This is an ACT-R model that models two experiments. One is the experiment performed by Friedman, Burke, Cole, Keller, Millward, and Estes (1964). In the experiment subjects were to choose one of two buttons, on each of several trials. The probability of a button being reinforced was varied from .1 to .9. The responses were recoreded as a function of the probability of that button being reinforced. The data modeled is from the last half of 48 trial blocks where probabilities of choice have appeared to have stabilized. The data shows that subjects do not exactly probability match in this experiment. The best fitting linear equation to their data to predict probability of choice as a function of experimental probability (P) is
Choice probability = .124 + .722P
The fact that this equation is not a simple identity (i.e., Choice Probability = P) points to the fact that subjects were not probability matching. In this experiment they were undermatching (i.e., not responding as extremely as the experienced probabilities). This undermatching is reflected in the slope .722 which is less than 1.
One thing that should influence the response probability is the value of G. If a constant noise is added to PG-C, the larger the value of G the greater the effect of P. Thus, more extreme response probabilities probabilities should occur when G is increased. Myers, Fort, Katz, and Suydam (1963) performed an experiment in which subjects either were not paid or were given 10 cents for each correct response. Presumably this should influence probability of choice, and in the experiment the subjects choose the more probable alternative considerably more frequently when there is a payoff for doing so.
ACT-R Model of general experiment
ACT-R Model of Friedman et al Experiment
ACT-R Model of Myers et al Experiment