Ultimate Choice between two Attractive Goals: Predictions from a Model

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Abstract
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.

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