The arithmetic of discounting

Killeen, Peter R.

doi:10.1002/jeab.130

Cited by 22 publications

(22 citation statements)

References 38 publications

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“…The minimal (maximum entropy) assumption about a distribution on the positive line, when we know only its mean μ, is f(x) = e -x/μ /μ. Assume that this is the delay of reinforcement gradient (Killeen, 2011 gives reasons), and that it applies to conditioned stimuli (CSs) as well as responses (as suggested in Killeen, 2001bKilleen, , 2009Killeen, , 2015. The total strength of a CS of duration d accumulates as the integral of the decay function from x = 0 to d. The average strength is that integral divided by d: Fig.…”

Section: Appendix a Regulation Modelmentioning

confidence: 99%

Bidding for delayed rewards: Accumulation as delay discounting, delay discounting as regulation, demand functions as corollary

Killeen

2019

J Exper Analysis Behavior

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In the accumulation paradigm animals press one manipulandum to accumulate pellets or seconds of access to food, and then press another manipulandum, or run some distance, to collect it. The accumulation may be interpreted as delay discounting, with the animals adjusting the distal amount to compensate for its distance or delay. The amount accumulated before being collected is a linear function of the distance or time that the experimental paradigm stipulates for collecting it. That linear function follows from the Unit‐Price/Unit‐Amount axiom. The inverse of the linear compensation functions gives a delay‐discount hyperbola. The advantages of the accumulation paradigm and analytic framework for delay discounting studies are noted. Compensation functions are then derived from a behavioral regulation model, which generalizes them to contexts where the individual's budget for response cost becomes over‐taxed. In turn, such compensation/regulation models lead directly to representative demand functions. In sum, regulation models provide a theoretical grounding for demand functions, compensation functions, and delay discounting hyperbolas. The parameter that links them is the unit amount k, the slope of the compensation function and of the discount function, the setpoint for consumption in a regulation model, and the ideal quantity consumed at minimal price in a demand analysis.

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Section: Appendix a Regulation Modelmentioning

confidence: 99%

Bidding for delayed rewards: Accumulation as delay discounting, delay discounting as regulation, demand functions as corollary

Killeen

2019

J Exper Analysis Behavior

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“…An exception may be taken for those questionnaires that equate non-monetary reward amounts with monetary equivalents out of $100 (e.g., if a respondent indicated 100 pizza slices is worth $100, then item 11 would be mathematically equivalent to 11 pizza slices now or 30 pizza slices in 7 days). Note, however, that non-monetary equivalents to amounts used in monetary discounting may not be discounted similarly (Killeen, 2009(Killeen, , 2015.…”

Section: Limitations and Considerationsmentioning

confidence: 99%

Automating Scoring of Delay Discounting for the 21- and 27-Item Monetary Choice Questionnaires

et al. 2016

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Delay discounting describes the process wherein rewards lose value as a function of their delayed receipt; how quickly rewards lose value is termed the rate of delay discounting. Rates of delay discounting are robust predictors of much behavior of societal importance. One efficient approach to obtaining a human subject's rate of delay discounting is via the 21-and 27-item Monetary Choice Questionnaires, brief dichotomous choice tasks that assess preference between small immediate and larger delayed monetary outcomes. Unfortunately, the scoring procedures for the Monetary Choice Questionnaires are rather complex, which may serve as a barrier to their use. This report details a freely available Excel-based spreadsheet tool that automatically scores Monetary Choice Questionnaire response sets, using both traditional and contemporary/ advanced approaches. An overview of the Monetary Choice Questionnaire and its scoring algorithm is provided. We conclude with general considerations for using the spreadsheet tool.

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“…However, there have been inconsistent findings across studies, likely due in part to variability in characteristics of the task. Specifically, delay discounting is influenced by reward magnitude (Myerson & Green, 1995), delay length, type of reward (e.g., monetary versus non-monetary) (Chapman & Elstein, 1995; Demurie, Roeyers, Baeyens, & Sonuga-Barke, 2013; Friedel, DeHart, Madden, & Odum, 2014; Killeen, 2015), and whether the rewards are immediately consumable (e.g., food versus money) (Forzano, Michels, Sorama, Etopio, & English, 2014). We recently found ADHD-associated increases in delay discounting to be specific to girls and specific to a novel real-time discounting task involving immediately consumable rewards, but not a classic monetary discounting task, suggesting that inconsistent findings across studies may also be due to task differences or individual characteristics such as sex (Rosch & Mostofsky, 2016).…”

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confidence: 99%

Investigating the Impact of Cognitive Load and Motivation on Response Control in Relation to Delay Discounting in Children with ADHD

Martinelli

Mostofsky

Rosch

2016

J Abnorm Child Psychol

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Attention-deficit/hyperactivity disorder (ADHD) is characterized by deficits in impulse control across a range of behaviors, from simple actions to those involving complex decision-making (e.g., preference for smaller-sooner versus larger later rewards). This study investigated whether changes in motor response control with increased cognitive load and motivational contingencies are associated with decision-making in the form of delay discounting among 8-12 year old children with and without ADHD. Children with ADHD (n = 26; 8 girls) and typically developing controls (n = 40; 11 girls) completed a standard go/no-go (GNG) task, a GNG task with motivational contingencies, a GNG task with increased cognitive load, and two measures of delay discounting: a real-time task in which the delays and immediately consumable rewards are experienced in real-time, and a classic task involving choices about money at longer delays. Children with ADHD, particularly girls, exhibited greater delay discounting than controls during the real-time discounting task, whereas diagnostic groups did not significantly differ on the classic discounting task. The effect of cognitive load on response control was uniquely associated with greater discounting on the real-time task for children with ADHD, but not for control children. The effect of motivational contingencies on response control was not significantly associated with delay discounting for either diagnostic group. The findings from this study help to inform our understanding of the factors that influence deficient self-control in ADHD, suggesting that impairments in cognitive control may contribute to greater delay discounting in ADHD.

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The arithmetic of discounting

Cited by 22 publications

References 38 publications

Bidding for delayed rewards: Accumulation as delay discounting, delay discounting as regulation, demand functions as corollary

Bidding for delayed rewards: Accumulation as delay discounting, delay discounting as regulation, demand functions as corollary

Automating Scoring of Delay Discounting for the 21- and 27-Item Monetary Choice Questionnaires

Investigating the Impact of Cognitive Load and Motivation on Response Control in Relation to Delay Discounting in Children with ADHD

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