Delay and Probability Discounting

Green, Leonard; Myerson, Joel; Vanderveldt, Ariana

doi:10.1002/9781118468135.ch13

Cited by 46 publications

(51 citation statements)

References 135 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In both cases, the exponent, s , was significantly less than 1.0 (both p s < .001). This finding is consistent with that obtained in other discounting studies and suggests that a simple hyperbola in which s is equal to 1.0 is insufficient to account for human discounting decision making (Green et al, , ).…”

Section: Resultssupporting

confidence: 90%

“…Delay discounting refers to the devaluation of an outcome as the delay until its receipt increases, and probability discounting refers to the devaluation of an outcome as the odds against its receipt increases. Delay and probability discounting are both well described by a hyperboloid function (Green & Myerson, ) when choosing between an immediate‐certain reward and a delayed or a probabilistic reward:

V = \frac{A}{{((), 1 + b X)}^{s}}

where V is the amount of an immediate‐certain reward equal in subjective value to the delayed or the probabilistic amount, A ; X is either the delay to A (termed D ) or the odds against receiving A (termed θ , where θ = (1 − p )/ p ); and b and s are free parameters that may differ depending on the type of reward, context of reward, and characteristics and history of the organism making the choice (Green, Myerson, & Ostaszewski, ; Green, Myerson, & Vanderveldt, ; Odum, Baumann, & Rimington, ). The expected waiting time for a probabilistic reward over a series of chances, assuming for the moment no waiting time to the first chance, equals θt , where t is the interval between repetitions.…”

Section: Calculation Of Sv Of the 10 Most Probable Strings Of An Evenmentioning

confidence: 99%

See 1 more Smart Citation

Discounting by Probabilistic Waiting

Vanderveldt

Green

Rachlin

2015

Behavioral Decision Making

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Resultssupporting

confidence: 90%

V = \frac{A}{{((), 1 + b X)}^{s}}

Section: Calculation Of Sv Of the 10 Most Probable Strings Of An Evenmentioning

confidence: 99%

Discounting by Probabilistic Waiting

Vanderveldt

Green

Rachlin

2015

Behavioral Decision Making

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many everyday decisions involve outcomes that are both delayed and probabilistic, yet most research on discounting has focused on one dimension or the other (Green, Myerson, & Vanderveldt, 2014; Madden & Bickel, 2010). In two experiments, we examined the discounting of rewards that were both delayed and probabilistic, systematically varying both dimensions in a combined discounting procedure.…”

Section: Discussionmentioning

confidence: 99%

“…Much progress has been made toward understanding choice between rewards that differ on two dimensions (Green & Myerson, & Vanderveldt, 2014; Madden & Bickel, 2010). Considerable research has examined what economists call intertemporal and risky choice, also termed delay and probability discounting.…”

mentioning

confidence: 99%

Discounting of monetary rewards that are both delayed and probabilistic: Delay and probability combine multiplicatively, not additively.

Vanderveldt¹,

Green²,

Myerson³

2015

Journal of Experimental Psychology: Learning, Memory, and Cogni

Self Cite

158

View full text Add to dashboard Cite

The value of an outcome is affected both by the delay until its receipt (delay discounting) and by the likelihood of its receipt (probability discounting). Despite being well-described by the same hyperboloid function, delay and probability discounting involve fundamentally different processes, as revealed, for example, by the differential effects of reward amount. Previous research has focused on the discounting of delayed and probabilistic rewards separately, with little research examining more complex situations in which rewards are both delayed and probabilistic. In two experiments, participants made choices between smaller rewards that were both immediate and certain and larger rewards that were both delayed and probabilistic. Analyses revealed significant interactions between delay and probability factors inconsistent with an additive model. In contrast, a hyperboloid discounting model in which delay and probability were combined multiplicatively provided an excellent fit to the data. These results suggest that the hyperboloid is a good descriptor of decision making in complicated monetary choice situations like those people encounter in everyday life.

show abstract

“…With probability discounting, the subjective value of an outcome decreases as the likelihood of its receipt increases. There are many interesting similarities and differences between delay and probability discounting, and both are well-described by a similar mathematical function (the hyperboloid discounting function; see Green, Myerson, & Vanderveldt, 2014, for a review). Because far less work has examined probability discounting in nonhuman animals, we restrict our review of the animal discounting literature to that of delay discounting.…”

mentioning

confidence: 99%

Delay discounting: Pigeon, rat, human—does it matter?

Vanderveldt¹,

Oliveira

Green

2016

Journal of Experimental Psychology: Animal Learning and Cogniti

Self Cite

117

115

View full text Add to dashboard Cite

Delay discounting refers to the decrease in subjective value of an outcome as the time to its receipt increases. Across species and situations, animals discount delayed rewards, and their discounting is well-described by a hyperboloid function. The current review begins with a comparison of discounting models and the procedures used to assess delay discounting in nonhuman animals. We next discuss the generality of discounting, reviewing the effects of different variables on the degree of discounting delayed reinforcers by nonhuman animals. Despite the many similarities in discounting observed between human and nonhuman animals, several differences have been proposed (e.g., the magnitude effect; nonhuman animals discount over a matter of seconds whereas humans report willing to wait months, if not years before receiving a reward), raising the possibility of fundamental species differences in intertemporal choice. After evaluating these differences, we discuss delay discounting from an adaptationist perspective. The pervasiveness of discounting across species and situations suggests it is a fundamental process underlying decision making.

show abstract

Delay and Probability Discounting

Cited by 46 publications

References 135 publications

Discounting by Probabilistic Waiting

Discounting by Probabilistic Waiting

Discounting of monetary rewards that are both delayed and probabilistic: Delay and probability combine multiplicatively, not additively.

Delay discounting: Pigeon, rat, human—does it matter?

Contact Info

Product

Resources

About