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.     

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.     

Tests of an indifference rule in variable‐delay and double‐reward choice procedures with humans

Four hundred and fifty participants were recruited from Amazon Mechanical Turk across 3 experiments to test the predictions of a hyperbolic discounting equation in accounting for human choices involving variable delays or multiple rewards (Mazur, 1984, 1986). In Experiment 1, participants made hypothetical choices between 2 monetary alternatives, 1 consisting of a fixed delay and another consisting of 2 delays of equal probability (i.e., a variable‐delay procedure). In Experiment 2, participants made hypothetical monetary choices between a single, immediate reward and 2 rewards, 1 immediate and 1 delayed (i.e., a double‐reward procedure). Experiment 3 also used a double‐reward procedure, but with 2 delayed rewards. Participants in all 3 experiments also completed a standard delay‐discounting task. Finally, 3 reward amounts were tested in each type of task ($100, $1000, and $5000). In the double‐reward conditions (Experiments 2 and 3), the results were in good qualitative and quantitative agreement with Mazur's model (1984, 1986). In contrast, when participants made choices involving variable delays (Experiment 1), there was relatively poor qualitative and quantitative agreement with this model. These results, along with our previous findings, suggest the structure of questions in hypothetical tasks with humans can be a strong determinant of the choice pattern.     

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.     

Notes on discounting

In general, if a variable can be expressed as a function of its own maximum value, that function may be called a discount function. Delay discounting and probability discounting are commonly studied in psychology, but memory, matching, and economic utility also may be viewed as discounting processes. When they are so viewed, the discount function obtained is hyperbolic in form. In some cases the effective discounting variable is proportional to the physical variable on which it is based. For example, in delay discounting, the physical variable, delay (D), may enter into the hyperbolic equation as kD. In many cases, however, the discounting data are not well described with a single-parameter discount function. A much better fit is obtained when the effective variable is a power function of the physical variable (kDS in the case of delay discounting). This power-function form fits the data of delay, probability, and memory discounting as well as other two-parameter discount functions and is consistent with both the generalized matching law and maximization of a constant-elasticity-of-substitution utility     

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.     

Temporal discounting predicts student responsiveness to exchange delays in a classroom token system

Typical assessments of temporal discounting involve presenting choices between hypothetical monetary outcomes. Participants choose between smaller immediate rewards and larger delayed rewards to determine how the passage of time affects the subjective value of reinforcement. Few studies, however, have compared such discounting to actual manipulations of reward delay. The present study examined the predictive validity of a temporal discounting procedure developed for use with children. Forty-six sixth-grade students completed a brief discounting assessment and were then exposed to a classwide intervention that involved both immediate and delayed reinforcement in a multiple baseline design across classrooms. The parameters derived from two hyperbolic models of discounting correlated significantly with actual on-task behavior under conditions of immediate and delayed exchange. Implications of temporal discounting assessments for behavioral assessment and treatment are discussed.     

Comparing rapid assessments of delay discounting with real and hypothetical rewards in children

Recent advances in assessment methodology have resulted in a highly efficient procedure for obtaining delay discounting rates for adults: a 5‐trial adjusting delay task (ADT‐5) examining intertemporal choice for hypothetical rewards. The low participant burden of this task makes it potentially useful for children, with whom delay discounting research is relatively limited. However, it is unknown whether results from this task match choice for real rewards. The present study assessed delay discounting for real and hypothetical monetary rewards using a modified ADT‐5 with 9 children admitted to a psychiatric day treatment program. Participants completed up to 3 tasks with each reward type in alternating order. No difference in discounting rate, via log(k), was observed between the first task of each reward type. This finding was replicated across subsequent tasks for the subset of participants (n = 6) who completed all 6 tasks. However, delay discounting of real and hypothetical rewards was not found to be statistically equivalent. These results suggest that a modified ADT‐5 using hypothetical rewards may be a viable option for assessing delay discounting in children with psychiatric diagnoses, but additional research is needed to explicitly examine whether hypothetical and real rewards are discounted equivalently in this population.     

Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts

Hyperbolic and exponential discounting functions were compared as models of subjects′ present valuations of delayed rewards. Previous comparisons have been limited by relying on the assumption that discounting rate is independent of reward size; we avoided this limitation by making all comparisons within reward sizes. In Experiment 1, using real rewards in a simulated auction, and in Experiment 2, using hypothetical rewards, we offered subjects five monetary rewards at six delays each and asked them to indicate the smallest amount that they would accept immediately in exchange for those rewards. Both discounting functions were then fit to the six reported amounts for each reward using nonlinear regressions. In both experiments, although both functions fit the data very well, the hyperbolic function fit better for all of the delayed rewards. Furthermore, the hyperbolic function better described the data for 20 of 21 and 14 of 18 subjects in Experiments 1 and 2, respectively.     

