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.     

Stimulus Equivalence: Effects Of A Default-response Option On Emergence Of Untrained Stimulus Relations

Human subjects were exposed to a concurrent-chains schedule in which reinforcer amounts, delays, or both were varied in the terminal links, and consummatory responses were required to receive points that were later exchangeable for money. Two independent variable-interval 30-s schedules were in effect during the initial links, and delay periods were defined by fixed-time schedules. In Experiment 1, subjects were exposed to three different pairs of reinforcer amounts and delays, and sensitivity to reinforcer amount and delay was determined based on the generalized matching law. The relative responding (choice) of most subjects was more sensitive to reinforcer amount than to reinforcer delay. In Experiment 2, subjects chose between immediate smaller reinforcers and delayed larger reinforcers in five conditions with and without timeout periods that followed a shorter delay, in which reinforcer amounts and delays were combined to make different predictions based on local reinforcement density (i.e., points per delay) or overall reinforcement density (i.e., points per total time). In most conditions, subjects' choices were qualitatively in accord with the predictions from the overall reinforcement density calculated by the ratio of reinforcer amount and total time. Therefore, the overall reinforcement density appears to influence the preference of humans in the present self-control choice situation.     

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.     

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.     

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.     

Contrived motivating operations alter delay‐discounting values of disordered gamblers

The present study required 9 disordered gamblers to make hypothetical selections between smaller and larger amounts of money at varying delays. Participants were also required to respond to the task given the contrived hypothetical conditions of earning twice or half as much as they did at their current jobs. The results demonstrated how participants’ delay discounting was altered via contrived motivating operations, strengthening the argument that discounting may be a state variable.     

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.     

Tradeoffs in choice between risk and delay depend on monetary amounts

In Experiments 1 and 2, 25 and 48 college students made binary choices between hypothetical money amounts. In Part A, choices were between small amounts available with certainty and larger amounts ($10 to $10,000) available with risk. Choices in Part B were between immediate small amounts and delayed larger amounts. As money amount grew, risk aversion and delay aversion both changed but in opposite ways: Risk aversion grew but delay aversion shrank. Part C of Experiment 1 pitted risky amounts against delayed amounts, and its results were consistent with those of Parts A and B. Equivalences of particular risks and delays depended on the particular monetary amounts to which they attached. In Experiment 3, 20 college students made binary choices between money amounts, knowing that they would actually receive some of the selections they made. In Part A, choices were between certain small amounts and risky larger amounts ($1 and $10). Choice problems in Part B were between immediate small amounts and delayed receipt of $1 or $10. The results were like those of Experiment 1, though weaker. These results argue against models of choice that posit an equivalence of risk and delay that is independent of monetary amount.     

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.     

Transitional and steady-state choice behavior under an adjusting-delay schedule

Twelve rats made repeated choices on an adjusting-delay schedule between a smaller reinforcer (A) that was delivered immediately after a response and a larger reinforcer (B) that was delivered after a delay which increased or decreased by 20% depending on the subject's choices in successive blocks of trials. In two phases of the experiment (100 sessions and 40 sessions), reinforcer sizes were selected which enabled theoretical parameters expressing the rate of delay discounting and sensitivity to reinforcer size to be estimated from the ratio of the indifference delays obtained in the two phases. Indifference delays, calculated from adjusting delays in the last 10 sessions of each phase, were shorter when the sizes of A and B were 14 and 25 μl of a 0.6 M sucrose solution than when they were 25 and 100 μl of the same solution. The ratio of the indifference delays was significantly smaller than that predicted on the basis of an assumed linear relation between reinforcer size and instantaneous reinforcer value, consistent with a previous proposal that this relation may be hyperbolic in form. Estimates of the rate of delay discounting based on the ratio of the two indifference delays (mean, 0.08 s(-1)) were similar to values obtained previously using different intertemporal choice protocols. Estimates of the size-sensitivity parameter (mean 113 μl) were similar to estimates recently derived from performance on progressive-ratio schedules. In both phases of the experiment, adjusting delays in successive blocks of trials were analyzed using the Fourier transform. The power spectrum obtained from individual rats had a dominant frequency that corresponded to a period of oscillation of the adjusting delay between 30 and 100 trial blocks (mean, 78). Power in the dominant frequency band was highest in the early sessions of the first phase and declined with extended training. It is suggested that this experimental protocol may have utility in neurobehavioral studies of intertemporal choice.     

Preference reversals with losses

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

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.     

