Waiting When Both Certainty and Magnitude Are Increasing: Certainty Overshadows Magnitude

In everyday decision making, people often face decisions with outcomes that differ on multiple dimensions. The trade‐off in preferences between magnitude, temporal proximity, and probability of an outcome is a fundamental concern in the decision‐making literature. Yet, their joint effects on behavior in an experience‐based decision‐making task are understudied. Two experiments examined the relative influences of the magnitude and probability of an outcome when both were increasing over a 10‐second delay. A first‐person shooter video game was adapted for this purpose. Experiment 1 showed that participants waited longer to ensure a higher probability of the outcome than to ensure a greater magnitude when experienced separately and together. Experiment 2 provided a precise method of comparing their relative control on waiting by having each increase at different rates. Both experiments revealed a stronger influence of increasing probability than increasing magnitude. The results were more consistent with hyperbolic discounting of probability than with cumulative prospect theory's decision weight function. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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     

Delay discounting of different outcomes: Review and theory

Steep delay discounting is characterized by a preference for small immediate outcomes relative to larger delayed outcomes and is predictive of drug abuse, risky sexual behaviors, and other maladaptive behaviors. Nancy M. Petry was a pioneer in delay discounting research who demonstrated that people discount delayed monetary gains less steeply than they discount substances with abuse liability. Subsequent research found steep discounting for not only drugs, but other nonmonetary outcomes such as food, sex, and health. In this systematic review, we evaluate the hypotheses proposed to explain differences in discounting as a function of the type of outcome and explore the trait- and state-like nature of delay discounting. We found overwhelming evidence for the state-like quality of delay discounting: Consistent with Petry and others' work, nonmonetary outcomes are discounted more steeply than monetary outcomes. We propose two hypotheses that together may account for this effect: Decreasing Future Preference and Decreasing Future Worth. We also found clear evidence that delay discounting has trait-like qualities: People who steeply discount monetary outcomes steeply discount nonmonetary outcomes as well. The implication is that changing delay discounting for one outcome could change discounting for other outcomes.     

Delay discounting in the pigeon: In search of a magnitude effect

The magnitude effect, where larger outcomes are discounted proportionally less than smaller outcomes, is a well‐established phenomenon in delay discounting by human participants. To this point in the literature magnitude effects have not been reliably evidenced in nonhuman animals. , however, used a concurrent‐chains arrangement with pigeon and found evidence for a magnitude effect. Grace et al. suggested that in many delay discounting experimental arrangements with nonhuman animals (e.g., adjusting amount, adjusting delay) the organism is not given the opportunity to directly compare outcomes of different sizes. They suggest that because of the lack of direct comparison it is difficult for the organism to determine the relative size of each outcome, which in turn mutes the effect of the amount differences between outcomes. As a test of this “comparison hypothesis,” the present experiment was conducted to assess whether the magnitude effect would be evidenced in pigeon when using an adjusting amount procedure where outcomes of different amounts were presented proximally. In the present arrangement, pigeons were presented two choice panels in an operant chamber where each panel was associated with an independent adjusting amount delay discounting task, but with differing outcome amounts (i.e., a 32‐food pellet panel and an 8‐food pellet panel). In this arrangement the choice panels alternated in their availability within a session from trial block to trial block. The present findings indicate no reliable effect of amount, even when the outcomes were proximal and thus readily comparable. This result suggests that the lack of magnitude effect is not driven by the organism's ability to compare the difference in amount between choice alternatives.     

The sign effect,systematic devaluations and zero discounting

The sign effect is the steeper discounting of gains compared to losses. However, we see a greater sign effect on an individual level compared to an aggregate level. In this experiment, we compare discounting of gains and losses on an individual and aggregate level, to explore further details about when and to what extent human adults discount. Thirty-one participants went through a computer-based choice-task procedure of hypothetical monetary gains and losses. The results show clear qualitative differences between discounting of gains and losses, adding empirical data to support the sign effect. The results also support previous findings that show that aggregate and individual results do not always correspond. Further, the within-subject details showing zero discounting or nonsystematic changes concerning losses, replicate earlier studies suggesting that discounting of gains and losses involve different reinforcing contingencies. The present study expands on this research area by including verbal reports, supplementing details about the unobserved reinforcing contingencies. Implications of research on discounting may indicate how to deal with decision-making challenges and might shed light on why predictions about complex decision making sometimes fail.     

