Ultimate choice between two attractive goals: Predictions from a model

A mathematical model for two-choice behavior in situations where both choices are desirable is discussed. According to the model, one or the other choice is ultimately preferred, and a functional equation is given for the fraction of the population ultimately preferring a given choice. The solution depends upon the learning rates and upon the initial probabilities of the choices. Several techniques for approximating the solution of this functional equation are described. One of these leads to an explicit formula that gives good accuracy. This solution can be generalized to the two-armed bandit problem with partial reinforcement in each arm, or the equivalent T-maze problem. Another suggests good ways to program the calculations for a high-speed computer.Support for this research has been received from the National Science Foundation (Grant NSF-G2258), the National Institute of Mental Health (Grant M-2293), and the Laboratory of Social Relations, Harvard University.We wish to acknowledge and express our appreciation for the cooperation and assistance given by Phillip J. Rulon, Albert Beaton, Wai-Ching Ho, and Donald Spearritt, who set up, programmed, and executed numerous calculations connected with the linear equations method of solution, and by Cleo Youtz for extensive calculations at every stage of the work. We also wish to thank Ray Twery and Robert R. Bush for permission to use in Table 3 some of the unpublished results of their calculations. Those calculations were made on the Illiac through the cooperation of the Digital Computer Laboratory of the University of Illinois, Dr. John P. Nash, Director.