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.     

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.     

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.     

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 for monetary and close relationship outcomes

The present study extended research on intertemporal choice—in which individuals choose between outcomes that may be received immediately or after a delay—to close relationships. In Experiment 1, New Zealand university students aged 18 to 25 made decisions about hypothetical monetary and relationship outcomes, and in Experiment 2, about relationship outcomes which emphasized companionate or sexual aspects (Ns = 64). Both experiments found effects of delay and magnitude on temporal discounting rates, and domain independence for choices about close relationships, similar to previous studies with monetary outcomes. There were no significant gender differences. Overall, results suggest that people make intertemporal choices about relationships according to a similar process used to make decisions involving other types of outcomes.     

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。     

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.     

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.     

Delay discounting: I'm a k, you're a k

Delay discounting is the decline in the present value of a reward with delay to its receipt. Across a variety of species, populations, and reward types, value declines hyperbolically with delay. Value declines steeply with shorter delays, but more shallowly with longer delays. Quantitative modeling provides precise measures to characterize the form of the discount function. These measures may be regarded as higher-order dependent variables, intervening variables, or hypothetical constructs. I suggest the degree of delay discounting may be a personality trait. In the end, the ontological status of measures of delay discounting is irrelevant. Whatever delay discounting may be, its study has provided the field of behavior analysis and other areas measures with robust generality and predictive validity for a variety of significant human problems. Research on moderating the degree of delay discounting has the potential to produce substantial societal benefits.     

情绪对跨期决策的影响：来自单维占优模型的解释

跨期决策的研究表明, 积极情绪和消极情绪状态下的跨期决策行为存在显著差异。本研究从单维占优模型的角度, 揭示情绪影响跨期决策的过程机制。实验1通过诱发被试的积极和消极情绪, 发现积极情绪下被试的时间折扣率更低, 有更强的选择延迟选项的倾向。实验2运用“模拟天平任务”测量了跨期决策时的维度间差异比较, 检验单维占优模型对情绪影响跨期决策的解释性。结果发现, 维度间差异比较在情绪对跨期决策的影响中起中介作用。实验3a和实验3b分别运用时间和金钱启动策略操纵维度间差异比较过程, 再次验证单维占优模型的解释作用。 结果发现, 情绪对跨期决策的效应随着时间和金钱的启动而消失, 进一步支持了维度间差异比较的中介作用。本研究从决策过程的角度, 揭示了情绪影响跨期决策的心理机制, 并进一步为单维占优模型对跨期决策行为的解释性增加了支持性证据。     

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.     

适应性时间管理：死亡意识对时间知觉和跨期决策的影响

死亡意识是个体对自身死亡必然性的认识; 基于进化适应性的考量, 作者认为具有前瞻性的死亡意识作为人类特有的认知能力和个体生命史的终极坐标, 不仅可能引起恐惧感和防御反应, 更重要的是可以帮助人们做出适应性的时间管理。据此推论, 死亡意识的启动会加强人们对时间有限性的关注, 体验出更强的时间流逝感, 影响人们对时间的评估, 以及人们对不同时间点的成本与收益进行权衡而做出的跨期决策。本研究采用死亡凸显范式启动死亡意识, 通过两个实验探讨了死亡意识、时间知觉和跨期决策三者之间的关系。结果发现, 死亡意识启动使被试低估时间距离, 并表现出较低的跨期决策延迟折扣率, 从而在较小的即时获益与更大的延迟的获益之间更为偏好未来导向的选项。进一步的分析显示, 时间知觉在死亡意识和跨期决策延迟折扣率之间起到部分中介变量的作用。以上的研究结果初步揭示了死亡意识在时间管理上的适应性价值。     

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。     

Time discounting and time preference in animals: A critical review

Animals are an important model for studies of impulsivity and self-control. Many studies have made use of the intertemporal choice task, which pits small rewards available sooner against larger rewards available later (typically several seconds), repeated over many trials. Preference for the sooner reward is often taken to indicate impulsivity and/or a failure of self-control. This review shows that very little evidence supports this assumption; on the contrary, ostensible discounting behavior may reflect a boundedly rational but not necessarily impulsive reward-maximizing strategy. Specifically, animals may discount weakly, or even adopt a long-term rate-maximizing strategy, but fail to fully incorporate postreward delays into their choices. This failure may reflect learning biases. Consequently, tasks that measure animal discounting may greatly overestimate the true discounting and may be confounded by processes unrelated to time preferences. If so, animals may be much more patient than is widely believed; human and animal intertemporal choices may reflect unrelated mental operations; and the shared hyperbolic shape of the human and animal discount curves, which is used to justify cross-species comparisons, may be coincidental. The discussion concludes with a consideration of alternative ways to measure self-control in animals.     

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.     

愤怒情绪对延迟折扣的影响：确定感和控制感的中介作用

本研究基于评估倾向理论, 通过3项实验考察了特定负性情绪(愤怒)对延迟折扣的影响, 并探究确定感和控制感评估倾向在这一关系中的作用。实验1考察愤怒情绪对延迟折扣的影响, 结果发现, 愤怒组被试的延迟满足倾向显著强于恐惧组和控制组。实验2采用实验因果链设计考察确定感和控制感评估倾向在愤怒情绪影响个体延迟折扣中的作用, 结果发现, 愤怒情绪可以有效增强个体的确定感和控制感(实验2a), 同时确定感和控制感能够增强个体的延迟满足倾向(实验2b)。实验3采用中介测量设计考察确定感和控制感评估倾向在愤怒情绪影响个体延迟折扣中的作用, 结果发现, 确定感和控制感评估倾向在愤怒情绪影响个体延迟折扣中起完全中介作用。本研究结果表明, 当个体进行跨期决策时, 体验到与确定感和控制感有关的偶然愤怒情绪会增强其延迟满足倾向。本研究对探究特定负性情绪对个体延迟折扣的影响具有一定的启示意义。     

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.     

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.     

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.     

From individual preference construction to group decisions: Framing effects and group processes

Two choice tasks known to produce framing effects in individual decisions were used to test group sensitivity to framing, relative to that of individuals, and to examine the effect of prior, individual consideration of a decision on group choice. Written post-decision reasons and pre-decision group discussions were analyzed to investigate process explanations of choices made by preexisting, naturalistic groups. For a risky choice problem, a similar framing effect was observed for groups and individuals. For an intertemporal choice task where consumption was either delayed or accelerated, naïve groups (whose members had not preconsidered the decision) showed a framing effect, less discounting in the delay frame, opposite to that observed in individuals. Predecided groups showed a non-significant effect in the other, expected direction. In all cases, process measures better explained variability in choices across conditions than frame alone. Implications for group decision research and design considerations for committee decisions are addressed.