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.     

Temporal discounting when the choice is between two delayed rewards

The present experiments extend the temporal discounting paradigm from choice between an immediate and a delayed reward to choice between 2 delayed rewards: a smaller amount of money available sooner and a larger amount available later. Across different amounts and delays, the data were consistently well described by a hyperbola-like discounting function, and the degree of discounting decreased systematically as the delay to the sooner reward increased. Three theoretical models (the elimination-by-aspects, present-value comparison, and common-aspect attenuation hypotheses) were evaluated. The best account of the data was provided by the common-aspect attenuation hypothesis, according to which the common aspect of the choice alternatives (i.e., the time until the sooner reward is available) receives less weight in the decision-making process.     

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 DUE TO MYOPIC DISCOUNTING OF DELAYED REWARD

Abstract— A basic stationarity axiom of economic theory assumes stable preference between two deferred goods separated by a fixed time. To test this assumption, we offered subjects choices between delayed rewards, while manipulating the delays to those rewards. Preferences typically reversed with changes in delay, as predicted by hyperbolic discounting models of impulsiveness. Of 36 subjects, 34 reversed preference from a larger, later reward to a smaller, earlier reward as the delays to both rewards decreased. We conclude that the stationarity axiom is not appropriate in models of human choice.     

Heaven can wait. How religion modulates temporal discounting

Evidence suggests that religious systems have specific effects on attentional and action control processes. The present study investigated whether religions also modulate choices that involve higher-order knowledge and the delay of gratification in particular. We tested Dutch Calvinists, Italian Catholics, and Atheists from both countries/cultures using an intertemporal choice task where participants could choose between a small immediate and a larger delayed monetary reward. Based on the Calvinist theory of predestination and the Catholic concept of a cycle of sin–confession–expiation, we predicted a reduced delay tolerance, i.e., higher discount rate, for Italian Catholics than for Dutch Calvinists, and intermediate rates for the two atheist groups. Analyses of discount rates support our hypotheses. We also found a magnitude effect on temporal discounting and faster responses for large than for small rewards across religions and countries/cultures. We conclude that temporal discounting is specifically modulated by religious upbringing rather than by generic cultural differences.     

DISCOUNTING OF DELAYED REWARDS:

Abstract— In this study, children, young adults, and older adults chose between immediate and delayed hypothetical monetary rewards The amount of the delayed reward was held constant while its delay was varied All three age groups showed delay discounting, that is, the amount of an immediate reward judged to be of equal value to the delayed reward decreased as a function of delay The rate of discounting was highest for children and lowest for older adults, predicting a life-span developmental trend toward increased selfcontrol Discounting of delayed rewards by all three age groups was well described by a single function with agesensitive parameters (all R²s>94) Thus, even though there are quantitative age differences in delay discounting, the existence of an age-invanant form of discount function suggests that the process of choosing between rewards of different amounts and delays is qualitatively similar across the life span     

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.     

Choice between rewards differing in amount and delay: Toward a choice model of self control

A concurrent-chain procedure was used to study pigeons' choices between rewards differing in both amount and delay. The shorter delay terminated with a 2-second access to grain whereas the longer delay terminated with a 6-second access to grain. The ratio of the delays was constant within a given condition while their absolute values were varied. Over conditions, ratios of 6:1, 3:1, and 3:2 were studied. As the absolute values of the delays to reinforcement increased, preference for the longer-delayed but larger reward decreased under both the 6:1 and 3:1 ratios, but increased under the 3:2 ratio. These results are inconsistent with choice models predicting no change in preference when the ratios of delays and amounts are held constant. In addition, the change in preference under the 3:1 ratio is inconsistent with a simple multiplicative interaction of the trade off between reinforcer amount and delay, and suggests that delay is a more potent determinant of choice than is amount. These results have implications for models that view choice between small immediate rewards and large but delayed rewards as underlying the behavior commonly called self control.     

