Delay discounting and probability discounting as related to cigarette smoking status in adults

This study examined relations between adult smokers and non-smokers and the devaluation of monetary rewards as a function of delay (delay discounting, DD) or probability (probability discounting, PD). The extent to which individuals discount value, either as a function of a reward being delayed or probabilistic, has been taken to reflect individual differences in impulsivity. Those who discount most are considered most impulsive. Previous research has shown that adult smokers discount the value of delayed rewards more than adult non-smokers. However, in the one published study that examined probability discounting in adult smokers and non-smokers, the smokers did not discount the value of probabilistic rewards more than the non-smoker controls. From this past research, it was hypothesized that measures of delay discounting would differentiate between smokers and non-smokers but that probability discounting would not. Participants were 54 (25 female) adult smokers (n = 25) and non-smokers (n = 29). The smokers all reported smoking at least 20 cigarettes per day, and the non-smokers reported having never smoked. The results indicated that the smokers discounted significantly more than the non-smokers by both delay and probability. Unlike past findings, these results suggest that both delay and probability discounting are related to adult cigarette smoking; however, it also was determined that DD was a significantly stronger predictor of smoking than PD.     

On the scaling interpretation of exponents in hyperboloid models of delay and probability discounting

Previously, we (McKerchar et al., 2009) showed that two-parameter hyperboloid models ( [Green and Myerson, 2004] and [Rachlin, 2006]) provide significantly better fits to delay discounting data than simple, one-parameter hyperbolic and exponential models. Here, we extend this effort by comparing fits of the two-parameter hyperboloid models to data from a larger sample of participants (N = 171) who discounted probabilistic as well as delayed rewards. In particular, we examined the effects of amount on the exponents in the two hyperboloid models of delay and probability discounting in order to evaluate key theoretical predictions of the standard psychophysical scaling interpretation of these exponents. Both the Rachlin model and the Green and Myerson model provided very good fits to delay and probability discounting of both small and large amounts at both the group and individual levels (all R²s > .97 at the group level; all median R²s > .92 at the individual level). For delay discounting, the exponent in both models did not vary as a function of delayed amount, consistent with the psychophysical scaling interpretation. For probability discounting, however, the exponent in both models increased as the probabilistic amount increased—a finding inconsistent with the scaling interpretation.     

Humans can adopt optimal discounting strategy under real-time constraints

Critical to our many daily choices between larger delayed rewards, and smaller more immediate rewards, are the shape and the steepness of the function that discounts rewards with time. Although research in artificial intelligence favors exponential discounting in uncertain environments, studies with humans and animals have consistently shown hyperbolic discounting. We investigated how humans perform in a reward decision task with temporal constraints, in which each choice affects the time remaining for later trials, and in which the delays vary at each trial. We demonstrated that most of our subjects adopted exponential discounting in this experiment. Further, we confirmed analytically that exponential discounting, with a decay rate comparable to that used by our subjects, maximized the total reward gain in our task. Our results suggest that the particular shape and steepness of temporal discounting is determined by the task that the subject is facing, and question the notion of hyperbolic reward discounting as a universal principle.     

Rats bred for high alcohol drinking are more sensitive to delayed and probabilistic outcomes

Alcoholics and heavy drinkers score higher on measures of impulsivity than nonalcoholics and light drinkers. This may be because of factors that predate drug exposure (e.g. genetics). This study examined the role of genetics by comparing impulsivity measures in ethanol-naive rats selectively bred based on their high [high alcohol drinking (HAD)] or low [low alcohol drinking (LAD)] consumption of ethanol. Replicates 1 and 2 of the HAD and LAD rats, developed by the University of Indiana Alcohol Research Center, completed two different discounting tasks. Delay discounting examines sensitivity to rewards that are delayed in time and is commonly used to assess 'choice' impulsivity. Probability discounting examines sensitivity to the uncertain delivery of rewards and has been used to assess risk taking and risk assessment. High alcohol drinking rats discounted delayed and probabilistic rewards more steeply than LAD rats. Discount rates associated with probabilistic and delayed rewards were weakly correlated, while bias was strongly correlated with discount rate in both delay and probability discounting. The results suggest that selective breeding for high alcohol consumption selects for animals that are more sensitive to delayed and probabilistic outcomes. Sensitivity to delayed or probabilistic outcomes may be predictive of future drinking in genetically predisposed individuals.     

