The matching law and amount-dependent exponential discounting as accounts of self-control choice

Studies with humans have found evidence for amount-dependent temporal discounting, that is, that the sensitivity of choice to reinforcer delay varies inversely with reinforcer magnitude. To test whether similar results could be obtained with nonhumans, pigeons were trained on a two-component concurrent-chains procedure in which the durations of food reinforcement in the terminal links were equal within components but unequal between components. Terminal-link schedules were varied over four conditions to allow separate estimates of sensitivity to delay to be obtained for the large and small reinforcer-magnitude components. Although sensitivity to delay was greater in the small-magnitude component for all subjects, the effect was quite small. The difference in sensitivity was generally less than one standard error, and t tests on parameter differences failed to reach significance. Several models for temporal discounting, including an amount-dependent exponential function, were fitted to the data from the first four conditions. The resulting parameter estimates were used to make predictions for a self-control condition in which one terminal link arranged a smaller less delayed reinforcer and the other arranged a larger, more delayed reinforcer. For all models, predictions were considerably more accurate when sensitivity to delay was the same regardless of reinforcer magnitude. The results support the independence of delay and magnitude as required by a version of the matching law, and provide strong evidence against amount-dependent exponential discounting as an account of self-control choice. A new two-parameter discounting function, consistent with the matching law, is proposed that has wide empirical generality for both human and nonhuman data.