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Probability Matching

Published online by Cambridge University Press:  01 January 2025

M. Frank Norman  and
John I. Yellott Jr.
M. Frank Norman
Affiliation:
Institute for Mathematical Studies in the Social Sciences Stanford, California
John I. Yellott Jr.
Affiliation:
Institute for Mathematical Studies in the Social Sciences Stanford, California
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Abstract

The class of symmetric path-independent models with experimenter-controlled events is considered in conjunction with two-choice probability learning experiments. Various refinements of the notion of probability matching are defined, and the incidence of these properties within this class is studied. It is shown that the linear models are the only models of this class that predict a certain phenomenon that we call stationary probability matching. It is also shown that models within this class that possess an additional property called marginal constancy predict approximate probability matching.

Information

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 1 , March 1966 , pp. 43 - 60
Copyright
Copyright © 1966 Psychometric Society

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Footnotes

*

This research grew out of questions posed by William K. Estes. We are also indebted to Professor Estes for his encouragement and assistance at all stages of this research. During the course of this research J. I. Y. received support from the U. S. Public Health Service (N. I. M. H.). M. F. N.'s present address is the University of Pennsylvania. J. I. Y.'s present address is the University of Minnesota.

References

Bush, R. R. and Mosteller, F. Stochastic models for learning, New York: Wiley, 1955.CrossRefGoogle Scholar
Estes, W. K. Probability learning. In Melton, A. W. (Eds.), Categories of human learning. New York: Academic Press, 1964, 89–128.CrossRefGoogle Scholar
Estes, W. K. and Suppes, P. Foundations of linear models. In Bush, R. R. and Estes, W. K. (Eds.), Studies in mathematical learning theory. Stanford: Stanford Univ. Press, 1959, 137–179.Google Scholar
Estes, W. K. and Suppes, P. Foundations of statistical learning theory, II. The stimulus sampling model. Tech. Rept. No. 26, Psychol. Ser., Inst. Math. Studies Soc. Sci., Stanford Univer., 1959.Google Scholar
Feldman, J. and Newell, A. A note on a class of probability matching models. Psychometrika, 1961, 26, 333–337.CrossRefGoogle Scholar
Friedman, M. P., Burke, C. J., Cole, M., Keller, L., Millward, R. B., and Estes, W. K. Two-choice behavior under extended training with shifting probabilities of reinforcement. In Atkinson, R. C. (Eds.), Studies in mathematical psychology. Stanford: Stanford Univ. Press, 1964, 250–316.Google Scholar
Karlin, S. Some random walks arising in learning models. Pacific J. Math., 1953, 3, 725–756.CrossRefGoogle Scholar
Knopp, K. Theory of functions (Part I), New York: Dover, 1945.Google Scholar
Luce, R. D. Individual choice behavior, New York: Wiley, 1959.Google Scholar
Rose, R. M. Models for experiments with two complementary reinforcing events. Unpublished doctoral dissertation, Univ. Pennsylvania, 1964.Google Scholar
Sternberg, S. Stochastic learning theory. In Luce, R. D., Bush, R. R., and Galanter, E. (Eds.), Handbook of mathematical psychology (vol. II). New York: Wiley, 1963, 1–120.Google Scholar