人们如何设想未来：未来情景思维对个体心理和行为的影响

未来情景思维(Episodic Future Thinking, EFT)主要指人们基于当前情景或过去经历来思考、想象未来的过程, 是人们对于未来的一种设想。根据已有的行为实验和神经影像学等多个方面的研究结果, 系统论述了未来情景思维的概念和特征, 以及个体过去的生活经历及相应记忆和个体生活目标对其的影响, 通过概括和分析行为和脑神经两方面的证据来论述未来情景思维会对人们具体生活实践产生积极与消极的双向影响。当然, 未来还需要进一步加强未来情景思维研究的广度和深度, 特别是要细化未来情景思维的类型, 探讨未来情景思维可能导致的不适应行为以及影响个体心理和行为的作用机制, 从而为人们如何更积极地适应未来提供更充分的实证证据和理论构想。     

Measuring delay discounting in a crowdsourced sample: An exploratory study

Delay discounting is a measure of preferences for smaller immediate rewards over larger delayed rewards. Discounting has been assessed in many ways; these methods have variably and inconsistently involved measures of different lengths (single vs. multiple items), forced‐choice methods, self‐report methods, online and laboratory assessments, monetary and non‐monetary compensation. The majority of these studies have been conducted in laboratory settings. However, over the past 20 years, behavioral data collection has increasingly shifted online. Usually, these experiments involve completing short tasks for small amounts of money, and are thus qualitatively different than experiments in the lab, which are typically more involved and in a strongly controlled environment. The present study aimed to determine how to best measure future discounting in a crowdsourced sample using three discounting measures (a single shot measure, the 27‐item Kirby Monetary Choice Questionnaire, and a one‐time Matching Task). We examined associations of these measures with theoretically related variables, and assessed influence of payment on responding. Results indicated that correlations between the discounting tasks and conceptually related measures were smaller than in prior laboratory experiments. Moreover, our results suggest providing monetary compensation may attenuate correlations between discounting measures and related variables. These findings suggest that incentivizing discounting measures changes the nature of measurement in these tasks.     

Delay Discounting as a Function of Intrinsic/Extrinsic Religiousness,Religious Fundamentalism,and Regular Church Attendance

Delay discounting occurs when the subjective value of an outcome decreases because its delivery is delayed. Previous research has suggested that the rate at which some, but not all, outcomes are discounted varies as a function of regular church attendance. In the present study, 509 participants completed measures of intrinsic religiousness, extrinsic religiousness, religious fundamentalism, and whether they regularly attended church services. They then completed a delay-discounting task involving five outcomes. Although religiousness was not a significant predictor of discounting for all outcomes, participants scoring high in intrinsic religiousness tended to display less delay discounting than participants scoring low. Likewise, participants scoring high in religious fundamentalism tended to display more delay discounting than participants scoring low. These results partially replicate previous ones in showing that the process of discounting may vary as a function of religiousness. The results also provide some direction for those interested in altering how individuals discount.     

Discounting by Probabilistic Waiting

In everyday life, many probabilistic situations may be characterized as probabilistic waiting. A gambler, for example, bets repeatedly at the racetrack, the casino, or the card table. The gambler may not win on the first try, but if a gamble is repeated enough times, a win is almost certain to occur eventually. If repeated gambles are structured as strings of losses ending in a win (probabilistic waiting) and the amount won is discounted by the delay caused by the series of losses, then strings with many losses will be discounted more than those with fewer losses, thereby causing subjective value of the series of gambles as a whole to increase. The current study used the opposite effect that amount has on the degree of delay and probability discounting as a marker to determine whether people evaluate situations involving probabilistic waiting as they evaluate situations involving delayed outcomes or as situations involving probabilistic outcomes. We find that the more likely a probabilistic waiting situation is to end in reward (e.g., a gamble is repeated indefinitely until reward is obtained), the more that situation conforms to delay discounting; the less likely a probabilistic waiting situation is to end in reward (e.g., a fixed, small number of gambles), the more that situation conforms to probability discounting. We argue that the former situation is applicable to pathological gambling, and that people with steep delay discount functions would therefore be more likely to have gambling problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Reinforcer pathology,probabilistic choice,and medication adherence in patients with multiple sclerosis

The reinforcer pathology model posits that core behavioral economic mechanisms, including delay discounting and behavioral economic demand, underlie adverse health decisions and related clinical disorders. Extensions beyond substance use disorder and obesity, however, are limited. Using a reinforcer pathology framework, this study evaluates medical adherence decisions in patients with multiple sclerosis. Participants completed behavioral economic measures, including delay discounting, probability discounting, and a medication purchase task. A medical decision-making task was also used to evaluate how sensitivity to mild side effect risk and efficacy contributed to the likelihood of taking a hypothetical disease-modifying therapy. Less steep delay discounting and more intense (greater) medication demand were independently associated with greater adherence to the medication decision-making procedure. More generally, the pattern of interrelations between the medication-specific and general behavioral economic metrics was consistent with and contributes to the reinforcer pathology model. Additional research is warranted to expand these models to different populations and health behaviors, including those of a positive health orientation (i.e., medication adherence).     

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     

Examining children's ability to delay reward: Is the delay discounting task a suitable measure?

