a finitistic framework simple and generalized (“partial”) exchangeability are characterized and related to probability kinematics.


Sample Space Reflection Principle Sufficiency Condition Kinematical Formula Dutch Book Argument 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Achinstein, Peter and Owen Hannaway (eds.) (1985) Observation, Experiment, and Hypothesis in Modern Physical Science (Cambridge, Mass.: Bradford-MIT Press).Google Scholar
  2. Bernardo, J. M., M. H. DeGroot, D. V. Lindley, and A. F. M. Smith (eds.) (1985) Bayesian Statistics 2 (Amsterdam: Elsevier, North-Holland).Google Scholar
  3. Blackwell, David and M. A. Girshick (1954) Theory of Games and Statistical Decisions (New York: Wiley).Google Scholar
  4. Carnap, Rudolf (1950) Logical Foundations of Probabdity (University of Chicago Press; 2nd ed., 1962).Google Scholar
  5. de Finetti, Bruno (1937) ‘La prévision: ses lois logiques, ses sources subjectives’, Annales de l’Institut Henri Poincaré 7, 1–38. Translated in Kyburg and Smokier (1964, 1980).Google Scholar
  6. de Finetti, Bruno (1972) Probability, Induction and Statistics (New York: Wiley).Google Scholar
  7. de Finetti, Bruno (1938) ‘Sur la condition d’équivalence partielle’, Actualités Scientifiques et Industrielles, No. 739 (Paris: Hermann & Cie.) Translated in Jeffrey (1980).Google Scholar
  8. Diaconis, Persi (1977) ‘Finite forms of de Finetti’s theorem on exchangeability’, Synthese 36, 271–281.CrossRefGoogle Scholar
  9. Diaconis, Persi and David Freedman (1980a) ‘De Finetti’s generalizations of exchangeability’, Jeffrey (1980), 233–249.Google Scholar
  10. Diaconis, Persi and David Freedman (1980b) ‘Finite exchangeable sequences’, Annals of Prob. 8, 745–764.CrossRefGoogle Scholar
  11. Diaconis, Persi and David Freedman (1982) ‘Partial exchangeability and sufficiency’, Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions, Calcutta, 16–19 December, 1981, pp. 205–236 (Calcutta: Indian Statistical Institute).Google Scholar
  12. Diaconis, Persi and Sandy Zabell (1982) ‘Updating subjective probability’, J. Am. Stat. Assn. 77, 822–830.CrossRefGoogle Scholar
  13. Diaconis, Persi and Sandy Zabell (1986) ‘Some alternatives to Bayes’s rule’, in Grofman and Owen, pp. 25–38.Google Scholar
  14. Field, Hartry (1978) ‘A note on Jeffrey conditionalization’, Philosophy of Science 45, 361–367.CrossRefGoogle Scholar
  15. Freedman, David (1977) ‘A remark on the difference between sampling with the without replacement’, J. Am. Stat. Assn. 72, 681.CrossRefGoogle Scholar
  16. Freedman, David and Roger A. Purves (1969) ‘Bayes’ method for bookies’, Annals of Math. Stat. 40, 1177–1186.CrossRefGoogle Scholar
  17. Garber, Daniel (1980) ‘Field and Jeffrey conditionalization’, Philosophy of Science 47, 142–145.CrossRefGoogle Scholar
  18. Goldstein, Michael (1983) ‘The prevision of a prevision’, J. Am. Stat. Assn. 78, 817–819.CrossRefGoogle Scholar
  19. Goldstein, Michael (1985) ‘Temporal coherence’, in Bernardo et al., 231–248.Google Scholar
  20. Good, I. J. (1981) ‘The weight of evidence provided by uncertain testimony or from an uncertain event’, Journal of Statistical Computation and Simulation 13, 56–60.CrossRefGoogle Scholar
  21. Grofman, Bernard and Guillermo Owen (eds.) (1986) Information Processing and Group Decision Making (Greenwich, Conn.: JAI Press).Google Scholar
