Within-subject comparison of real and hypothetical money rewards in delay discounting

A within-subject design, using human participants, compared delay discounting functions for real and hypothetical money rewards. Both real and hypothetical rewards were studied across a range that included $10 to $250. For 5 of the 6 participants, no systematic difference in discount rate was observed in response to real and hypothetical choices, suggesting that hypothetical rewards may often serve as a valid proxy for real rewards in delay discounting research. By measuring discounting at an unprecedented range of real rewards, this study has also systematically replicated the robust finding in human delay discounting research that discount rates decrease with increasing magnitude of reward. A hyperbolic decay model described the data better than an exponential model.     

Physical and cognitive effort discounting of hypothetical monetary rewards

Effort discounting refers to the decrease in the subjective value of a reward as the effort required to obtain the reward increases. The main aims of this study were to ascertain whether the amount of the reward affects the steepness of the effort discounting process for hypothetical monetary rewards, to identify whether this steepness depends on the type of effort that is required, and to determine whether the steepness of different types of effort covary at the individual level. Two types of effort were studied under hypothetical choice situations: physical effort and cognitive effort. Both physical and cognitive effort discounting were well described by the hyperbolic model. Large rewards were discounted less steeply than small rewards for both types of effort. This finding agrees with the results of prior studies which have found that larger rewards have greater motivational power. In addition, the steepness of physical effort discounting was positively correlated with the steepness of cognitive effort discounting, which suggests that the effort discounting process is a trait‐like characteristic within an individual.     

Social discounting and delay discounting

Social discounting was measured as the amount of money a participant was willing to forgo to give a fixed amount (usually $75) to another person. In the first experiment, amount forgone was a hyperbolic function of the social distance between the giver and receiver. In the second experiment, degree of social discounting was an increasing function of reward magnitude whereas degree of delay discounting was a decreasing function of reward magnitude. In the third experiment, the shape of the function relating delayed rewards to equally valued immediate rewards for another person was predicted from individual delay and social discount functions. All in all, the studies show that the social discount function, like delay and probability discount functions, is hyperbolic in form. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay discounting in the pigeon: In search of a magnitude effect

The magnitude effect, where larger outcomes are discounted proportionally less than smaller outcomes, is a well‐established phenomenon in delay discounting by human participants. To this point in the literature magnitude effects have not been reliably evidenced in nonhuman animals. , however, used a concurrent‐chains arrangement with pigeon and found evidence for a magnitude effect. Grace et al. suggested that in many delay discounting experimental arrangements with nonhuman animals (e.g., adjusting amount, adjusting delay) the organism is not given the opportunity to directly compare outcomes of different sizes. They suggest that because of the lack of direct comparison it is difficult for the organism to determine the relative size of each outcome, which in turn mutes the effect of the amount differences between outcomes. As a test of this “comparison hypothesis,” the present experiment was conducted to assess whether the magnitude effect would be evidenced in pigeon when using an adjusting amount procedure where outcomes of different amounts were presented proximally. In the present arrangement, pigeons were presented two choice panels in an operant chamber where each panel was associated with an independent adjusting amount delay discounting task, but with differing outcome amounts (i.e., a 32‐food pellet panel and an 8‐food pellet panel). In this arrangement the choice panels alternated in their availability within a session from trial block to trial block. The present findings indicate no reliable effect of amount, even when the outcomes were proximal and thus readily comparable. This result suggests that the lack of magnitude effect is not driven by the organism's ability to compare the difference in amount between choice alternatives.     

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.     

A second type of magnitude effect: Reinforcer magnitude differentiates delay discounting between substance users and controls

Basic research on delay discounting, examining preference for smaller–sooner or larger–later reinforcers, has demonstrated a variety of findings of considerable generality. One of these, the magnitude effect, is the observation that individuals tend to exhibit greater preference for the immediate with smaller magnitude reinforcers. Delay discounting has also proved to be a useful marker of addiction, as demonstrated by the highly replicated finding of greater discounting rates in substance users compared to controls. However, some research on delay discounting rates in substance users, particularly research examining discounting of small‐magnitude reinforcers, has not found significant differences compared to controls. Here, we hypothesize that the magnitude effect could produce ceiling effects at small magnitudes, thus obscuring differences in delay discounting between groups. We examined differences in discounting between high‐risk substance users and controls over a broad range of magnitudes of monetary amounts ($0.10, $1.00, $10.00, $100.00, and $1000.00) in 116 Amazon Mechanical Turk workers. We found no significant differences in discounting rates between users and controls at the smallest reinforcer magnitudes ($0.10 and $1.00) and further found that differences became more pronounced as magnitudes increased. These results provide an understanding of a second form of the magnitude effect: That is, differences in discounting between populations can become more evident as a function of reinforcer magnitude.     

