Delay discounting as impaired valuation: Delayed rewards in an animal obesity model

Obesity is a major public health problem, which, like many forms of addiction, is associated with an elevated tendency to choose smaller immediate rather than larger delayed rewards, a response pattern often referred to as excessive delay discounting. Although some accounts of delay discounting conceptualize this process as impulsivity (placing the emphasis on overvaluing the smaller immediate reward), others have conceptualized delay discounting as an executive function (placing the emphasis on delayed rewards failing to retain their value). The present experiments used a popular animal model of obesity that has been shown to discount delayed rewards at elevated rates (i.e., obese Zucker rats) to test two predictions that conceptualize delay discounting as executive function. In the first experiment, acquisition of lever pressing with delayed rewards was compared in obese versus lean Zucker rats. Contrary to predictions based on delay discounting as executive function, obese Zucker rats learned to press the lever more quickly than controls. In the second experiment, progressive ratio breakpoints (a measure of reward efficacy) with delayed rewards were compared in obese versus lean Zucker rats. Contrary to the notion that obese rats fail to value delayed rewards, the obese Zucker rats' breakpoints were (at least) as high as those of the lean Zucker rats.     

Impulsivity in rodents with a genetic predisposition for excessive alcohol consumption is associated with a lack of a prospective strategy

Increasing evidence supports the hypothesis that impulsive decision-making is a heritable risk factor for an alcohol use disorder (AUD). Clearly identifying a link between impulsivity and AUD risk, however, is complicated by the fact that both AUDs and impulsivity are heterogeneous constructs. Understanding the link between the two requires identifying the underlying cognitive factors that lead to impulsive choices. Rodent models have established that a family history of excessive drinking can lead to the expression of a transgenerational impulsive phenotype, suggesting heritable alterations in the decision-making process. In the present study, we explored the cognitive processes underlying impulsive choice in a validated, selectively bred rodent model of excessive drinking—the alcohol-preferring (“P”) rat. Impulsivity was measured via delay discounting (DD), and P rats exhibited an impulsive phenotype as compared to their outbred foundation strain—Wistar rats. Steeper discounting in P rats was associated with a lack of a prospective behavioral strategy, which was observed in Wistar rats and was directly related to DD. To further explore the underlying cognitive factors mediating these observations, a drift diffusion model of DD was constructed. These simulations supported the hypothesis that prospective memory of the delayed reward guided choice decisions, slowed discounting, and optimized the fit of the model to the experimental data. Collectively, these data suggest that a deficit in forming or maintaining a prospective behavioral plan is a critical intermediary to delaying reward, and by extension, may underlie the inability to delay reward in those with increased AUD risk.     

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.     

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.     

An experimental analysis of impulsivity and impulse control in humans

In choosing between small, immediate and large, delayed reward, an organism behaves impulsively if it chooses the small reward and shows impulse control if it chooses the large reward. Work with nonhumans suggests that impulsivity and impulse control may be derived from gradients of delayed reinforcement. A model developed by Ainslie and by Rachlin suggests that preference for the rewards should be a function of when the choice is made: small reward with no delay may be preferred to large reward with delay X, but adding delay T to both alternatives should shift preference to the large reward. Three experiments investigated this preference reversal in humans, using termination of 90 dba white noise as the reinforcing event. Experiment 1 showed that under some instructional conditions 90-sec noise off with no delay was preferred over 120-sec noise off after a 60-sec delay, but that preference shifted to the large reward when a 15-sec delay (T) was added to both alternatives. Experiment 2 replicated this preference reversal under two conditions of large, delayed reward, and with three rather than two values of T. Experiment 3 confirmed this effect of T and showed that some humans committed themselves to the large reward when commitment could be made some time before presentation of the reward alternatives. These data support the Ainslie-Rachlin model and extend it to human choice behavior.     

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.     

