Discounting of outcomes in which immediate gains are followed by delayed losses.

Previous discounting research has focused on relatively simple situations (e.g., choosing between immediate and delayed gains, or between immediate and delayed losses) and the relations among amount, delay, and subjective value in such situations are now well established. Many everyday choice situations, however, are more complex, involving alternatives that combine gains and losses. In two experiments, participants discounted a monetary outcome that combined an immediate gain with a delayed loss. Consistent with the discounting framework, the value of the combination was approximately equal to the difference between the (undiscounted) value of the immediate gain and the (discounted) value of the delayed loss. More precise predictions of the relative subjective value of the delayed loss component of a combination were given by the same hyperboloid function that describes discounting in simple choice situations where outcomes only involve gains or losses, not both. As in previous studies, when the outcome was a simple one consisting of only a delayed loss, discounting was not affected by the amount of that loss. Surprisingly, however, when the loss was preceded by a gain, the degree to which the combination was discounted was affected by the amount of the loss. Notably, discounting of the delayed loss component of the combination decreased with the amount of the loss in a fashion similar to that observed with simple delayed gains, where smaller amounts are discounted more steeply than larger amounts. Choice situations involving immediate gains followed by delayed losses pose iconic self-control problems, and the present findings support the application of the discounting framework to these important everyday problems.

When immediate losses are followed by delayed gains: Additive hyperboloid discounting models.

Discounting research has tended to focus on one simple situation, choice between an immediate, smaller gain and a larger, delayed gain, that is assumed by many to capture the essence of self-control. In everyday life, however, most choice situations are more complex, often involving combinations of gains and losses. We examined discounting in situations involving an immediate loss followed by a delayed gain that resulted in either a net gain (Experiment 1) or a net loss (Experiment 2) and compared it with discounting when there was only a delayed gain and no immediate loss. Larger delayed gains were discounted less steeply than smaller regardless of whether or not they were preceded by an immediate loss. Discounting functions of the same general hyperboloid form that describe the discounting of delayed gains in simple choice situations accurately described the discounting of combinations of gains and losses, although results differed depending on whether the combination would result in a net gain or a net loss. Participants consistently discounted loss-gain combinations less steeply than gains not preceded by an immediate loss when the combination represented a net loss (Experiment 2), but not when the combination represented a net gain (Experiment 1), a result analogous to the sign effect in simple choice situations (i.e., delayed gains are discounted more steeply than delayed losses). Taken together, these findings support the view that complicated choices like those common in everyday life can be understood within the discounting framework.

Preference reversals with losses.

People who prefer larger, later gains over smaller, sooner gains when considering outcomes far in the future often reverse their preference as the alternatives become closer in time. This finding, which is contrary to a normative economic account of intertemporal choice, has been interpreted as support for hyperboloid discounting, but the results can also be explained by steeper discounting of smaller amounts. The present study is the first to demonstrate that analogous preference reversals occur with losses: People who preferred a smaller, sooner loss over a larger, later loss when the outcomes were far in the future reversed their preference when these alternatives were closer in time. Because there was no magnitude effect (i.e., smaller losses were not discounted more steeply than larger losses), the present findings strongly support the proposition that reversals in preference between delayed outcomes occur because of the hyperboloid shape of the discounting function.

Do adjusting-amount and adjusting-delay procedures produce equivalent estimates of subjective value in pigeons?

The current experiment examined whether adjusting-amount and adjusting-delay procedures provide equivalent measures of discounting. Pigeons' discounting on the two procedures was compared using a within-subject yoking technique in which the indifference point (number of pellets or time until reinforcement) obtained with one procedure determined the value of the corresponding variable in the yoked condition with the other procedure. Behavior on each procedure was well described by a hyperbolic discounting function. Results revealed no systematic differences in the degree of discounting as measured by the discounting rate parameter of the hyperbola in Experiment 1, which used 20-mg pellets. These results were replicated in Experiment 2 using smaller, 14-mg pellets, which potentially yield more precise measurement of indifference points on the adjusting-amount procedure. The finding that estimates of the k parameter in the hyperbolic discounting function obtained with one procedure did not differ systematically from estimates obtained from the same subjects with the other procedure represents strong support for the hypothesis that the same process underlies the discounting of delayed rewards on both adjusting-amount and adjusting-delay procedures.