Discounting the value of delayed rewards has primarily been measured in children with the delay of gratification task and in adolescents and adults with the delay discounting task. In the present study, we assessed the suitability of the delay discounting task as a measure of temporal discounting in children. A sample of 7- to 9-year-olds (N = 98) completed a delay discounting task, a delay of gratification task, a sensation seeking measure, and IQ measures. In addition, teacher-based assessments of attention-deficit/hyperactivity disorder traits were measured. The results indicated that the majority of children produced meaningful data on the discounting task and discounted rewards hyperbolically. Children with an elevated risk of attention-deficit/hyperactivity disorder showed a trend towards discounting future rewards on the delay discounting task more steeply than did those at low risk. However, delay discounting was unrelated to either delay of gratification or sensation seeking. We interpret these results as providing some support for the use of delay discounting as a measure of intertemporal choice in children, although the results also suggest that delay discounting and delay of gratification tasks may tap different processes in this population.     

Delay discounting of monetary gains and losses in adolescents with ADHD: Contribution of delay aversion to choice

Adolescents with attention-deficit/hyperactivity disorder (ADHD) are known to have stronger preferences for smaller immediate rewards over larger delayed rewards in delay discounting tasks than their peers, which has been argued to reflect delay aversion. Here, participants performed a delay discounting task with gains and losses. In this latter condition, participants were asked whether they were willing to wait in order to lose less money. Following the core assumption of the delay aversion model that individuals with ADHD have a general aversion to delay, one would predict adolescents with ADHD to avoid waiting in both conditions. Adolescents (12–17 years) with ADHD (n = 29) and controls (n = 28) made choices between smaller immediate and larger delayed gains, and between larger immediate and smaller delayed losses. All delays (5–25 s) and gains/losses (2–10 cents) were experienced. In addition to an area under the curve approach, a mixed-model analysis was conducted to disentangle the contributions of delay duration and immediate gain/delayed loss amount to choice. The ADHD group chose the immediate option more often than controls in the gain condition, but not in the loss condition. The contribution of delay duration to immediate choices was stronger for the ADHD group than the control group in the gain condition only. In addition, the ADHD group scored higher on self-reported delay aversion, and delay aversion was associated with delay sensitivity in the gain condition, but not in the loss condition. In sum, we found no clear evidence for a general aversion to delay in adolescents with ADHD.     

Hyperbolic modeling and assessment of hypothetical health behaviors during a viral outbreak using crowdsourced samples

The COVID-19 pandemic provided an opportunity to investigate factors related to public response to public health measures, which could help better prepare implementation of similar measures for inevitable future pandemics. To understand individual and environmental factors that influence likelihood in engaging in personal and public health measures, three crowdsourced convenience samples from Amazon Mechanical Turk (MTurk) completed likelihood-discounting tasks of engaging in health behaviors given a variety of hypothetical viral outbreak scenarios. Experiment 1 assessed likelihood of mask wearing for a novel virus. Experiment 2 assessed vaccination likelihood based on efficacy and cost. Experiment 3 assessed likelihood of seeking health care based on number of symptoms and cost of treatment. Volume-based measures and three-dimensional modeling were used to analyze hypothetical decision making. Hypothetical public and personal health participation increased as viral fatality increased and generally followed a hyperbolic function. Public health participation was moderated by political orientation and trust in science, whereas treatment-seeking was only moderated by income. Analytic methods used in this cross-sectional study predicted population-level outcomes that occurred later in the pandemic and can be extended to various health behaviors.     

An overview of Bayesian reasoning in the analysis of delay‐discounting data

Statistical inference (including interval estimation and model selection) is increasingly used in the analysis of behavioral data. As with many other fields, statistical approaches for these analyses traditionally use classical (i.e., frequentist) methods. Interpreting classical intervals and p‐values correctly can be burdensome and counterintuitive. By contrast, Bayesian methods treat data, parameters, and hypotheses as random quantities and use rules of conditional probability to produce direct probabilistic statements about models and parameters given observed study data. In this work, we reanalyze two data sets using Bayesian procedures. We precede the analyses with an overview of the Bayesian paradigm. The first study reanalyzes data from a recent study of controls, heavy smokers, and individuals with alcohol and/or cocaine substance use disorder, and focuses on Bayesian hypothesis testing for covariates and interval estimation for discounting rates among various substance use disorder profiles. The second example analyzes hypothetical environmental delay‐discounting data. This example focuses on using historical data to establish prior distributions for parameters while allowing subjective expert opinion to govern the prior distribution on model preference. We review the subjective nature of specifying Bayesian prior distributions but also review established methods to standardize the generation of priors and remove subjective influence while still taking advantage of the interpretive advantages of Bayesian analyses. We present the Bayesian approach as an alternative paradigm for statistical inference and discuss its strengths and weaknesses.     

Female Prairie Deer Mice Prefer Conspecific Flesh Over Contraspecific Flesh

Hungry adult female deer mice were presented with freshly asphyxiated conspecifics and house mice. The deer mice showed a reliable preference for the conspecific flesh during the first 2 hr of testing, but this preference was attenuated during the following 20 hr of testing. Previous research has shown that male deer mice prefer contraspecific flesh. The preference of female deer mice for conspecific flesh is attributed to their tendency to be more aggressive toward living conspecifics than are male deer mice and their tendency to avoid living contraspecifics more than do male deer mice.     

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.