Abstract
This paper essentially makes two remarks that are pertinent to many of the axiomatisations of subjective probability. First, the auxiliary experiment used to quantify qualitative feelings of relative likelihood is essentially distinct from the field of events of actual interest and may be kept so in the axiomatisation. Second, all theories of subjective probability agree that beliefs are conditional on the present state of knowledge and on the present mood and attitude of the individual concerned. As the individual moves through time this conditioning set, his knowledge and psychological state, change. This ever present change has implications for the conditions under which Bayes' Theorem may be invoked to prescribe how the individual should rationally update his beliefs in the light of a particular observation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
De Finetti, B.: 1974, ‘Theory of Probability’, Vol. 1 (John Wiley, New York).
DeGroot, M. H.: 1970, ‘Optimal Statistical Decisions’, (McGraw Hill, New York).
Dempster, A. P.' 1968, ‘A Generalisation of Bayesian Inference’, J. Royal Statistical Society B 30, 205–247.
Fine, T.: 1973, ‘Theories of Probability’, (Academic Press, New York).
French, S.: 1979, ‘Some Comments on Conditional Expected Utility plus Yet Another Axiomatisation of Subjective Expected Utility’, Notes in Decision Theory No. 79, (Department of Decision Theory, University of Manchester).
French, S.: 1980, ‘Updating of Belief in the Light of Someone Else's Opinion’, J. Royal Statistical Society A 143, 43–48.
Hampton, J., Moore, P. G., and Thomas, H.: 1973, ‘Subjective Probability and its Measurement’, J Royal Statistical Society A 136, 21–42.
Herstein, I. N. and Milnor, J.: 1953, ‘An Axiomatic Approach to Measurable Utiluty’, Econometrica 21, 291–297.
Jeffrey, H;: 1961, ‘Theory of Probability’, 3rd edn. (Oxford University Press).
Krantz, D. H., Luce, E. D., Suppes, P., and Tversky, A.: 1971, ‘Foundations of Measurement’, Vol. 1 (Academic Press, New York).
Lindley, D. V., Tversky, A., and Brown, R.: 1979, ‘On the Reconciliation of Probability Assessments’, J. Royal Statistical Society A 142, 146–180.
Luce, R. D. and Krantz, D. H.: 1971, ‘Conditional Expected Utility’, Econometrica 39, 253–271.
Pratt, J. N., Raiffa, H., and Schlaifer, R.: 1964, ‘The Foundations of Decision under Uncertainty: An Elementary Exposition’, J. American Statistical Association 59, 353–375.
Savage, L. J.: 1972, The Foundations of Statistics, 2nd edn. (Dover, New York).
Villigas, C.: 1964, ‘On Qualitative Probability σ-Algebras’, Ann. Mathematical Statistics 35, 1787–1796.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
French, S. On the axiomatisation of subjective probabilities. Theor Decis 14, 19–33 (1982). https://doi.org/10.1007/BF00135142
Issue Date:
DOI: https://doi.org/10.1007/BF00135142