时间贴现的分段性

以延迟和相对延迟时间贴现的实验范式, 用选择法、匹配法确定价值主观相等点, 探讨时间贴现的分段性。三个实验和一个问卷调查发现, 时间贴现具有分段性。被试的时间贴现有三次显著变化, 表现为三个时段时间贴现心理状态的不同: 从现在到未来2周内规避损失、偏好风险、愿意短期等待, 从未来2周起直到未来10年采取非补偿性策略、需求与风险并重、愿意长期等待, 和从未来10年起直到未来50年规避风险、聊胜于无、不愿意等待。     

The Matching Law And Amount-dependent Exponential Discounting As Accounts Of Self-control Choice

Studies with humans have found evidence for amount-dependent temporal discounting, that is, that the sensitivity of choice to reinforcer delay varies inversely with reinforcer magnitude. To test whether similar results could be obtained with nonhumans, pigeons were trained on a two-component concurrent-chains procedure in which the durations of food reinforcement in the terminal links were equal within components but unequal between components. Terminal-link schedules were varied over four conditions to allow separate estimates of sensitivity to delay to be obtained for the large and small reinforcer-magnitude components. Although sensitivity to delay was greater in the small-magnitude component for all subjects, the effect was quite small. The difference in sensitivity was generally less than one standard error, and t tests on parameter differences failed to reach significance. Several models for temporal discounting, including an amount-dependent exponential function, were fitted to the data from the first four conditions. The resulting parameter estimates were used to make predictions for a self-control condition in which one terminal link arranged a smaller, less delayed reinforcer and the other arranged a larger, more delayed reinforcer. For all models, predictions were considerably more accurate when sensitivity to delay was the same regardless of reinforcer magnitude. The results support the independence of delay and magnitude as required by a version of the matching law, and provide strong evidence against amount-dependent exponential discounting as an account of self-control choice. A new two-parameter discounting function, consistent with the matching law, is proposed that has wide empirical generality for both human and nonhuman data.     

Introduction to the special issue on comparative cognition

Prior research has shown that nonhumans show an extreme preference for variable‐ over fixed‐delays to reinforcement. This well‐established preference for variability occurs because a reinforcer's strength or “value” decreases according to a curvilinear function as its delay increases. The purpose of the present experiments was to investigate whether this preference for variability occurs with human participants making hypothetical choices. In three experiments, participants recruited from Amazon Mechanical Turk made choices between variable and fixed monetary rewards. In a variable‐delay procedure, participants repeatedly chose between a reward delivered either immediately or after a delay (with equal probability) and a reward after a fixed delay (Experiments 1 and 2). In a double‐reward procedure, participants made choices between an alternative consisting of two rewards, one delivered immediately and one after a delay, and a second alternative consisting of a single reward delivered after a delay (Experiments 1 and 3). Finally, all participants completed a standard delay‐discounting task. Although we observed both curvilinear discounting and magnitude effects in the standard discounting task, we found no consistent evidence of a preference for variability—as predicted by two prominent models of curvilinear discounting (i.e., a simple hyperbola and a hyperboloid)—in our variable‐delay and double‐reward procedures. This failure to observe a preference for variability may be attributed to the hypothetical, rule‐governed nature of choices in the present study. In such contexts, participants may adopt relatively simple strategies for making more complex choices.     

Contributions of the nucleus accumbens and its subregions to different aspects of risk-based decision making

The nucleus accumbens (NAc) has been implicated in mediating different forms of decision making in humans and animals. In the present study, we observed that inactivation of the rat NAc, via infusion of GABA agonists, reduced preference for a large/risky option and increased response latencies on a probabilistic discounting task. Discrete inactivations of the NAc shell and core revealed further differences between these regions in mediating choice and response latencies, respectively. The effect on choice was attributable to reduced win–stay performance (i.e., choosing risky after a being rewarded for a risky choice on a preceding trial). Moreover, NAc inactivation altered choice only when the large/risky option had greater long-term value, in terms of the amount of food that could be obtained over multiple trials relative to the small/certain option. Inactivation of the NAc or the shell subregion also slightly reduced preference for larger rewards on a reward magnitude discrimination. Thus, the NAc seems to play a small role in biasing choice toward larger rewards, but its contribution to behavior is amplified when delivery of these rewards is uncertain, helping to direct response selection toward more favorable outcomes.     

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.     