The effect of variable delays on self-control

Five pigeons served as subjects in an experiment that examined the effects of variable as opposed to fixed delays on preference in a self-control paradigm (choice between larger, more delayed and smaller, less delayed reinforcers). Nonindependent concurrent variable-interval schedules were used to measure choice. When delays to the larger, more delayed reinforcers were variable as opposed to fixed, the subjects showed an increased preference for that alternative (the self-control alternative). A series of regressions revealed that the hyperbolic decay model and incentive theory provided poor fits to the data, but a modified version of the generalized matching law provided an adequate fit. Together, consistent with a general prediction made by discounting models, the data supported the conclusion that variable delays can increase self-control. However, specific discounting models were not able to explain the present data well.     

ISOLATING BEHAVIORAL MECHANISMS OF INTERTEMPORAL CHOICE: NICOTINE EFFECT ON DELAY DISCOUNTING AND AMOUNT SENSITIVITY

Many drugs of abuse produce changes in impulsive choice, that is, choice for a smaller—sooner reinforcer over a larger—later reinforcer. Because the alternatives differ in both delay and amount, it is not clear whether these drug effects are due to the differences in reinforcer delay or amount. To isolate the effects of delay, we used a titrating delay procedure. In phase 1, 9 rats made discrete choices between variable delays (1 or 19 s, equal probability of each) and a delay to a single food pellet. The computer titrated the delay to a single food pellet until the rats were indifferent between the two options. This indifference delay was used as the starting value for the titrating delay for all future sessions. We next evaluated the acute effects of nicotine (subcutaneous 1.0, 0.3, 0.1, and 0.03 mg/kg) on choice. If nicotine increases delay discounting, it should have increased preference for the variable delay. Instead, nicotine had very little effect on choice. In a second phase, the titrated delay alternative produced three food pellets instead of one, which was again produced by the variable delay (1 s or 19 s) alternative. Under this procedure, nicotine increased preference for the one pellet alternative. Nicotine‐induced changes in impulsive choice are therefore likely due to differences in reinforcer amount rather than differences in reinforcer delay. In addition, it may be necessary to include an amount sensitivity parameter in any mathematical model of choice when the alternatives differ in reinforcer amount.     

Self-control in mentally retarded adolescents: choice as a function of amount and delay of reinforcement.

Three severely mentally retarded adolescents were studied under discrete-trial procedures in which a choice was arranged between edible reinforcers that differed in magnitude and, in some conditions, delay. In the absence of delays the larger reinforcer was consistently chosen. Under conditions in which the smaller reinforcer was not delayed, increasing the delay to delivery of the larger reinforcer decreased the percentage of trials in which that reinforcer was chosen. All subjects directed the majority of choice responses to the smaller reinforcer when the larger reinforcer was sufficiently delayed, although the value at which this occurred differed across subjects. Under conditions in which the larger reinforcer initially was sufficiently delayed to result in preference for the smaller one, progressively increasing in 5-s increments the delay to both reinforcers increased percentage of trials with the larger reinforcer chosen. At sufficiently long delays, 2 of the subjects consistently chose the larger, but more delayed, reinforcer, and the 3rd subject chose that reinforcer on half of the trials. These results are consistent with the findings of prior studies in which adult humans responded to terminate noise and pigeons responded to produce food.     

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.     

Positive mood effects on delay discounting

Delay discounting is the process by which the value of an expected reward decreases as the delay to obtaining that reward increases. Individuals with higher discounting rates tend to prefer smaller immediate rewards over larger delayed rewards. Previous research has indicated that personality can influence an individual's discounting rates, with higher levels of Extraversion predicting a preference for immediate gratification. The current study examined how this relationship would be influenced by situational mood inductions. While main effects were observed for both Extraversion and cognitive ability in the prediction of discounting rates, a significant interaction was also observed between Extraversion and positive affect. Extraverted individuals were more likely to prefer an immediate reward when first put in a positive mood. Extraverts thus appear particularly sensitive to impulsive, incentive-reward-driven behavior by temperament and by situational factors heightening positive affect.     

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.     

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.     

Asymmetry of the group context effect on delay discounting

Binary choice delay discounting tasks require participants to indicate preference between smaller, immediate, and larger, delayed rewards. Previous research indicates that when the delayed reward is shared with others, the delayed outcome is preferred compared with when the outcomes are for the self only, resulting in lower rates of delay discounting. The present series of studies sought to replicate and extend this finding. Study 1 compared delay discounting on a standard task in which both immediate and delayed outcomes are for the self and a group context task where the delayed outcome was shared with one other person. Replicating previous results, group context resulted in lower rates of delay discounting, and this effect was independent of how the shared outcome was presented. Study 2 compared delay discounting on a standard task and a group context task where the immediate outcome was shared. In contrast to Study 1, group context resulted in higher rates of delay discounting, suggesting that preference in intertemporal choice tracks the shared outcome. Moreover, this effect was not independent of how the shared outcome was presented. This is the first study to reveal that group context, when applied to the immediate outcome, can result in higher rates of delay discounting.