The subjective value of delayed and probabilistic outcomes: Outcome size matters for gains but not for losses

The subjective value of a reward (gain) is related to factors such as its size, the delay to its receipt and the probability of its receipt. We examined whether the subjective value of losses was similarly affected by these factors in 128 adults. Participants chose between immediate/certain gains or losses and larger delayed/probabilistic gains or losses. Rewards of $100 were devalued as a function of their delay (“discounted”) relatively less than $10 gains while probabilistic $100 rewards were discounted relatively more than $10 rewards. However, there was no effect of outcome size on discounting of delayed or probabilistic losses. For delayed outcomes of each size, the degree to which gains were discounted was positively correlated with the degree to which losses were discounted, whereas for probabilistic outcomes, no such correlation was observed. These results suggest that the processes underlying the subjective valuation of losses are different from those underlying the subjective valuation of gains.     

Measurement of delay discounting using trial-by-trial consequences

DELAY DISCOUNTING IN HUMANS WAS INVESTIGATED USING THREE DIFFERENT PROCEDURES: a frequently used discounting procedure with hypothetical rewards and delays; a procedure with hypothetical rewards and delays compressed down to much smaller values; and a contingent procedure in which each choice had a direct consequence. In the contingent procedure, on every trial, participants actually experienced the delay and obtained the reward amount associated with their choice. Each participant was exposed to all three procedures. Orderly temporal discounting patterns were obtained in all three procedures and described well by a hyperbolic model. Comparisons of the data revealed patterns unique to each procedure. The distributions of the discounting measures differed across the three procedures. In the contingent procedure, several subjects showed no discounting, e.g. complete self-control. Procedural factors in studies of impulsivity are discussed, and suggestions are offered for experiments in which the contingent-discounting procedure may prove useful.     

Strain differences in delay discounting using inbred rats

A heightened aversion to delayed rewards is associated with substance abuse and numerous other neuropsychiatric disorders. Many of these disorders are heritable, raising the possibility that delay aversion may also have a significant genetic or heritable component. To examine this possibility, we compared delay discounting in six inbred strains of rats (Brown Norway, Copenhagen, Lewis, Fischer, Noble and Wistar Furth) using the adjusting amount procedure, which provides a measure of the subjective value of delayed rewards. The subjective value of rewards decreased as the delay to receipt increased for all strains. However, a main effect of strain and a strain × delay interaction indicated that some strains were more sensitive to the imposition of delays than others. Fitting a hyperbolic discount equation showed significant strain differences in sensitivity to delay ( k ). These data indicate that there are significant strain differences in delay discounting. All strains strongly preferred the 10% sucrose solution (the reinforcer in the delay discounting task) over water and the amount of sucrose consumed was correlated with sensitivity to delay. Locomotor activity was not correlated with delay discounting behavior. Additional research will be required to disentangle genetic influences from maternal effects and to determine how these factors influence the underlying association between heightened delay discounting and neuropsychiatric disorders.     

Delay discounting of real and hypothetical rewards III: steady-state assessments, forced-choice trials, and all real rewards

Human research in delay discounting has omitted several procedures typical of animal studies: forced-choice trials, consequences following each response, and assessment of stable response patterns. The present study manipulated these procedures across two conditions in which real or hypothetical rewards were arranged. Six college students participated in daily sessions, in which steady-state discounting of hypothetical and real rewards was assessed. No systematic effects of repeated exposure to hypothetical rewards was detected when compared with first day assessments of discounting. Likewise, no systematic effect of reward type (real versus hypothetical) was detected. When combined with previous research failing to detect a difference between hypothetical and potentially real rewards, these findings suggest that assessing discounting of hypothetical rewards in single sessions is a practical and valid procedure in the study of delay discounting.     

