Choice, delay, probability, and conditioned reinforcement

The hyperbolic-decay model is a mathematical expression of the relation between delay and reinforcer value. The model has been used to predict choices in discrete-trial experiments on delay-amount tradeoffs, on preference for variable over fixed delays, and on probabilistic reinforcement. Experiments manipulating the presence or absence of conditioned reinforcers on trials that end without primary reinforcement have provided evidence that the hyperbolic-decay model actually predicts the strength of conditioned reinforcers rather than the strength of delayed primary reinforcers. The model states that the strength of a conditioned reinforcer is inversely related to the time spent in its presence before a primary reinforcer is delivered. A possible way to integrate the model with Grace's (1994) contextual-choice model for concurrent-chain schedules is presented. Also discussed are unresolved difficulties in determining exactly when a stimulus will or will not serve as a conditioned reinforcer.