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.     

Are people really more patient than other animals? Evidence from human discounting of real liquid rewards

In previous studies, researchers have found that humans discount delayed rewards orders of magnitude less steeply than do other animals. Humans also discount smaller delayed reward amounts more steeply than larger amounts, whereas animals apparently do not. These differences between humans and animals might reflect differences in the types of rewards studied and/or the fact that animals actually had to wait for their rewards. In the present article, we report the results of three experiments in which people made choices involving liquid rewards delivered and consumed after actual delays, thereby bridging the gap between animal and human studies. Under these circumstances, humans, like animals, discounted the value of rewards delayed by seconds; however, unlike animals, they still showed an effect of reward amount. Human discounting was well described by the same hyperboloid function that has previously been shown to describe animal discounting of delayed food and water rewards, as well as human discounting of real and hypothetical monetary rewards.     

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.     

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.     

Effects of inflation on the subjective value of delayed and probabilistic rewards

In the years prior to 1994, there were very high rates of inflation in Poland, and the zloty depreciated relative to the U.S. dollar. However, the new zloty, introduced in 1995, was associated with greatly decreased rates of inflation and provided a more stable currency. We report a series of three experiments that take advantage of these changes to examine the effects of inflation on the subjective value of delayed and probabilistic rewards. Subjects were Polish citizens familiar with both zlotys and dollars. The first two experiments, conducted in 1994, used dollars and old zlotys, and the third experiment, conducted in 1996, used dollars and new zlotys. In all three experiments, the dollar and zloty rewards were of equivalent worth, according to the then current exchange rates. In Experiment 1, subjects chose between immediate and delayed rewards and, in Experiment 2, chose between certain and probabilistic rewards. The subjective value of a delayed reward was greater when its amount was specified in dollars than when it was specified in old zlotys. In contrast, the currency in which a reward was specified had no effect on the subjective value of probabilistic rewards. The results of these two experiments suggest a selective effect of inflation on decisions involving delayed rewards. This was verified in the third experiment, in which, using new zlotys, no differences in discounting were observed between the two currencies with either probabilistic or delayed rewards. Importantly, in all three experiments, the discounting of both delayed and probabilistic rewards was well described by the same simple mathematical model, suggesting that similar decision-making processes underlie both phenomena. However, the present results argue against a single-process theory in which the discounting of probabilistic rewards is derived from the discounting of delayed rewards.     

Temporal discounting of monetary rewards in children and adolescents with ADHD and autism spectrum disorders

It has been difficult to differentiate attention‐deficit/hyperactivity disorder (ADHD) and autism spectrum disorder (ASD) in terms of some aspects of their cognitive profile. While both show deficits in executive functions, it has been suggested that they may differ in their response to monetary reward. For instance, children with ADHD prefer small immediate over large delayed rewards more than typically developing controls. One explanation for this is that they discount the value of rewards to a higher degree as they are moved into the future. The current study investigated whether children with ADHD can be differentiated from those with ASD in terms of reward discounting. Thirty‐nine children (8–16 y) with ADHD, 34 children with ASD and 46 typically developing controls performed a hypothetical monetary temporal discounting task. Participants were instructed to make repeated choices between small variable rewards (0, 5, 10, 20, 30€) delivered immediately and large rewards delivered after a variable delay. Children with ADHD but not ASD discounted future rewards at a higher rate than typically developing controls. These data confirm steeper discounting of future rewards in ADHD and add to a small but growing literature showing that the psychological profile of ADHD can be distinguished from that of ASD in terms of disrupted motivational processes.     

Good or Bad,We Want it Now: Fixed‐cost Present Bias for Gains and Losses Explains Magnitude Asymmetries in Intertemporal Choice

Intertemporal tradeoffs are ubiquitous in decision making, yet preferences for current versus future losses are rarely explored in empirical research. Whereas rational‐economic theory posits that neither outcome sign (gains vs. losses) nor outcome magnitude (small vs. large) should affect delay discount rates, both do, and moreover, they interact: in three studies, we show that whereas large gains are discounted less than small gains, large losses are discounted more than small losses. This interaction can be understood through a reconceptualization of fixed‐cost present bias, which has traditionally described a psychological preference for immediate rewards. First, our results establish present bias for losses—a psychological preference to have losses over with now. Present bias thus predicts increased discounting of future gains but decreased (or even negative) discounting of future losses. Second, because present bias preferences do not scale with the magnitude of possible gains or losses, they play a larger role, relative to other motivations for discounting, for small magnitude intertemporal decisions than for large magnitude intertemporal decisions. Present bias thus predicts less discounting of large gains than small gains but more discounting of large losses than small losses. The present research is the first to demonstrate that the effect of outcome magnitude on discount rates may be opposite for gains and losses and also the first to offer a theory (an extension of present bias) and process data to explain this interaction. The results suggest that policy efforts to encourage future‐oriented choices should frame outcomes as large gains or small losses. Copyright © 2012 John Wiley & Sons, Ltd.     