Impulsivity, risk taking, and timing

This study examined the relations among measures of impulsivity and timing. Impulsivity was assessed using delay and probability discounting, and self-report impulsivity (as measured by the Barratt Impulsiveness Scale; BIS-11). Timing was assessed using temporal perception as measured on a temporal bisection task and time perspective (as measured by the Zimbardo Time Perspective Inventory). One hundred and forty three college students completed these measures in a computer laboratory. The degree of delay discounting was positively correlated with the mean and range of the temporal bisection procedure. The degree of delay and probability discounting were also positively correlated. Self-reported motor impulsiveness on the BIS-11 was positively correlated with present hedonism and negatively correlated with future orientation on the ZTPI. Self-reported non-planning on the BIS-11 was positively correlated with fatalism on the ZTPI. These results show that people who overestimate the passage of time (perceive time as passing more quickly) hold less value in delayed rewards. They also confirm previous results regarding the relation between delay and probability discounting, as well as highlight similarities in self-report measures of impulsivity and time perspective.     

Tradeoffs among delay, rate, and amount of reinforcement

In Experiment 1, an adjusting-delay procedure was used to measure pigeons' choices between a single delayed reinforcer and a range of different variable-time schedules. Indifference points showed an inverse relation between rate of reinforcement and delay that was well described by a hyperbolic equation. An adjusting-amount procedure was used in Experiment 2, in which pigeons chose between an adjusting amount of food delivered after a 0.5-s delay and 3 s of food delivered after a range of different delays, and the effects of delay were similar to those found in Experiment 1. The results from both experiments indicated that, for pigeons, the strength of a reinforcer decreased rapidly with increasing delay. Estimates of a decay rate parameter in the hyperbolic equation were similar to those found in other studies with pigeons, but the rates of temporal discounting were three or four times faster than those found in studies with rats, suggesting a possible species difference.     

Discounting of sequences of delayed rewards of different amounts

The main purpose of this study was to determine whether the magnitude effect is present in cases where delayed sequences of rewards are discounted. The magnitude effect refers to the inverse relationship between the amount of a reward and the steepness of temporal discounting. This study was conducted with a computer program to estimate the indifference points, which served as indicators of the present subjective value of delayed sequences of small and large rewards. In the indifference point the subjective value of a single, immediate reward was equal to the subjective value of the delayed sequence (or to the value of a single delayed reward). As a control condition, we added an experimental task involving choices between single immediate and single delayed rewards. The experiment showed that the sequences of large rewards are discounted less steeply than are the sequences of small rewards. This finding suggests that the magnitude effect is present within the delayed sequences of rewards. In addition, when outcomes are relatively large, the results suggest that a single reward is discounted less steeply than the sequence of a total nominal value equal to this single reward. However, for relatively small rewards, the difference is not statistically significant. The less steep discounting of sequences of large rewards may explain the reward-bundling effect, which refers to less steep discounting of longer sequences than of shorter ones: longer sequences usually have greater overall nominal value. The present study was conducted on hypothetical rewards, and the results should be validated using real rewards.     

The present values of delayed rewards are approximately additive

In two experiments, human subjects were asked to estimate their present values of single delayed rewards and their present values of temporal sequences of three rewards. Present values were solicited by asking subjects to indicate an amount of money v for which they would be indifferent between receiving v at the end of the session and receiving the delayed reward(s). A procedure was used for which responding the true value of v was the optimal strategy, and the actual payoff that each subject received was determined by one randomly selected trial. In Experiment 1 (n=29) each delayed reward was 9.90 dollars in cash. In Experiment 2 (n=19) the delayed rewards were dated 15 dollars gift certificates to a local restaurant. In both experiments, the present values of the sequences were approximately equal to the sums of the present values of their component rewards. The presence of outliers suggests that a few subjects may have valued sequences less than the sums of their single rewards. Effects of a preference for uniform sequences, if any, were too small to be detected. Discounting of sequences was well fit by a parallel hyperbolic discounting equation, consistent with Mazur's [Mazur, J.E., 1986. Choice between single and multiple delayed reinforcers. J. Exp. Anal. Behav. 46 (1), 67-77] results using multiple reinforcers.     

