Humans discount larger delayed rewards less steeply than smaller rewards, whereas no such magnitude effect has been observed in rats (and pigeons). It remains possible that rats' discounting is sensitive to differences in the quality of the delayed reinforcer even though it is not sensitive to amount. To evaluate this possibility, Experiment 1 examined discounting of qualitatively different food reinforcers: highly preferred versus nonpreferred food pellets. Similarly, Experiment 2 examined discounting of highly preferred versus nonpreferred liquid reinforcers. In both experiments, an adjusting-amount procedure was used to determine the amount of immediate reinforcer that was judged to be of equal subjective value to the delayed reinforcer. The amount and quality of the delayed reinforcer were varied across conditions. Discounting was well described by a hyperbolic function, but no systematic effects of the quantity or the quality of the delayed reinforcer were observed.

Two experiments tested the effects of food deprivation on discounting in pigeons. An adjusting-amount procedure was used to estimate the subjective value of food at delays ranging from 1 to 24 s. Experiment 1 compared pigeons’ discounting of delayed food reinforcers at 75-80% and 90-95% of free-feeding weight. Experiment 2 compared discounting under 1-hr and 23-hr food deprivation. In both experiments at both deprivation levels, discounting was well described by the hyperboloid discounting function. No systematic effect of level of deprivation on degree of discounting was observed in either experiment. This finding is consistent with the view that pigeons’ choices are controlled by the relative, rather than the absolute, value of reinforcers.

Pigeons' discounting of probabilistic and delayed food reinforcers was studied using adjusting-amount procedures. In the probability discounting conditions, pigeons chose between an adjusting number of food pellets contingent on a single key peck and a larger, fixed number of pellets contingent on completion of a variable-ratio schedule. In the delay discounting conditions, pigeons chose between an adjusting number of pellets delivered immediately and a larger, fixed number of pellets delivered after a delay. Probability discounting (i.e., subjective value as a function of the odds against reinforcement) was as well described by a hyperboloid function as delay discounting was (i.e., subjective value as a function of the time until reinforcement). As in humans, the exponents of the hyperboloid function when it was fitted to the probability discounting data were lower than the exponents of the hyperboloid function when it was fitted to the delay discounting data. The subjective values of probabilistic reinforcers were strongly correlated with predictions based on simply substituting the average delay to their receipt in each probabilistic reinforcement condition into the hyperboloid discounting function. However, the subjective values were systematically underestimated using this approach. Using the discounting function proposed by Mazur (1989), which takes into account the variability in the delay to the probabilistic reinforcers, the accuracy with which their subjective values could be predicted was increased. Taken together, the present findings are consistent with Rachlin's (Rachlin, 1990; Rachlin, Logue, Gibbon, & Frankel, 1986) hypothesis that choice involving repeated gambles may be interpreted in terms of the delays to the probabilistic reinforcers.

Studies of delay discounting typically have involved choices between smaller, immediate outcomes and larger, delayed outcomes. In a study of delay discounting in humans, Green et al. (2005) added a period of time prior to both outcomes, creating a delay common to both. They found that the subjective value of the more delayed reward was well described by a hyperboloid discounting function and that the degree to which that outcome was discounted decreased as the common delay increased. In two experiments, we examined the effect of adding a common delay on the discounting of food rewards in pigeons. In Experiment 1, an adjusting-amount procedure was used to establish discounting functions when the common delay was 0, 3, 5, and 10 s, and different stimuli signaled time to the smaller, sooner and larger, later rewards. In contrast to humans, the pigeons showed increases in the degree of discounting when a common delay was added. In Experiment 2, the delay common to both rewards and the delay unique to the larger, later reward were each specifically signaled. With this procedure, the degree of discounting decreased as the common delay increased, a result consistent with that obtained with humans (Green et al., 2005). These findings reveal fundamental similarities between pigeons’ and humans’ choice behavior, and provide strong interspecies support for the hypothesis that choice between delayed outcomes is based on comparison of their hyperbolically discounted present subjective values.

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