Integrated versus segregated accounting and the magnitude effect in temporal discounting

Temporal discounting rates in humans generally decrease as the amount of reward increases, a phenomenon known as themagnitude effect. In the present study, we examined whether temporal discounting and the magnitude effect are related to segregation of choices in terms of gains or losses for waiting for or expediting receipt of a reward. Subjects (N = 24) responded to a series of hypothetical choices about amounts of money available either immediately or after a delay. The immediate and delayed amounts either were presented as integrated amounts in the baseline condition or were segregated as differential gains or losses for choosing delayed or expedited consumption (delay and speedup conditions, respectively). Temporal discounting rates decreased in the segregated conditions, in accord with the standard discounted utility model but contrary to the hypothesis that the subjects were choosing on the basis of reward differentials in the baseline condition. The size of the magnitude effect was comparable in the baseline and the delay conditions but decreased in the speed-up condition. These results challenge explanations of the magnitude effect in terms of an increasing proportional sensitivity property of the utility function (Loewenstein & Prelec, 1992) and the hypothesis that subjects choose on the basis of differentials even when the rewards are presented as integrated amounts.     

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 effect of temporal constraints on the value of money and other commodities

The value of hypothetical rewards of various delays and durations, consisting of money or other commodities, such as automobile use and vacations, was measured by the psychophysical up-down staircase method using an amount of unrestricted immediate money as the titrated variable. A model of temporal discounting based on implied constraints on anticipated consumption rate described the data. Further explicit constraints on consumption produced predictable deviations from the model. The concept that consumption is normally constrained together with time discounting may also explain the interaction between amount and delay of monetary reward in determining value and may provide the basis for a theory of addiction based on learning to increase consumption rate.     

Delayed matching-to-sample performance: Effects of relative reinforcer frequency and of signaled versus unsignaled reinforcer magnitudes

Six pigeons were trained on a delayed red-green matching-to-sample task that arranged four delays within sessions. Matching responses intermittently produced either 1.5-s access to food or 4.5-s access to food, and nonmatching responses produced either 1.5-s or 4.5-s blackout. Two phases were conducted: a signaled phase in which the reinforcer magnitudes (small and large) were signaled by houselights (positioned either on the left or right of the chamber), and an unsignaled phase in which there was no correlation between reinforcer magnitude and houselight position. In both phases, the relative frequency with which red and green matching responses produced food was varied across five values. Both matching accuracy and the sensitivity of performance to the distribution of reinforcers for matching responses decreased with increasing delays in both phases. In addition, accuracy and reinforcer sensitivity were significantly lower on signaled small-reinforcer trials compared with accuracy and sensitivity values on signaled large-reinforcer trials and on both types of unsignaled trials. These results are discussed in the context of research on both nonhuman animal and human memory.     

The relation between temperament and rate of temporal discounting

The present study examines the relationship between several temperamental traits (sensation seeking, extraversion–introversion, and impulsivity) and rate of temporal discounting, that is the rate of decrease in the subjective value of a reward as the delay to its receipt increases. Participants made choices between hypothetical monetary rewards that could be obtained immediately or after a specified delay. Temporal discounting functions were calculated and differences in rate of discounting between different groups were evaluated. For all groups of participants, hyperbolic discounting functions described well the decreases in subjective value with delay (R² ranged from 0.700 to 0.985). The rate of discounting was equivalent in high and low sensation seekers. However, both extraverts and high impulsive individuals showed higher temporal discounting rates than introverts and low impulsive individuals. The relationship between temperament and temporal discounting may be related to differences in time perception and/or to differences in susceptibility to rewards in extraverts versus introverts and in high- versus low-impulsive individuals.     

Gambling and Delay Discounting in Japanese Students

The present study examined the relationship between gambling behavior and delay discounting with Japanese residents. Japanese university students were selected into pathological gambler and non‐gambling control groups using a Japanese version of the South Oaks Gambling Screen. In a discounting task, participants chose individually between a large delayed reward and a smaller immediate reward with varied delays. The discounting rate (k‐value) and the area under the curve were significantly higher and smaller, respectively, for the gambler group than for the control group. These findings show that Japanese gamblers discount delayed rewards more steeply than non‐gambling controls, as has been found in U.S. residents.