Discounting of monetary and directly consumable rewards.

We compared temporal and probability discounting of a nonconsumable reward (money) and three directly consumable rewards (candy, soda, and beer). When rewards were delayed, monetary rewards were discounted less steeply than directly consumable rewards, all three of which were discounted at equivalent rates. When rewards were probabilistic, however, there was no difference between the discounting of monetary and directly consumable rewards. It has been reported that substance abusers discount delayed drug rewards more steeply than delayed money, but this difference may reflect special characteristics of drugs or drug abusers, or it may reflect a general property of consumable rewards. The present findings suggest that abused substances (like beer) share the properties of other directly consumable rewards, whereas delayed monetary rewards are special because they are fungible, generalized (conditioned) reinforcers.

Differential effects of amount on temporal and probability discounting of gains and losses.

In four experiments, we compared the effects of delay, probability, and monetary amount on the subjective value of gains and losses. For delayed gains, smaller amounts were discounted more steeply than larger amounts, whereas the opposite pattern was observed with probabilistic gains. For both delayed and probabilistic losses, however, amount had much smaller and less reliable effects on discounting. Taken together, the pattern of differential magnitude effects leads to delayed gains' being discounted significantly more steeply than delayed losses, but only at smaller amounts, whereas probabilistic gains are discounted significantly more steeply than probabilistic losses, but only at larger amounts. Even though the same hyperbola-like function described both individual and group discounting of delayed and probabilistic gains and losses, the present findings suggest that different processes are involved in discounting positive and negative outcomes. Raw data may be downloaded from www.psychonomic.org/archive.

Discounting of delayed food rewards in pigeons and rats: is there a magnitude effect?

Temporal discounting refers to the decrease in the present, subjective value of a reward as the time to its receipt increases. Results from humans have shown that a hyperbola-like function describes the form of the discounting function when choices involve hypothetical monetary rewards. In addition, magnitude effects have been reported in which smaller reward amounts are discounted more steeply than larger amounts. The present research examines the cross-species generality of these findings using real rewards, namely food pellets, with both pigeons and rats. As with humans, an adjusting amount procedure was used to estimate the amount of immediate reward judged equal in value to a delayed reward. Different amounts of delayed food rewards (ranging from 5 to 32 pellets in pigeons and from 5 to 20 pellets in rats) were studied at delays varying from 1 s to 32 s. A simple hyperbola, similar to the hyperbola-like mathematical function that describes the discounting of hypothetical monetary rewards in humans, described the discounting of food rewards in both pigeons and rats. These results extend the generality of the mathematical model of discounting. Rates of discounting delayed food rewards were higher for pigeons than for rats. Unlike humans, however, neither pigeons nor rats showed a reliable magnitude effect: Rate of discounting did not vary systematically as a function of the amount of the delayed reward.

Preference reversals with food and water reinforcers in rats.

Rats were given a choice between a smaller, immediately available reward and a larger reward available after a delay. In one phase, the reward was food and in another phase, the reward was water. Constant delays were added between the choice presentation and the delivery of the reward alternatives. As the time between choice and reward delivery increased from 0 to 25 s, all rats (except one in the water phase) reversed their preference from the smaller, sooner alternative to the larger, later alternative. These findings extend the generality of the preference-reversal animal model to qualitatively different reinforcers. Furthermore, the presence of both impulsive and self-control choices within the same animal is consistent with the view that self-control may be understood as choice behavior, and that species differences in self-control may be differences in degree, not kind.