Associations between a one-shot delay discounting measure and age, income, education and real-world impulsive behavior

There has been discussion over the extent to which delay discounting – as prototypically shown by a preference for a smaller-sooner sum of money over a larger-later sum – measures the same kind of impulsive preferences that drive non-financial behavior. To address this issue, a dataset was analyzed containing 42,863 participants’ responses to a single delay-discounting choice, along with self-report behaviors that can be considered as impulsive. Choice of a smaller-sooner sum was associated with several demographics: younger age, lower income, and lower education; and impulsive behaviors: earlier age of first sexual activity and recent relationship infidelity, smoking, and higher body mass index. These findings suggest that at least an aspect of delay discounting preference is associated with a general trait influencing other forms of impulsivity, and therefore that high delay discounting is another form of impulsive behavior.     

Associations between a one-shot delay discounting measure and age,income, education and real-world impulsive behavior

There has been discussion over the extent to which delay discounting – as prototypically shown by a preference for a smaller-sooner sum of money over a larger-later sum – measures the same kind of impulsive preferences that drive non-financial behavior. To address this issue, a dataset was analyzed containing 42,863 participants’ responses to a single delay-discounting choice, along with self-report behaviors that can be considered as impulsive. Choice of a smaller-sooner sum was associated with several demographics: younger age, lower income, and lower education; and impulsive behaviors: earlier age of first sexual activity and recent relationship infidelity, smoking, and higher body mass index. These findings suggest that at least an aspect of delay discounting preference is associated with a general trait influencing other forms of impulsivity, and therefore that high delay discounting is another form of impulsive behavior.     

Commitment, choice and self-control

When offered a choice (Choice Y) between a small immediate reward (2-sec exposure to grain) and a large reward (4-sec exposure to grain) delayed by 4 sec, pigeons invariably preferred the small, immediate reward. However, when offered a choice (Choice X) between a delay of T seconds followed by Choice Y and a delay of T seconds followed by restriction to the large delayed reward only, the pigeon's choice depended on T. When T was small, the pigeons chose the alternative leading to Choice Y (and then chose the small, immediate reward). When T was large, the pigeons chose the alternative leading to the large delayed reward only. The reversal of preference as T increases is predicted by several recent models for choice between various amounts and delays of reward. The preference for the large delayed alternative with long durations of T parallels everyday instances of advance commitment to a given course of action. Such commitment may be seen as a prototype for self-control.     

A tribute to Howard Rachlin and his two-parameter discounting model: Reliable and flexible model fitting

Delay discounting reflects the rate at which a reward loses its subjective value as a function of delay to that reward. Many models have been proposed to measure delay discounting, and many comparisons have been made among these models. We highlight the two-parameter delay discounting model popularized by Howard Rachlin by demonstrating two key practical features of the Rachlin model. The first feature is flexibility; the Rachlin model fits empirical discounting data closely. Second, when compared with other available two-parameter discounting models, the Rachlin model has the advantage that unique best estimates for parameters are easy to obtain across a wide variety of potential discounting patterns. We focus this work on this second feature in the context of maximum likelihood, showing the relative ease with which the Rachlin model can be utilized compared with the extreme care that must be used with other models for discounting data, focusing on two illustrative cases that pass checks for data validity. Both of these features are demonstrated via a reanalysis of discounting data the authors have previously used for model selection purposes.     

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.     

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.     

Choice behavior of rats in a concurrent-chains schedule: Amount and delay of reinforcement

Rats were exposed to concurrent-chains schedules in which the terminal links were equal fixed-interval schedules terminating in one or three food pellets. Choice proportions for large reward increased with increases in delay intervals programmed on fixed-interval schedules and supported the predictions derived from a general choice model originally formulated by Fantino and later developed by Navarick and Fantino. In addition, a functional equivalence of two alternatives was established by increasing delay intervals with large reward, whereas delay intervals for small reward were held constant. Functionally equivalent delay intervals with large reward, for each delay interval with small reward, can be described by a power function with exponent smaller than 1.0. A better prediction of choice proportions resulted when this function was used to derive predicted choice proportions.     

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.     