  22. Harper, William and C. A. Hooker (eds.) (1976) Foundations of Probabdity Theory, Statistical Inference, and Statistical Theories of Science (Dordrecht: D. Reidel Pub. Co.).Google Scholar
  23. Jaynes, E. T. (1959) Probability Theory in Science and Engineering (mimeographed) (Dallas: Field Research Laboratory, Socony Mobil Oil Co.).Google Scholar
  24. Jeffrey, Richard (1957) Contributions to the Theory of Inductive Probability (Ph. D. Dissertation, Princeton University).Google Scholar
  25. Jeffrey, Richard (1965) The Logic of Decision (New York: McGraw-Hill Pub. Co.: 2nd edition, University of Chicago Press, 1983).Google Scholar
  26. Jeffrey, Richard (1975) ‘Carnap’s empiricism’, in Maxwell and Anderson (1975).Google Scholar
  27. Jeffrey, Richard (ed.) (1980) Studies in inductive Logic and Probability, vol 2 (Berkeley and Los Angeles: University of California Press).Google Scholar
  28. Jeffrey, Richard (1985) ‘Probability and the Art of Judgment’, in Achinstein and Hannaway (1985), 95–126.Google Scholar
  29. Kyburg, Henry E., Jr. and Howard E. Smokier (eds.) (1964) Studies in Subjective Probability (New York: Wiley. 2nd ed., Robert E. Krieger: Huntington, New York, 1980).Google Scholar
  30. Lewis, C. I. (1946) An Analysis of Knowledge and Valuation (La Salle, Ill.: Open Court).Google Scholar
  31. Maxwell, Grover and Robert M. Anderson (eds.) (1975) Induction, Probability, and Confirmation (Minneapolis: University of Minnesota Press).Google Scholar
  32. Mellor, D. H. (ed.) (1980) Prospects for Pragmatism (Cambridge: The University Press).Google Scholar
  33. Skyrms, Brian (1980a) Causal Necessity (New Haven: Yale University Press).Google Scholar
  34. Skyrms, Brian (1980b) ‘Higher-order degrees of belief’, in Mellor (1980), 107–137.Google Scholar
  35. Skyrms, Brian (1984) Pragmatics and Empiricism (New Haven: Yale University Press).Google Scholar
  36. Skyrms, Brian (1987) ‘The value of knowledge’, in Justification, Discovery and the Evolution of Scientific Theories, C. Wade Savage (ed.), (Minneopolis: University of Minnesota Press).Google Scholar
  37. Suppes, Patrick (ed.) (1980) Studies in the Foundations of Quantum Mechanics (East Lansing, Michigan: Philosophy of Science Association).Google Scholar
  38. Suppes, Patrick and Mario Zanotti (1980) ‘A new proof of the impossibility of hidden variables using the principles of exchangeability and identity of conditional distributions’, in Suppes (ed.), 173–191.Google Scholar
  39. Teller, Paul (1976) ‘Conditionalization, observation, and change of preference’, in Harper and Hooker (1976), pp. 205–259.Google Scholar
  40. van Fraassen, Bas (1980) ‘Rational belief and probability kinematics’, Philosophy of Science 47, 165–187.CrossRefGoogle Scholar
  41. van Fraassen, Bas (1984) ‘Belief and the will’, J. Phil. 81, 235–256.CrossRefGoogle Scholar
  42. von Mises, Richard (1919) ‘Grundlagen der Wahrscheinlichkeitsrechnung’, Mathematische Zeitschrift 5, 52–99.CrossRefGoogle Scholar
  43. von Mises (1957) Probability, Statistics, and Truth, 2nd rev. ed. (London: George Allen and Unwin. Dover reprint, 1981).Google Scholar
  44. Zaman, Arif (1984) ‘Urn models for Markov exchangeability’, Annals of Probability 11, 223–229.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Richard Jeffrey
    • 1
  1. 1.Department of PhilosophyPrinceton UniversityUSA

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