Reformative self‐control and discounting of reward value by delay or effort1

Abstract: The relation between reformative self‐control and discounting of reward value by delay or effort was examined. Thirty‐two Japanese undergraduates were selected based on their scores on a standardized pencil and paper test of self‐control, the Redressive–Reformative Self‐Control Scale ( Sugiwaka, 1995 ). The subjects indicated their preference (i) between a hypothetical 100 000 yen reward available with various delays and a certain reward of variable amount available immediately; or (ii) between a hypothetical 100 000 yen reward available with various efforts and a certain reward of variable amount available without effort. The discounting of delayed reward value was described well by a hyperbolic function proposed by Mazur (1987 ). The slopes of the delayed discounting curves were steeper for subjects who scored low on the Reformative Self‐Control Scale, which is a measure of reformative self‐control and a subscale of the Redressive–Reformative Self‐Control Scale. The discounting by effort was also described well by the hyperbolic function. The slopes of the effortful discounting curves did not correlate to those of the delayed discounting curves. The slopes were not systematically different across the groups of subjects with different scores on the reformative self‐control scale.     

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.     

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.     

Subjective probability and delay.

Human subjects indicated their preference between a hypothetical $1,000 reward available with various probabilities or delays and a certain reward of variable amount available immediately. The function relating the amount of the certain-immediate reward subjectively equivalent to the delayed $1,000 reward had the same general shape (hyperbolic) as the function found by Mazur (1987) to describe pigeons' delay discounting. The function relating the certain-immediate amount of money subjectively equivalent to the probabilistic $1,000 reward was also hyperbolic, provided that the stated probability was transformed to odds against winning. In a second experiment, when human subjects chose between a delayed $1,000 reward and a probabilistic $1,000 reward, delay was proportional to the same odds-against transformation of the probability to which it was subjectively equivalent.     

Age‐related differences in delay discounting: Immediate reward,reward magnitude,and social influence

Delay discounting refers to the tendency of individuals to subjectively devalue rewards that are to be received in the future, with high rates of delay discounting being associated with a variety of maladaptive life outcomes (e.g., unhealthy dietary and exercise behaviors). The current study explored the psychological and social processes involved in adult age‐related differences in delay discounting of monetary rewards. Younger adults exhibited higher levels of delay discounting than older adults. This increased level of patience in older adults was found whether smaller‐sooner rewards were to be received immediately or in the future. However, there was an interaction with reward magnitude, whereby younger adults exhibited higher levels of delay discounting for smaller reward magnitudes but not larger reward magnitudes. Social influence on delay discounting was investigated by having participants complete three phases of the delay‐discounting task: an individual precollaboration phase, a collaboration phase in age‐group‐matched dyads, and an individual postcollaboration phase. A convergence effect was observed in that dyad members' postcollaboration choices were significantly more similar compared to their baseline choices during the precollaboration phase. Moreover, levels of convergence were comparable between younger and older adults, suggesting age invariance in social influence on delay discounting. The current results demonstrate a degree of malleability in delay discounting that extends into older adulthood, making interventions targeting the construct a promising avenue for future research.     

The Effects of Social Status and Culture on Delay Discounting

People generally tend to discount future outcomes in favor of smaller but immediate gains (i.e., delay discounting). This study examines the hypothesis that culture and social status moderate this tendency, as well as the alternative hypothesis that social status and culture influence delay discounting independently of each other. American and Japanese adults were asked to choose receiving hypothetical monetary rewards either immediately or receiving rewards of different amounts with a delay of 1 year. The results replicated previous findings and supported the alternative hypothesis. Delay discounting was lower when subjective socioeconomic status (i.e., an individual’s perception of her or his social rank) was higher. Also, the Japanese were less likely to discount future rewards than the Americans. However, there was no interaction between social status and culture in influencing the rates of delay discounting.     

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.     

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.     

Modeling the effect of reward amount on probability discounting

The present study with college students examined the effect of amount on the discounting of probabilistic monetary rewards. A hyperboloid function accurately described the discounting of hypothetical rewards ranging in amount from $20 to $10,000,000. The degree of discounting increased continuously with amount of probabilistic reward. This effect of amount was not due to changes in the rate parameter of the discounting function, but rather was due to increases in the exponent. These results stand in contrast to those observed with the discounting of delayed monetary rewards, in which the degree of discounting decreases with reward amount due to amount-dependent decreases in the rate parameter. Taken together, this pattern of results suggests that delay and probability discounting reflect different underlying mechanisms. That is, the fact that the exponent in the delay discounting function is independent of amount is consistent with a psychophysical scaling interpretation, whereas the finding that the exponent of the probability-discounting function is amount-dependent is inconsistent with such an interpretation. Instead, the present results are consistent with the idea that the probability-discounting function is itself the product of a value function and a weighting function. This idea was first suggested by Kahneman and Tversky (1979), although their prospect theory does not predict amount effects like those observed. The effect of amount on probability discounting was parsimoniously incorporated into our hyperboloid discounting function by assuming that the exponent was proportional to the amount raised to a power. The amount-dependent exponent of the probability-discounting function may be viewed as reflecting the effect of amount on the weighting of the probability with which the reward will be received.     

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.     

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.