Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space

A mathematical model is developed in an attempt to relate errors in multiple stimulus-response situations to psychological inter-stimulus and inter response distances. The fundamental assumptions are (a) that the stimulus and response confusions go on independently of each other, (b) that the probability of a stimulus confusion is an exponential decay function of the psychological distance between the stimuli, and (c) that the probability of a response confusion is an exponential decay function of the psychological distance between the responses. The problem of the operational definition of psychological distance is considered in some detail.This paper is based upon the theoretical sections of a Ph.D. dissertation submitted to the Graduate School of Yale University and upon subsequent modification carried out on a National Academy of Sciences-National Research Council Postdoctoral Associateship at the Naval Research Laboratory. The author is particularly indebted to Drs. C. I. Hovland, R. P. Abelson, and B. S. Rosner for their generous advice and support. Helpful criticisms have also been contributed by Drs. G. A. Miller, F. A. Logan, W. D. Garvey, J. G. Holland, and H. Glaser.