Temporal framing and the hidden‐zero effect: rate‐dependent outcomes on delay discounting

Recent research suggests that presenting time intervals as units (e.g., days) or as specific dates, can modulate the degree to which humans discount delayed outcomes. Another framing effect involves explicitly stating that choosing a smaller–sooner reward is mutually exclusive to receiving a larger–later reward, thus presenting choices as an extended sequence. In Experiment 1, participants (N = 201) recruited from Amazon Mechanical Turk completed the Monetary Choice Questionnaire in a 2 (delay framing) by 2 (zero framing) design. Regression suggested a main effect of delay, but not zero, framing after accounting for other demographic variables and manipulations. We observed a rate‐dependent effect for the date‐framing group, such that those with initially steep discounting exhibited greater sensitivity to the manipulation than those with initially shallow discounting. Subsequent analyses suggest these effects cannot be explained by regression to the mean. Experiment 2 addressed the possibility that the null effect of zero framing was due to within‐subject exposure to the hidden‐ and explicit‐zero conditions. A new Amazon Mechanical Turk sample completed the Monetary Choice Questionnaire in either hidden‐ or explicit‐zero formats. Analyses revealed a main effect of reward magnitude, but not zero framing, suggesting potential limitations to the generality of the hidden‐zero effect.     

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.     

Control your cravings: Self-controlled food choice varies by eating attitudes,sex, and food type among Division I collegiate athletes

Eating attitudes are predictive of disordered eating, which can be quite prevalent among collegiate athletes. The present study tested if disordered eating attitudes and the sex of collegiate athletes are related to “self-controlled food choice” for four food types: a dessert, fried food, fruit, and vegetable. In total, 102 athletes completed a disordered eating attitudes assessment and a delay discounting task. For the delay discounting task, athletes chose between one large delayed reward and one successively smaller immediate reward for four food types, and indifference points were computed with lower indifference points indicating greater self-controlled food choice. In this study female athletes showed greater self-controlled food choice for all three tempting food types (dessert, fried food, and fruit), but not the control food type (vegetable). For males, results were moderated by their level of disordered eating attitudes. Overall, these data show that “self-controlled food choice,” measured using a delay discounting task, is a key factor related to sex differences in disordered eating attitudes among college athletes.     

跨期选择的认知机制与神经基础

跨期选择是指个体对发生在不同时间的成本与收益进行权衡的决策过程。跨期选择的计算模型从经济学的角度用数学模型来建构时间折扣函数,而认知成分模型则从心理学的角度来研究跨期选择中的心理效应与认知成分。跨期选择的神经基础有三种不同的研究取向：双机制加工取向、单机制加工取向、自我控制取向。未来研究应该在跨期选择的认知机制、神经通路及运行机制、跨期选择的应用,以及从进化的角度对人与动物的跨期选择行为进行更深入的研究。     

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.     

Discounting: A practical guide to multilevel analysis of choice data

Multilevel modeling provides the ability to simultaneously evaluate the discounting of individuals and groups by examining choices between smaller sooner and larger later rewards. A multilevel logistic regression approach is advocated in which sensitivity to relative reward magnitude and relative delay are considered as separate contributors to choice. Examples of how to fit choice data using multilevel logistic models are provided to help researchers in the adoption of these methods.     

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.     

Risk should be objectively defined: comment on Pelé and Sueur

Pelé and Sueur (2013) propose that optimal decisions depend on delay of reinforcement, accuracy (probability or magnitude of reinforcement), and risk. The problem with this model is delay and accuracy are easy to define, but according to Pelé and Sueur the third, risk, depends on the animal’s perceived or “interpreted” risk rather than actual (experienced) risk. Thus, choice of the smaller more immediate reward over the larger delayed reward (the delay discounting function) is viewed by the authors as optimal because delay is associated with increased risk (due to potential competition or predation). But perceived risk is assessed by the decision made (e.g., the slope of the discounting function), and since there is virtually no actual risk involved, by default if there is no independent means of measuring risk, according to Pelé and Sueur, all choices can be viewed as optimal. Thus, optimality is an untestable concept. We suggest that risk be defined by the actual risk (given sufficient experience to judge it) and under conditions in which there is no actual risk (or risk is controlled), when animals choose an alternative that provides a lower rate of access to food, that one considers such choice to be suboptimal.     

Mixing virtue and vice: combining the immediacy effect and the diversification heuristic

Many of the most significant choices that people make are between vices, which exchange small immediate rewards for large delayed costs, and virtues, which exchange small immediate costs for large delayed rewards. We investigate the consequences of making a series of such choices either simultaneously or sequentially. We made two predictions. First, because many alternatives chosen under simultaneous choice will only be experienced following a delay, and because hyperbolic time discounting predicts that people will prefer delayed virtues but immediate vices, we predicted that people would choose more virtues in simultaneous than sequential choice. Second, due to the tendency to diversify portfolios of choices, we predicted a greater mix of virtues and vices in simultaneous than sequential choice. These predictions were confirmed in two experiments involving real choices; one between ‘highbrow’ and ‘lowbrow’ movies, and the other between ‘instant‐win’ and ‘prize‐draw’ lottery tickets. We conclude by posing the question of whether simultaneous or sequential choice results in decisions that more closely approximate what people ‘really’ want. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

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.