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.     

Executive Functioning and Delay Discounting of Four Different Outcomes in University Students

The study investigated a potential relationship between level of executive functioning and rates of delay discounting (i.e., the subjective decrease in the value of an outcome if its delivery is delayed). University students completed an executive-functioning questionnaire and then a delay-discounting task involving four different outcomes (money, cigarettes, dating partner, body image). Results showed that the overall measure of executive functioning was a significant predictor of rates of discounting of three of the four outcomes, and approached significance for the fourth outcome. Further, different subscales of executive functioning were significantly correlated with discounting of different outcomes. These results suggest that executive functioning plays a role in discounting of delayed outcomes and that procedures designed to affect either executive function or delay discounting might result in concomitant changes in the other measure.     

Altering Impulsive Decision Making With an Acceptance-Based Procedure

Delay discounting is one facet of impulsive decision making and involves subjectively devaluing a delayed outcome. Steeply discounting delayed rewards is correlated with substance abuse and other problematic behaviors. To the extent that steep delay discounting underlies these clinical disorders, it would be advantageous to find psychosocial avenues for reducing delay discounting. Acceptance-based interventions may prove useful as they may help to decrease the distress that arises while waiting for a delayed outcome. The current study was conducted to determine if a 60–90 minute acceptance-based training would change delay discounting rates among 30 undergraduate university students in comparison to a waitlist control. Measures given at pre- and posttraining included a hypothetical monetary delay discounting task, the Acceptance and Action Questionnaire-II (AAQ-II), and the Distress Tolerance Scale. Those assigned to the treatment group decreased their discounting of delayed money, but not distress intolerance or psychological inflexibility when compared to the waitlist control group. After the waiting period, the control group received the intervention. Combining all participants’ pre- to posttreatment data, the acceptance-based treatment significantly decreased discounting of monetary rewards and increased distress tolerance. The difference in AAQ-II approached significance. Acceptance-based treatments may be a worthwhile option for decreasing delay discounting rates and, consequently, affecting the choices that underlie addiction and other problematic behaviors.     

Discounting: A practical guide to multilevel analysis of choice data

Multilevel modeling provides the ability to simultaneously evaluate the discounting of individuals and groups by examining choices between smaller sooner and larger later rewards. A multilevel logistic regression approach is advocated in which sensitivity to relative reward magnitude and relative delay are considered as separate contributors to choice. Examples of how to fit choice data using multilevel logistic models are provided to help researchers in the adoption of these methods.     

Children's Sensitivity to Cost and Reward in Decision Making across Distinct Domains of Probability,Effort, and Delay

Many behavioral paradigms used to study individuals' decision‐making tendencies do not capture the decision components that contribute to behavioral outcomes, such as differentiating decisions driven toward a reward from decisions driven away from a cost. This study tested a novel decision‐making task in a sample of 403 children (age 9 years) enrolled in an ongoing longitudinal study. The task consisted of three blocks representing distinct cost domains (delay, probability, and effort), wherein children were presented with a deck of cards, each of which consisted of a reward and a cost. Children elected whether to accept or skip the card at each trial. Reward–cost pairs were selected by using an adaptive algorithm to strategically sample the decision space in the fewest number of trials. Using person‐specific regression models, decision preferences were quantified for each cost domain with respect to general tolerance (intercept), as well as parameters estimating the effect of incremental increases in reward or cost on the probability of accepting a card. Results support the relative independence of decision‐making tendencies across cost domains, with moderate correlations observed between tolerance for delay and effort. Specific decision parameters showed unique associations with cognitive and behavioral measures including executive function, academic motivation, anxiety, and hyperactivity. Evidence indicates that sensitivity to reward is an important factor in incentivizing decisions to work harder or wait longer. Dissociating the relative contributions of reward and cost sensitivity in multiple domains may facilitate the identification of heterogeneity in suboptimal decision making. Copyright © 2017 John Wiley & Sons, Ltd.     

Modeling effects of risk and social distance on vaccination choice

Despite vaccines' consistently demonstrated effectiveness, vaccination rates remain suboptimal due to vaccine refusal. Low vaccination rates are particularly problematic for individuals who cannot be vaccinated for medical reasons and thus must rely on herd immunity (i.e., protection of vulnerable individuals due to the high rate of vaccination of other—often socially distant—individuals). The current study uses a novel decision‐making task to examine how three variables impacted participants' highest acceptable probability of side effects to their children: 1) the severity of the side effects their children experience, 2) the social distance to the beneficiary of the vaccination, and 3) the probability that the vaccine will prevent disease for that designated beneficiary. Participants' willingness to risk potential side effects of vaccination systematically decreased as the 1) effectiveness of the vaccination decreased, 2) the beneficiary of the vaccination became more socially distant, and 3) the severity of side effects increased. These data were well‐described by behavioral economic models used to examine the discounting of other health behavior.     

Discounting model selection with area‐based measures: A case for numerical integration

A novel method for analyzing delay discounting data is proposed. This newer metric, a model‐based Area Under Curve (AUC) combining approximate Bayesian model selection and numerical integration, was compared to the point‐based AUC methods developed by Myerson, Green, and Warusawitharana (2001) and extended by Borges, Kuang, Milhorn, and Yi (2016). Using data from computer simulation and a published study, comparisons of these methods indicated that a model‐based form of AUC offered a more consistent and statistically robust measurement of area than provided by using point‐based methods alone. Beyond providing a form of AUC directly from a discounting model, numerical integration methods permitted a general calculation in cases when the Effective Delay 50 (ED50) measure could not be calculated. This allowed discounting model selection to proceed in conditions where data are traditionally more challenging to model and measure, a situation where point‐based AUC methods are often enlisted. Results from simulation and existing data indicated that numerical integration methods extended both the area‐based interpretation of delay discounting as well as the discounting model selection approach. Limitations of point‐based AUC as a first‐line analysis of discounting and additional extensions of discounting model selection were also discussed.     

Impulsive choice and pre‐exposure to delays: iv. effects of delay‐ and immediacy‐exposure training relative to maturational changes in impulsivity

Impulsive choice describes preference for smaller, sooner rewards over larger, later rewards. Excessive delay discounting (i.e., rapid devaluation of delayed rewards) underlies some impulsive choices, and is observed in many maladaptive behaviors (e.g., substance abuse, gambling). Interventions designed to reduce delay discounting may provide therapeutic gains. One such intervention provides rats with extended training with delayed reinforcers. When compared to a group given extended training with immediate reinforcers, delay‐exposed rats make significantly fewer impulsive choices. To what extent is this difference due to delay‐exposure training shifting preference toward self‐control or immediacy‐exposure training (the putative control group) shifting preference toward impulsivity? The current study compared the effects of delay‐ and immediacy‐exposure training to a no‐training control group and evaluated within‐subject changes in impulsive choice across 51 male Wistar rats. Delay‐exposed rats made significantly fewer impulsive choices than immediacy‐exposed and control rats. Between‐group differences in impulsive choice were not observed in the latter two groups. While delay‐exposed rats showed large, significant pre‐ to posttraining reductions in impulsive choice, immediacy‐exposed and control rats showed small reductions in impulsive choice. These results suggest that extended training with delayed reinforcers reduces impulsive choice, and that extended training with immediate reinforcers does not increase impulsive choice.