The absence of numbers to express the amount may affect delay discounting with humans

Human delay discounting is usually studied with experimental protocols that use symbols to express delay and amount. In order to further understand discounting, we evaluated whether the absence of numbers to represent reward amounts affects discount rate in general, and whether the magnitude effect is generalized to nonsymbolic situations in particular. In Experiment 1, human participants were exposed to a delay‐discounting task in which rewards were presented using dots to represent monetary rewards (nonsymbolic); under this condition the magnitude effect did not occur. Nevertheless, the magnitude effect was observed when equivalent reward amounts were presented using numbers (symbolic). Moreover, in estimation tasks, magnitude increments produced underestimation of large amounts. In Experiment 2, participants were exposed only to the nonsymbolic discounting task and were required to estimate reward amounts in each trial. Consistent with Experiment 1, the absence of numbers representing reward amounts produced similar discount rates of small and large rewards. These results suggest that value of nonsymbolic rewards is a nonlinear function of amount and that value attribution depends on perceived difference between the immediate and the delayed nonsymbolic rewards.     

Discounting by Probabilistic Waiting

In everyday life, many probabilistic situations may be characterized as probabilistic waiting. A gambler, for example, bets repeatedly at the racetrack, the casino, or the card table. The gambler may not win on the first try, but if a gamble is repeated enough times, a win is almost certain to occur eventually. If repeated gambles are structured as strings of losses ending in a win (probabilistic waiting) and the amount won is discounted by the delay caused by the series of losses, then strings with many losses will be discounted more than those with fewer losses, thereby causing subjective value of the series of gambles as a whole to increase. The current study used the opposite effect that amount has on the degree of delay and probability discounting as a marker to determine whether people evaluate situations involving probabilistic waiting as they evaluate situations involving delayed outcomes or as situations involving probabilistic outcomes. We find that the more likely a probabilistic waiting situation is to end in reward (e.g., a gamble is repeated indefinitely until reward is obtained), the more that situation conforms to delay discounting; the less likely a probabilistic waiting situation is to end in reward (e.g., a fixed, small number of gambles), the more that situation conforms to probability discounting. We argue that the former situation is applicable to pathological gambling, and that people with steep delay discount functions would therefore be more likely to have gambling problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Now for Me,Later for Us? Effects of Group Context on Temporal Discounting

Delayed rewards are less valuable than immediate rewards. This well‐established finding has focused almost entirely on individual outcomes. However, are delayed rewards similarly discounted if they are shared by a group? The current article reports on three experiments exploring the effect of group context on delay discounting. Results indicate that discount rates of individual and group rewards were highly correlated, but that respondents were more willing to wait (decreased discounting) for shared outcomes than for individual outcomes. An explanatory model is proposed suggesting that decreased discount rates in group contexts may be due to the way the effects of both delay and social discounting are combined. That is, in a group context, a person values both a future reward (discounted by delay) and a present reward to another person (discounted by the social distance between them). The results are explained by a combined discount function containing a delay factor and a factor representing the social distance between the decision maker and group members. Practical implications of the fact that shared consequences can increase individual self‐control are also discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Evidence for a magnitude effect in temporal discounting with pigeons

A magnitude effect in human intertemporal choice is well established-larger rewards or outcomes are discounted over time at a lower rate than are smaller rewards. However, many recent studies have failed to find a corresponding effect in nonhuman animals. Here we report a magnitude effect in temporal discounting for pigeons' choices involving a tradeoff between reward delay and amount. Pigeons chose between a small reward (1-s access to food) after a 2-s delay, and a large reward (4.5-s access to food) after a 28-s delay. Across conditions, the delays to the small and large rewards were increased or decreased, respectively. Temporal discounting functions obtained through a value-estimation procedure showed clear evidence of a magnitude effect: The value of the large reward decreased more slowly with increasing delay than the value of the small reward. We linked this result to a nonlinear relationship between choice and the delays associated with the small and large rewards. The nonlinearity was contrary to the generalized matching law but was predicted by the contextual choice model. Our results confirm the existence of a magnitude effect in nonhuman temporal discounting, showing that this adaptation is not unique to humans.     

Pathological gamblers, with and without substance use disorders, discount delayed rewards at high rates

Pathological gambling is classified as a disorder of impulse control, yet little research has evaluated behavioral indices of impulsivity in gamblers. The rates at which rewards delayed in time are subjectively devalued may be a behavioral marker of impulsivity. This study evaluated delay discounting in 60 pathological gamblers and 26 control participants. Gamblers were divided into those with (n = 21) and without (n = 39) substance use disorders. A hypothetical $1,000 reward was delayed at intervals ranging from 6 hr to 25 years, and immediate rewards varied from $1 to $999. Pathological gamblers discounted delayed rewards at higher rates than control participants, and gamblers with substance use disorders discounted delayed rewards at higher rates than non-substance-abusing gamblers. These data provide further evidence that rapid discounting of delayed rewards may be a feature central to impulse control and addictive disorders, including pathological gambling.     