Intertemporal Similarity: Discounting as a Last Resort

Standard models of intertemporal choice assume that individuals discount future payoffs by integrating reward amounts and time delays to generate a discounted value. Alternative models propose that, rather than integrate across them, individuals compare within attributes (amounts and delays) to determine if differences in one attribute outweigh differences in another attribute. For instance, the similarity model 1) compares the two reward amounts to determine whether they are similar, 2) compares the similarity of the two time delays, and then 3) makes a decision based on these similarity judgments. Here, I tested discounting models against attribute‐based models that use similarity judgments to make choices. I collected intertemporal choices and similarity judgments for the reward amounts and time delays from participants in three experiments. All experiments tested the ability of discounting and similarity models to predict intertemporal choices. Model generalization analyses showed that the best predicting models started with similarity judgments and then, if similarity failed to make a prediction, resorted to discounting models. Similarity judgments also matched intertemporal choice data demonstrating both the magnitude and sign effects, thereby accounting for behavioral data that contradict many discounting models. These results highlight the possibility that attribute‐based models such as the similarity models provide alternatives to discounting that may offer insights into the process of making intertemporal choices. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

Delay discounting: Interactions between personality and cognitive ability

Delay discounting describes the extent to which the value of a reward decreases as the delay to obtaining that reward increases. Lower discounting rates predict better outcomes in social, academic, and health domains. The current study investigates how personality and cognitive ability interact to predict individual differences in delay discounting. Extraversion was found to predict higher discounting rates at the low end of the cognitive distribution, while emotional stability was found to predict lower discounting rates at the high end of the cognitive distribution. These findings support recent models of discounting behavior and suggest that personality and cognitive ability interact in shaping decision making.     

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.     

Delay, Probability, and Social Discounting in A Public Goods Game

A human social discount function measures the value to a person of a reward to another person at a given social distance. Just as delay discounting is a hyperbolic function of delay, and probability discounting is a hyperbolic function of odds-against, social discounting is a hyperbolic function of social distance. Experiment 1 obtained individual social, delay, and probability discount functions for a hypothetical $75 reward; participants also indicated how much of an initial $100 endowment they would contribute to a common investment in a public good. Steepness of discounting correlated, across participants, among all three discount dimensions. However, only social and probability discounting were correlated with the public-good contribution; high public-good contributors were more altruistic and also less risk averse than low contributors. Experiment 2 obtained social discount functions with hypothetical $75 rewards and delay discount functions with hypothetical $1,000 rewards, as well as public-good contributions. The results replicated those of Experiment 1; steepness of the two forms of discounting correlated with each other across participants but only social discounting correlated with the public-good contribution. Most participants in Experiment 2 predicted that the average contribution would be lower than their own contribution.     

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.     

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     

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.     

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.     

Common and distinctive features in stimulus similarity: A modified version of the contrast model

Featural representations of similarity data assume that people represent stimuli in terms of a set of discrete properties. In this article, we consider the differences in featural representations that arise from making four different assumptions about how similarity is measured. Three of these similarity models— the common features model, the distinctive features model, and Tversky’s seminal contrast model—have been considered previously. The other model is new and modifies the contrast model by assuming that each individual feature only ever acts as a common or distinctive feature. Each of the four models is tested on previously examined similarity data, relating to kinship terms, and on a new data set, relating to faces. In fitting the models, we have used the geometric complexity criterion to balance the competing demands of data-fit and model complexity. The results show that both common and distinctive features are important for stimulus representation, and we argue that the modified contrast model combines these two components in a more effective and interpretable way than Tversky’s original formulation.     

不确定性容忍度对跨期选择的影响及其情景依赖性

采用2(不确定性容忍度：高、低)×2(跨期日期：今天/14天、今天/180天)×2(延迟奖赏值：200元、1000元)混合实验设计,探讨不同任务特征下不确定性容忍度对跨期选择的影响。结果表明：跨期日期为180天时,不确定性容忍度主效应边缘显著;不确定性容忍度与延迟奖赏值交互作用显著：在200元时低容忍度个体对延迟奖赏的折扣程度大于高容忍度个体,在1000元时无此效应;跨期日期为14天时,不确定性容忍度的主效应及其与延迟奖赏值交互作用均不显著。这表明,不确定性容忍度对跨期选择存在影响,但这种影响受到跨期日期和延迟奖赏值的调节,具有情景依赖性。