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.     

Delay or probability discounting in a model of impulsive behavior: effect of alcohol

Little is known about the acute effects of drugs of abuse on impulsivity and self-control. In this study, impulsivity was assessed in humans using a computer task that measured delay and probability discounting. Discounting describes how much the value of a reward (or punisher) is decreased when its occurrence is either delayed or uncertain. Twenty-four healthy adult volunteers ingested a moderate dose of ethanol (0.5 or 0.8 g/kg ethanol: n = 12 at each dose) or placebo before completing the discounting task. In the task the participants were given a series of choices between a small, immediate, certain amount of money and $10 that was either delayed (0, 2, 30, 180, or 365 days) or probabilistic (i.e., certainty of receipt was 1.0, .9, .75, .5, or .25). The point at which each individual was indifferent between the smaller immediate or certain reward and the $10 delayed or probabilistic reward was identified using an adjusting-amount procedure. The results indicated that (a) delay and probability discounting were well described by a hyperbolic function; (b) delay and probability discounting were positively correlated within subjects; (c) delay and probability discounting were moderately correlated with personality measures of impulsivity; and (d) alcohol had no effect on discounting.     

Evaluating the effect of delay spacing on delay discounting: carry‐over effects on steepness and the form of the discounting function

Most delay discounting studies use tasks that arrange delay progressions in which the spacing between consecutive delays becomes progressively larger. To date, little research has examined delay discounting using other progressions. The present study assessed whether the form or steepness of discounting varied across different delay progressions. Human participants completed three discounting tasks with delay progressions that varied in the time between consecutive delays: a standard (increasing duration between delays), linear (equal duration between delays), and an inverse progression (decreasing duration between delays). Steepness of discounting was generally reduced, and remained so, following experience with the inverse progression. Effects of the delay progression on the best fitting equation were order‐dependent. Overall the hyperbola model provided better fits, but the exponential model performed better with data from the inverse progression. Regardless, differences in which model fit best were often small. The finding that the best fitting model was dependent, in some cases, on the delay progression suggests that a single quantitative model of discounting may not be applicable to describe discounting across all procedural contexts. Ultimately, changes in steepness of discounting following experience with the inverse progression appeared similar to anchoring effects, whose mechanism will require further study to delineate.     

Delay discounting by pathological gamblers

Discounting of delayed rewards by pathological gamblers was compared to discounting of delayed rewards by matched control nongambling participants. All participants completed a hypothetical choice task in which they made repeated choices between dollars 1,000 available after a delay and an equal or lesser amount of money available immediately. The delay to the large amount of money was varied from 1 week to 10 years across conditions. Indifference points between immediate money and delayed money were identified at each delay condition by varying the amount of immediate money across choice trials. For the majority of participants, indifference points decreased monotonically across delays. Overall, gamblers discounted the delayed rewards more steeply than did control participants.     

Delay discounting of monetary gains and losses in adolescents with ADHD: Contribution of delay aversion to choice

Adolescents with attention-deficit/hyperactivity disorder (ADHD) are known to have stronger preferences for smaller immediate rewards over larger delayed rewards in delay discounting tasks than their peers, which has been argued to reflect delay aversion. Here, participants performed a delay discounting task with gains and losses. In this latter condition, participants were asked whether they were willing to wait in order to lose less money. Following the core assumption of the delay aversion model that individuals with ADHD have a general aversion to delay, one would predict adolescents with ADHD to avoid waiting in both conditions. Adolescents (12–17 years) with ADHD (n = 29) and controls (n = 28) made choices between smaller immediate and larger delayed gains, and between larger immediate and smaller delayed losses. All delays (5–25 s) and gains/losses (2–10 cents) were experienced. In addition to an area under the curve approach, a mixed-model analysis was conducted to disentangle the contributions of delay duration and immediate gain/delayed loss amount to choice. The ADHD group chose the immediate option more often than controls in the gain condition, but not in the loss condition. The contribution of delay duration to immediate choices was stronger for the ADHD group than the control group in the gain condition only. In addition, the ADHD group scored higher on self-reported delay aversion, and delay aversion was associated with delay sensitivity in the gain condition, but not in the loss condition. In sum, we found no clear evidence for a general aversion to delay in adolescents with ADHD.     