The rich get richer: Students’ discounting of hypothetical delayed rewards and real effortful extra credit

The present research compared choices among students with higher or lower grades for rewards that were devalued by imposing a delay to their receipt (Study 1) or by requiring more work for a larger reward (Study 2). In Study 1, students chose between hypothetical and noncontingent smaller immediate or larger delayed monetary rewards. In Study 2, students chose from among different amounts of real, response-contingent academic rewards (extra credit) that required different amounts of work. The results of both studies were similar: The highest scoring students discounted the value of the delayed money less than did their lower scoring counterparts, and the highest scoring students also chose to do and actually did more extra-credit work than lower scoring students did. Differences in the discounting of devalued rewards might represent a fundamental difference between the highest and lower scoring students.     

Delay discounting of qualitatively different reinforcers in rats

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.     

Discounting of probabilistic rewards is associated with gambling abstinence in treatment-seeking pathological gamblers

Individuals with addictive disorders, including substance abusers and pathological gamblers, discount or devalue rewards delayed in time more than controls. Theoretically, preference for probabilistic rewards is directly related to gambling, but limited empirical research has examined probabilistic discounting in individuals with pathological gambling. This study evaluated probability and delay discounting in treatment-seeking pathological gamblers and their association with gambling treatment outcomes during and after treatment. At time of treatment entry, 226 pathological gamblers completed probability and delay discounting tasks. They were then randomized to one of three treatment conditions, and gambling behavior was measured throughout treatment and at a 1-year follow-up assessment. After controlling for possibly confounding variables and treatment condition, more shallow probability discounting was associated with greater reductions in amounts wagered during treatment and likelihood of gambling abstinence at the end of treatment and throughout the follow-up period. No associations were noted between delay discounting and gambling treatment outcomes. These data suggest that probability discounting may be an important construct in understanding pathological gambling and its treatment.     

A Measure of Delay Discounting Within the Academic Domain

It is important to better understand the decision‐making processes involved in student procrastination, in order to develop interventions that reduce this common problem. Students may procrastinate because studying produces delayed reinforcers; however, no task measuring delay discounting of academic outcomes currently exists. In Experiment 1, we developed and piloted a measure of academic discounting modeled on titrating‐amount tasks successfully used in the discounting literature. Participants made hypothetical choices between working for money (the smaller, sooner reinforcer) and working on an assignment that was due at various times (the larger, later reinforcer). Participants showed systematic decreases in the subjective value of the assignment as a function of delay, and the hyperbolic and hyperboloid models described the shape of this decrease in value well. In general, larger delayed rewards are discounted less steeply than smaller delayed rewards (the magnitude effect). In Experiment 2, we observed the magnitude effect in academic discounting: Participants discounted a “not important” assignment more steeply than an “important” assignment. In the hyperboloid model, this change was captured by an increase in the s parameter. Results provide support for the validity of the academic discounting task. Copyright © 2018 John Wiley & Sons, Ltd.     

Do Measures of Executive Functioning and Manipulation of Ego Depletion Predict How University Students Discount Probabilistic Gains and Losses?

Discounting occurs when the subjective value of an outcome is altered because the outcome is delayed or uncertain. Previous research has suggested that how individuals discount delayed gains is related to executive functioning. The present study attempted to extend this relationship to discounting of probabilistic gains and losses, and to examine whether diminishing cognitive resources would impact how participants discounted monetary outcomes. In Experiment 1, university students completed an executive function measure and then a probability-discounting task that involved the hypothetical sum of either $1,000 or $100,000 framed as either a gain or a loss. The executive function of organization was a significant predictor of how participants discounted all four outcomes while motivational drive predicted discounting of losses, but not gains. In Experiment 2, participants completed the same measures with the addition of an ego-depletion task to deplete cognitive resources before making discounting decisions. The executive function of motivational drive and empathy were significant predictors of how participants discounted both loss outcomes. The results suggest that discounting of monetary outcomes is related to the executive function of organization for gains and motivational drive, and empathy for losses. They also support the notion that the discounting of gains may be a distinct process from the discounting of losses.     

Smokers discount their drug of abuse in the same way as other consumable rewards

Recent research shows that drug abusers discount delayed monetary rewards more than nonabusers do, and they discount delayed substances of abuse (e.g., drugs) more than delayed money. Furthermore, non-drug-abusers discount food and substances of abuse (e.g., alcohol), more than money. Here, we compare the delay and probability discounting of money with that of a directly consumable reward (chocolate) and with that of a substance of abuse (cigarettes), in a drug-using population (smokers). In line with previous research, we found in two experiments that delay discounting differentiated between smokers and nonsmokers, and between money and a nonabused directly consumable reward (chocolate). In addition, our results show that there appears to be no difference in the extent to which smokers discount their abused substance compared to another directly consumable reward. These findings support the contention that drugs and food are part of the same category of primary reinforcers, whereas money is discounted differently, as a conditioned reinforcer.