Abstract
This paper states the problem of imprecision in the assessment of personal probabilities of those uncertain events that are here called ‘non-stochastic’, since each event is not now reasonably considered to be a possible outcome of a well-defined stochastic process. It analyzes critically six previous attempts to solve the problem. Then it presents and defends a new solution based upon the standard concepts of personalistic Bayesian decision theory- The solution requires the decision maker to construct his Bayesian metamodel of his uncertain future assessments of the parameters (probabilities, and also utilities) in his decision model. He does this by assessing now his marginal personal probability distribution of each uncertain future assessment in a precise, coherent, and honest manner. It is proved that the expectation of each random variable is the precise, coherent, and honest assessment of the corresponding parameter. Analysis shows that this solution does not use second-order probability to represent imprecision in assessment.
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Bibliography
Berstein, R. J., John Dewey, Washington Square Press, Inc., New York, 1966.
Burros, R. H., ‘Axiomatic Analysis of Non-Transitivity of Preference and of In-difference’, Theory and Decision, to be published.
Dewey, J., Reconstruction in Philosophy, The New American Library of World Literature, Inc., New York, 1950.
Finetti, B. de, ‘Foresight: Its Logical Laws, Its Subjective Sources’ in Kyburg and Smokier (1964), 93 - 158.
Finetti, B. de, Probability, Induction and Statistics, John Wiley and Sons, London, 1972.
Fishburn, P. C., Decision and Value Theory, John Wiley and Sons, Inc., New York, 1964.
Fishburn, P. C., Utility Theory for Decision Making, John Wiley and Sons, Inc., New York, 1970.
Good, I. J., ‘Rational Decisions’, Journal of the Royal Statistical Society, Ser. B, 14 (1952) 107 - 114.
Good, I. J., ‘Kinds of Probability’, Science 129 (1959) 443–447.
Good, I. J., ‘Subjective Probability as the Measure of a Non-Measurable Set’, in Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress (cd. by E. Nagel, P. Suppes, and A. Tarski), Stanford University Press, Stanford, Calif., 1962, pp. 319–329.
Good, I. J., ‘How Rational Should a Manager Be?’ Management Science 8 (1962) 38S–393.
Good, I. J„ ‘Twenty-Seven Principles of Rationality’, unpublished appendix, 1970.
Kyburg, H. E. and Smokier, H. E. (eds.), Studies in Subjective Probability, John Wiley and Sons, Inc., New York, 1964.
Lindley, D. V., Making Decisions, John Wiley and Sons, Ltd., London, 1971.
Pratt, J. W., Raiffa, H.. and Schlaifer, R., Introduction to Statistical Decision Theory, McGraw-Hill Book Co., New York, 1965.
Raifla, H., Decision Analysis, Addison-Wesley, Publishing Co., Inc., Reading, Mass., 1968.
Ramsey, F. P., The Foundations of Mathematics, Littlefield, Adams, and Co., Paterson, N.J., 1960.
Savage, L. J., ’Elicitation of Personal Probabilities and Expectations’, Journal of the American Statistical Association 66 (1971) 783–801.
Savage, L. J., The Foundations of Statistics (Revised Edition), Dover Publications, Inc., New York, 1972.
Schlaifcr, R., Probability and Statistics for Business Decisions, McGraw-Hill Book Co., New York, 1959.
Schlaifcr, R., Analysis of Decisions under Uncertainty, McGraw-Hill Book Co., New York, 1969.
White, M. (ed.), The Age of Analysis, The New American Library of World Literature, Inc., New York, 1955.
Winkler, R. L., ‘Probabilistic Prediction: Some Experimental Results’, Journal of the American Statistical Association 66 (1971) 675 685.
Winkler, R. L. and Murphy, A. H., ‘“Good” Probability Assessors’, Journal of Applied heterology 7 (1968) 751–758.
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© 1974 D. Reidel Publishing Company, Dordrecht-Holland
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Burros, R.H. (1974). Methodological Analysis of Imprecision in the Assessment of Personal Probabilities. In: Leinfellner, W., Köhler, E. (eds) Developments in the Methodology of Social Science. Theory and Decision Library, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2259-0_11
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DOI: https://doi.org/10.1007/978-94-010-2259-0_11
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