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.     

Greater delay discounting among girls,but not boys,with ADHD correlates with cognitive control

Cognitive neuroscience models suggest both reward valuation and cognitive control contribute to reward-based decision-making. The current study examined the relationship between cognitive control and delay discounting (i.e., choosing smaller, immediate over larger, delayed rewards) in a large sample of boys and girls diagnosed with attention-deficit/hyperactivity disorder (ADHD; N = 95) and typically developing control children (TD; N = 59). Specifically, we examined performance on multiple measures of cognitive control (i.e., Go/No-Go task, Stop Signal task, and Spatial Span task) and delay discounting (i.e., Classic Delay Discounting and Real-Time Delay Discounting tasks), as well as the relationship between these measures. Results indicated that sex moderated the effects of group on task performance. Specifically, girls with ADHD, but not boys with the disorder, exhibited atypical delay discounting of real-time rewards. Results from correlational analyses indicated that delay discounting and cognitive control were not significantly correlated in the overall sample. Multiple regression analyses demonstrated that among girls with ADHD poorer spatial working memory and inhibitory control predicted greater real-time discounting. Collectively, findings provide support for distinct patterns of cognitive control and delay discounting among school-aged girls and boys with ADHD. Additionally, findings suggest that among girls with ADHD, those who exhibit relatively poor working memory and inhibitory control might be a particularly vulnerable subgroup with the greatest propensity to exhibit maladaptive decision-making.     

Effects of mindful eating training on delay and probability discounting for food and money in obese and healthy-weight individuals

Obese individuals tend to behave more impulsively than healthy weight individuals across a variety of measures, but it is unclear whether this pattern can be altered. The present study examined the effects of a mindful eating behavioral strategy on impulsive and risky choice patterns for hypothetical food and money. In Experiment 1, 304 participants completed computerized delay and probability discounting tasks for food-related and monetary outcomes. High percent body fat (PBF) predicted more impulsive choice for food, but not small-value money, replicating previous work. In Experiment 2, 102 randomly selected participants from Experiment 1 were assigned to participate in a 50-min workshop on mindful eating or to watch an educational video. They then completed the discounting tasks again. Participants who completed the mindful eating session showed more self-controlled and less risk-averse discounting patterns for food compared to baseline; those in the control condition discounted similarly to baseline rates. There were no changes in discounting for money for either group, suggesting stimulus specificity for food for the mindful eating condition.     

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     

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.     

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.     

The roles of delay and probability discounting in texting while driving: Toward the development of a translational scientific program

A sample of 109 college students completed a survey to assess how frequently they send or read text messages while driving. In a novel discounting task with a hypothetical scenario in which participants receive a text message while driving, they rated the likelihood of replying to a text message immediately versus waiting to reply until arriving at a destination. The scenario presented several delays to a destination and probabilities of a motor vehicle crash. The likelihood of waiting to reply decreased as a function of both the delay until the destination and the probability of a motor vehicle crash. Self‐reported higher frequencies of texting while driving were associated with greater rates of both delay and probability discounting. The degree of delay discounting was altered as a function of the probability of a motor vehicle crash and vice versa. These results suggest that both delay and probability discounting are important underlying mechanisms of drivers' decision to text while driving.     

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).     

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.     

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.     

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.     

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.     

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.     

Comparison of delay discounting of different outcomes in cigarette smokers,smokeless tobacco users,e-cigarette users,and non-tobacco users

Delay discounting is the process by which a commodity loses value as the delay to its receipt increases. Rapid discounting predicts various maladaptive behaviors including tobacco use. Typically, delay discounting of different outcomes has been compared between cigarette smokers and nonsmokers. To better understand the relationship of delay discounting to different modes of tobacco use, we examined the differences in delay discounting of different outcomes between cigarette smokers, smokeless tobacco users, e-cigarette users, and non-tobacco users. In the present study, all participants completed 8 titrating delay-discounting tasks: $100 gain, $500 gain, $500 loss, alcohol, entertainment, food, a temporary health gain, and a temporary cure from a disease. Non-tobacco users discounted most outcomes less than tobacco users overall; however, there were no differences in discounting among the different types of tobacco users. These results suggest that nicotine consumption of any kind is associated with a higher degree of impulsivity compared to non-tobacco users. Adoption of tobacco products that have been perceived as less harmful (e.g., e-cigarettes) is not associated with a baseline difference or decrease in delay discounting if adopted after a history of cigarette use.     

Area under the curve as a measure of discounting

We describe a novel approach to the measurement of discounting based on calculating the area under the empirical discounting function. This approach avoids some of the problems associated with measures based on estimates of the parameters of theoretical discounting functions. The area measure may be easily calculated for both individual and group data collected using any of a variety of current delay and probability discounting procedures. The present approach is not intended as a substitute for theoretical discounting models. It is useful, however, to have a simple, univariate measure of discounting that is not tied to any specific theoretical framework.     

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.     

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.     

Discounting of food,sex, and money

Discounting is a useful framework for understanding choice involving a range of delayed and probabilistic outcomes (e.g., money, food, drugs), but relatively few studies have examined how people discount other commodities (e.g., entertainment, sex). Using a novel discounting task, where the length of a line represented the value of an outcome and was adjusted using a staircase procedure, we replicated previous findings showing that individuals discount delayed and probabilistic outcomes in a manner well described by a hyperbola-like function. In addition, we found strong positive correlations between discounting rates of delayed, but not probabilistic, outcomes. This suggests that discounting of delayed outcomes may be relatively predictable across outcome types but that discounting of probabilistic outcomes may depend more on specific contexts. The generality of delay discounting and potential context dependence of probability discounting may provide important information regarding factors contributing to choice behavior.     

Episodic Future Thinking Reduces Delay Discounting of Gains and Losses: The Role of Regulatory Focus1,2

We examined the moderating effect of regulatory foci on the efficacy of episodic future thinking in reducing delay discounting. We hypothesized that the impact of imagining positive future events (vs. recent positive events) on delay discounting of gains would be stronger for individuals with a high promotion focus than for those with a high prevention focus (Hypothesis 1). Conversely, the effects of imagining adverse future events (vs. recent negative events) on delay discounting of losses would be stronger for individuals with a high prevention focus than for those with a high promotion focus (Hypothesis 2). We conducted two experiments in which participants, randomly allocated to episodic future thinking (EFT) or episodic recent thinking (ERT) groups, completed a delayed discounting task of gain (Experiment 1) or loss (Experiment 2). Experiment 1 (N = 73) weakly supported Hypothesis 1; Experiment 2 (N = 99) did not support Hypothesis 2. Our findings suggest positive EFT is particularly effective for individuals with a high promotion focus compared to individuals with a high prevention focus, which further reveals how EFT attenuates delay 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.