时间贴现的性质与脑机制

时间贴现是指个人对事件的价值量估计随着时间的流逝而下降的心理现象,它是行为选择理论的一个重要组成部分。着重介绍了时间贴现的数学模型（指数模型、双曲线模型族、非双曲线模型）、时间贴现现象和概率贴现现象的联系、延迟兑现与提前兑现时间贴现不对称现象及其理论解释,还讨论了时间贴现现象的神经机制研究。提出了时间贴现未来研究的几个主要问题     

Discounting of food and water in rats shows trait- and state-like characteristics

Delay discounting is the loss in value of an outcome as a function of its delay. The present study focused on examining a trait-like characteristic of delay discounting in a preclinical animal model. Specifically, we were interested in whether there was a positive relation between discounting of 2 different outcomes in rats. That is, would rats that discount delayed food steeply also discount delayed water steeply? In addition, we examined how session-to-session variability in discounting could be attributed to differences between subjects (trait variability) and to differences within subjects (state variability). Finally, we measured discounting from early- to mid-adulthood, allowing us to examine changes in discounting as a function of age. Overall, we found a moderate, positive correlation between discounting of food and discounting of water in rats, providing further evidence that the relative consistency with which individuals discount different outcomes is a trait-like characteristic. In addition, we found a high degree of within-subject variability in discounting, indicating strong state-like differences from session to session. Finally, overall, discounting decreased as a function of age; however, individual-subject data showed variability in how discounting changed across time. Overall, our results show that differences in delay discounting between individuals reflect variability in both trait- and state-like characteristics.     

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     

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。     

Social discounting and delay discounting

Social discounting was measured as the amount of money a participant was willing to forgo to give a fixed amount (usually $75) to another person. In the first experiment, amount forgone was a hyperbolic function of the social distance between the giver and receiver. In the second experiment, degree of social discounting was an increasing function of reward magnitude whereas degree of delay discounting was a decreasing function of reward magnitude. In the third experiment, the shape of the function relating delayed rewards to equally valued immediate rewards for another person was predicted from individual delay and social discount functions. All in all, the studies show that the social discount function, like delay and probability discount functions, is hyperbolic in form. Copyright © 2007 John Wiley & Sons, Ltd.     

跨期决策中的负折扣现象及其机制

主流跨期决策模型认为, 跨期决策存在一个时间折扣过程。时间折扣是指人们会根据将来获益或损失的延迟时间对其效用进行折扣, 折扣后的效用小于原来的效用, 而负折扣现象违背了时间折扣过程。负折扣现象出现在金钱、非金钱的获益与损失领域, 其可能的解释机制为预期情绪。目前关于负折扣现象的研究, 较少验证其影响机制, 未来的研究可以结合眼动追踪和fMRI技术探讨其机制, 并丰富对负折扣现象的影响因素研究。     

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.     

时间贴现在神经和行为上的年龄特征

时间贴现的年龄发展具有阶段性。前额皮质, 边缘系统和多巴胺能系统的发展成熟是从儿童期到成人期时间贴现发展变化的神经生物基础。成人期到老年期时间贴现年龄特征的研究结果不一致。概率贴现、未来定向、延迟满足等被用来探讨时间贴现年龄发展特征。可以从大脑不同区域的发展轨迹, 延迟时段的心理意义来进一步深入研究。     

A mechanism for reducing delay discounting by altering temporal attention

Rewards that are not immediately available are discounted compared to rewards that are immediately available. The more a person discounts a delayed reward, the more likely that person is to have a range of behavioral problems, including clinical disorders. This latter observation has motivated the search for interventions that reduce discounting. One surprisingly simple method to reduce discounting is an "explicit-zero" reframing that states default or null outcomes. Reframing a classical discounting choice as "something now but nothing later" versus "nothing now but more later" decreases discount rates. However, it is not clear how this "explicit-zero" framing intervention works. The present studies delineate and test two possible mechanisms to explain the phenomenon. One mechanism proposes that the explicit-zero framing creates the impression of an improving sequence, thereby enhancing the present value of the delayed reward. A second possible mechanism posits an increase in attention allocation to temporally distant reward representations. In four experiments, we distinguish between these two hypothesized mechanisms and conclude that the temporal attention hypothesis is superior for explaining our results. We propose a model of temporal attention whereby framing affects intertemporal preferences by modifying present bias.     