Delay discounting and gambling

Delay discounting describes the decline in the value of a reinforcer as the delay to that reinforcer increases. A review of the available studies revealed that steep delay discounting is positively correlated with problem or pathological gambling. One hypothesis regarding this correlation derives from the discounting equation proposed by Mazur (1989). According to the equation, steeper discounting renders the difference between fixed-delayed rewards and gambling-like variable-delayed rewards larger; with the latter being more valuable. The present study was designed to test this prediction by first assessing rats’ impulsive choices across four delays to a larger-later reinforcer. A second condition quantified strength of preference for mixed- over fixed-delays, with the duration of the latter adjusted between sessions to achieve indifference. Strength of preference for the mixed-delay alternative is given by the fixed delay at indifference (lower fixed-delay values reflect stronger preferences). Percent impulsive choice was not correlated with the value of the fixed delay at indifference and, therefore, the prediction of the hyperbolic model of gambling was not supported. A follow-up assessment revealed a significant decrease in impulsive choice after the second condition. This shift in impulsive choice could underlie the failure to observe the predicted correlation between impulsive choice and degree of preference for mixed- over fixed delays.     

Delay and probability discounting as related to different stages of adolescent smoking and non-smoking

This study examined relations between different patterns of adolescent cigarette smoking and discounting of monetary rewards due to delay (delay discounting) and probabilistic uncertainty (probability discounting). The study also examined the relation between smoking and the number of peer friends who smoke and level of parent education. Participants were 55 adolescents (28 females) between 14 and 16 years of age who were categorized according to the following patterns of smoking behavior: "never smokers" (n=19; 10 females) who had not tried even one cigarette; "triers" (n=17; 9 females) who had recently tried cigarettes for the first time; and "current smokers" (n=19; 9 females) who smoked a minimum of one cigarette every week for at least 6 months prior to data collection. It was hypothesized that current smokers would discount more than those who had never smoked. No specific hypotheses were made for participants only trying cigarettes. Unexpectedly, results indicated no differences in discounting between the current smokers and never smokers. However, the trier group discounted probabilistic rewards significantly more than the never- and current-smoker groups. Also, triers and current smokers both reported having more friends who smoked than never smokers, and fathers of never smokers had significantly more education than fathers of either triers or current smokers. These results suggest that impulsive discounting may be more related to adolescents trying cigarettes than to their becoming regular smokers, whereas number of peer friends who smoke and parent level of education seem to differentiate between those who have smoked to some extent (triers and current smokers) and those who have not even tried cigarettes (never smokers).     

Delay and Probability Discounting of Sexual and Monetary Outcomes in Individuals with Cocaine Use Disorders and Matched Controls

Individuals with cocaine use disorders are disproportionately affected by HIV/AIDS, partly due to higher rates of unprotected sex. Recent research suggests delay discounting of condom use is a factor in sexual HIV risk. Delay discounting is a behavioral economic concept describing how delaying an event reduces that event’s value or impact on behavior. Probability discounting is a related concept describing how the uncertainty of an event decreases its impact on behavior. Individuals with cocaine use disorders (n = 23) and matched non-cocaine-using controls (n = 24) were compared in decision-making tasks involving hypothetical outcomes: delay discounting of condom-protected sex (Sexual Delay Discounting Task), delay discounting of money, the effect of sexually transmitted infection (STI) risk on likelihood of condom use (Sexual Probability Discounting Task), and probability discounting of money. The Cocaine group discounted delayed condom-protected sex (i.e., were more likely to have unprotected sex vs. wait for a condom) significantly more than controls in two of four Sexual Delay Discounting Task partner conditions. The Cocaine group also discounted delayed money (i.e., preferred smaller immediate amounts over larger delayed amounts) significantly more than controls. In the Sexual Probability Discounting Task, both groups showed sensitivity to STI risk, however the groups did not differ. The Cocaine group did not consistently discount probabilistic money more or less than controls. Steeper discounting of delayed, but not probabilistic, sexual outcomes may contribute to greater rates of sexual HIV risk among individuals with cocaine use disorders. Probability discounting of sexual outcomes may contribute to risk of unprotected sex in both groups. Correlations showed sexual and monetary results were unrelated, for both delay and probability discounting. The results highlight the importance of studying specific behavioral processes (e.g., delay and probability discounting) with respect to specific outcomes (e.g., monetary and sexual) to understand decision making in problematic behavior.     