Social discounting of pain

Impatience can be formalized as a delay discount rate, describing how the subjective value of reward decreases as it is delayed. By analogy, selfishness can be formalized as a social discount rate, representing how the subjective value of rewarding another person decreases with increasing social distance. Delay and social discount rates for reward are correlated across individuals. However no previous work has examined whether this relationship also holds for aversive outcomes. Neither has previous work described a functional form for social discounting of pain in humans. This is a pertinent question, since preferences over aversive outcomes formally diverge from those for reward. We addressed this issue in an experiment in which healthy adult participants (N = 67) chose the timing and intensity of hypothetical pain for themselves and others. In keeping with previous studies, participants showed a strong preference for immediate over delayed pain. Participants showed greater concern for pain in close others than for their own pain, though this hyperaltruism was steeply discounted with increasing social distance. Impatience for pain and social discounting of pain were weakly correlated across individuals. Our results extend a link between impatience and selfishness to the aversive domain.     

Delay discounting of different outcomes: Review and theory

Steep delay discounting is characterized by a preference for small immediate outcomes relative to larger delayed outcomes and is predictive of drug abuse, risky sexual behaviors, and other maladaptive behaviors. Nancy M. Petry was a pioneer in delay discounting research who demonstrated that people discount delayed monetary gains less steeply than they discount substances with abuse liability. Subsequent research found steep discounting for not only drugs, but other nonmonetary outcomes such as food, sex, and health. In this systematic review, we evaluate the hypotheses proposed to explain differences in discounting as a function of the type of outcome and explore the trait- and state-like nature of delay discounting. We found overwhelming evidence for the state-like quality of delay discounting: Consistent with Petry and others' work, nonmonetary outcomes are discounted more steeply than monetary outcomes. We propose two hypotheses that together may account for this effect: Decreasing Future Preference and Decreasing Future Worth. We also found clear evidence that delay discounting has trait-like qualities: People who steeply discount monetary outcomes steeply discount nonmonetary outcomes as well. The implication is that changing delay discounting for one outcome could change discounting for other outcomes.     

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.     

A mechanism for reducing delay discounting by altering temporal attention

Rewards that are not immediately available are discounted compared to rewards that are immediately available. The more a person discounts a delayed reward, the more likely that person is to have a range of behavioral problems, including clinical disorders. This latter observation has motivated the search for interventions that reduce discounting. One surprisingly simple method to reduce discounting is an "explicit-zero" reframing that states default or null outcomes. Reframing a classical discounting choice as "something now but nothing later" versus "nothing now but more later" decreases discount rates. However, it is not clear how this "explicit-zero" framing intervention works. The present studies delineate and test two possible mechanisms to explain the phenomenon. One mechanism proposes that the explicit-zero framing creates the impression of an improving sequence, thereby enhancing the present value of the delayed reward. A second possible mechanism posits an increase in attention allocation to temporally distant reward representations. In four experiments, we distinguish between these two hypothesized mechanisms and conclude that the temporal attention hypothesis is superior for explaining our results. We propose a model of temporal attention whereby framing affects intertemporal preferences by modifying present bias.     

Pigeons' discounting of probabilistic and delayed 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.     

Effects of reward magnitude frames on measures of delay discounting in a hypothetical money scenario

The current study analyzed the effects of three frames of reward magnitude—quantity, volume, and duration—on the rate at which college students discounted hypothetical, delayed monetary rewards. Hypothetical scenarios were presented using the fill-in-the-blank discounting questionnaire and participants made choices between immediate and delayed hypothetical monetary rewards. Scenarios framed the monetary choices as (a) quantity of dollar bills, (b) height (inches) of a stack of dollar bills, and (c) duration of time spent in a hypothetical cash machine to collect dollar bills. For each scenario, participants' subjective values were used to calculate the area under the curve (AuC). Framing resulted in a moderate effect size: The duration frame yielded significantly smaller AuC values compared to the quantity and volume frames. Thus, the framing of reward magnitude was a significant variable in controlling discounting rates for hypothetical, delayed monetary rewards. Subsequent investigations should be aware of the independent effects of the reward magnitude frames on delay discounting rates.