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.     

The discounting model selector: Statistical software for delay discounting applications

Original, open‐source computer software was developed and validated against established delay discounting methods in the literature. The software executed approximate Bayesian model selection methods from user‐supplied temporal discounting data and computed the effective delay 50 (ED50) from the best performing model. Software was custom‐designed to enable behavior analysts to conveniently apply recent statistical methods to temporal discounting data with the aid of a graphical user interface (GUI). The results of independent validation of the approximate Bayesian model selection methods indicated that the program provided results identical to that of the original source paper and its methods. Monte Carlo simulation (n = 50,000) confirmed that true model was selected most often in each setting. Simulation code and data for this study were posted to an online repository for use by other researchers. The model selection approach was applied to three existing delay discounting data sets from the literature in addition to the data from the source paper. Comparisons of model selected ED50 were consistent with traditional indices of discounting. Conceptual issues related to the development and use of computer software by behavior analysts and the opportunities afforded by free and open‐sourced software are discussed and a review of possible expansions of this software are provided.     

概率贴现和时间贴现在人脑中的分离

本研究运用ERP技术来检验概率贴现和时间贴现是否反映了相同的神经机制过程。在本研究中,我们在一个刺激中同时操纵概率贴现（风险vs.安全）和时间贴现（1个月后vs.今天）水平。通过对两个过程上的ERN以及全时间段的ERP分析来确定它们是否反映了相同的认知过程。结果发现,这两者在ERN上存在差异,同时这两个效应在ERP的时程和出现的电极点上都存在差异。这些差异表明这两者可能包含着不同的神经机制过程。     

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.     

A Measure of Delay Discounting Within the Academic Domain

It is important to better understand the decision‐making processes involved in student procrastination, in order to develop interventions that reduce this common problem. Students may procrastinate because studying produces delayed reinforcers; however, no task measuring delay discounting of academic outcomes currently exists. In Experiment 1, we developed and piloted a measure of academic discounting modeled on titrating‐amount tasks successfully used in the discounting literature. Participants made hypothetical choices between working for money (the smaller, sooner reinforcer) and working on an assignment that was due at various times (the larger, later reinforcer). Participants showed systematic decreases in the subjective value of the assignment as a function of delay, and the hyperbolic and hyperboloid models described the shape of this decrease in value well. In general, larger delayed rewards are discounted less steeply than smaller delayed rewards (the magnitude effect). In Experiment 2, we observed the magnitude effect in academic discounting: Participants discounted a “not important” assignment more steeply than an “important” assignment. In the hyperboloid model, this change was captured by an increase in the s parameter. Results provide support for the validity of the academic discounting task. Copyright © 2018 John Wiley & Sons, Ltd.     

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

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

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。     

Inequality in personality and temporal discounting across socioeconomic status? Assessing the evidence

Personality traits such as conscientiousness and impulsivity correlate with temporal discounting, the degree to which individuals discount the value of future relative to present rewards. These variables have, in turn, been hypothesized to relate to income inequality in the United States. A key but untested assumption of this hypothesis is that the association among these variables is distinct across socioeconomic classes. The purpose of the present research is to test that assumption. N = 1100 adults with annual income ranging from at or below the poverty line ($0–$20,000) to upper-middle class ($200,000+) completed personality measures and a measure of temporal discounting. The results of our preregistered analyses indicated a positive association of income with trait planfulness, and a negative association with trait impulsivity and one parameter of temporal discounting that captures a bias to prefer sooner rewards to a greater degree if they are delivered that day. Our results can inform psychological theories of inequality and a broader conversation about effective public policy.     

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.     

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.