The evolution of social discounting in hierarchically clustered populations

The expression of a social behaviour may affect the fitness of actors and recipients living in the present and in the future of the population. When there is a risk that a future reward will not be experienced in such a context, the value of that reward should be discounted; but by how much? Here, we evaluate social discount rates for delayed fitness rewards to group of recipients living at different positions in both space and time than the actor in a hierarchically clustered population. This is a population where individuals are grouped into families, families into villages, villages into clans, and so on, possibly ad infinitum. The group-wide fitness effects are assumed to either increase or decrease the fecundity or the survival of recipients and can be arbitrarily extended in space and time. We find that actions changing the survival of individuals living in the future are generally more strongly discounted than fecundity-changing actions for all future times and that the value of future rewards increases as individuals live longer. We also find that delayed fitness effects may not only be discounted by a constant factor per unit delay (exponential discounting), but that, as soon as there is localized dispersal in a population, discounting per unit delay is likely to fall rapidly for small delays and then slowly for longer delays (hyperbolic discounting). As dispersal tends to be localized in natural populations, our results suggest that evolution is likely to favour individuals that express present-biased behaviours and that may be time-inconsistent with respect to their group-wide effects.     

Relations between delay discounting and low to moderate gambling, cannabis, and alcohol problems among university students

Research has generally demonstrated that the discounting of delayed rewards is associated with severity of addictive behaviour. Less clear, however, is the relative strength of the relation for specific addictive behaviours. University students (N = 218) completed a computerized delay discounting task for hypothetical monetary rewards, and gambling, cannabis, and alcohol problem severity was assessed. A multiple regression analysis revealed that while the overall model was significant, only gambling problem severity accounted for delay discounting scores above and beyond cannabis and alcohol problem severity. The results support the hypothesis that delay discounting of hypothetical monetary rewards is more associated with gambling than other addictive behaviour problems, including substance use problems.     

Insulin,Central Dopamine D2 Receptors,and Monetary Reward Discounting in Obesity

Animal research finds that insulin regulates dopamine signaling and reward behavior, but similar research in humans is lacking. We investigated whether individual differences in body mass index, percent body fat, pancreatic β-cell function, and dopamine D2 receptor binding were related to reward discounting in obese and non-obese adult men and women. Obese (n = 27; body mass index>30) and non-obese (n = 20; body mass index<30) adults were assessed for percent body fat with dual-energy X-ray absorptiometry and for β-cell function using disposition index. Choice of larger, but delayed or less certain, monetary rewards relative to immediate, certain smaller monetary rewards was measured using delayed and probabilistic reward discounting tasks. Positron emission tomography using a non-displaceable D2-specific radioligand, [¹¹C](N-methyl)benperidol quantified striatal D2 receptor binding. Groups differed in body mass index, percent body fat, and disposition index, but not in striatal D2 receptor specific binding or reward discounting. Higher percent body fat in non-obese women related to preference for a smaller, certain reward over a larger, less likely one (greater probabilistic discounting). Lower β-cell function in the total sample and lower insulin sensitivity in obese related to stronger preference for an immediate and smaller monetary reward over delayed receipt of a larger one (greater delay discounting). In obese adults, higher striatal D2 receptor binding related to greater delay discounting. Interestingly, striatal D2 receptor binding was not significantly related to body mass index, percent body fat, or β-cell function in either group. Our findings indicate that individual differences in percent body fat, β-cell function, and striatal D2 receptor binding may each contribute to altered reward discounting behavior in non-obese and obese individuals. These results raise interesting questions about whether and how striatal D2 receptor binding and metabolic factors, including β-cell function, interact to affect reward discounting in humans.