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Cited by 1,676Decision-Making and Behavioral EconomicsNeural and Behavioral Psychology StudiesExperimental Behavioral Economics Studies

A Discounting Framework for Choice With Delayed and Probabilistic Rewards.

Open access
Green, Leonard, Myerson, Joel·2004·Psychological Bulletin
DOI 10.1037/0033-2909.130.5.769PMC PMC1382186
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Abstract

When choosing between delayed or uncertain outcomes, individuals discount the value of such outcomes on the basis of the expected time to or the likelihood of their occurrence. In an integrative review of the expanding experimental literature on discounting, the authors show that although the same form of hyperbola-like function describes discounting of both delayed and probabilistic outcomes, a variety of recent findings are inconsistent with a single-process account. The authors also review studies that compare discounting in different populations and discuss the theoretical and practical implications of the findings. The present effort illustrates the value of studying choice involving both delayed and probabilistic outcomes within a general discounting framework that uses similar experimental procedures and a common analytical approach.

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Written from the paper’s full text.

TL;DR

This integrative review argues that both delayed and probabilistic rewards are well described by the same hyperbola-like discounting function, but that a single-process account is undermined by dissociations such as opposite amount effects. It reviews group differences and practical implications while calling for models that handle combined delayed, probabilistic, positive, and negative outcomes.

Key findings

  • A hyperbola-like function (Equation 3) fit temporal discounting better than exponential or simple hyperbola functions; for group median delayed $10,000 rewards, Equation 3 had R² = .977, versus .815 for the exponential and .937 for the hyperbola.
  • Probability discounting was also better described by a hyperbola-like function (Equation 5) than a simple hyperbola (Equation 4); in Green et al. (1999a) Experiment 1, 87% of 68 participants had exponent estimates below 1.0, replicated in Experiment 2 with 77% of 30 participants.
  • Amount had opposite effects on temporal and probability discounting: smaller delayed rewards were discounted more steeply, whereas smaller probabilistic rewards were discounted less steeply; Myerson et al. (2003) found amount had no significant effect on the temporal exponent, but the probability exponent increased significantly with amount, while temporal k decreased with amount and probability h did not change significantly.
  • Dissociations inconsistent with a single-process account included inflation affecting temporal but not probability discounting, Chinese participants discounting delayed rewards more steeply than Japanese while Japanese discounted probabilistic rewards more steeply than Chinese, and substance abusers showing steeper delayed monetary discounting than controls.

Methods

  • Design: Integrative review of experimental literature on temporal and probability discounting, using parallel experimental procedures and a common analytical approach.
  • Data/sample: Reviewed studies with humans and nonhuman animals, including hypothetical and real monetary rewards, nonmonetary commodities, different age and cultural groups, substance abusers, gamblers, and psychometric measures; the authors also reanalyzed data from other laboratories.
  • Main analysis: Compared fits of exponential, simple hyperbola, and hyperbola-like discounting functions using R² and full-versus-reduced model comparisons, and discussed area-under-the-curve as a single index of discounting.

Limitations

  • Stated: Age-related parameter findings must be interpreted cautiously because of small sample sizes and lack of independence in estimates of k and s; correlational studies generally need larger samples, and the reliability of behavioral discounting measures needs assessment.
  • Stated: A two-parameter function complicates use of a single discounting measure because differences may reflect either the rate parameter or the exponent, and discounting rate parameters are highly skewed; estimates of the two parameters are not independent.
  • Evident: As an integrative review, many conclusions depend on reanalyses of published group medians and cross-study comparisons rather than a single prospective design; some explanations for amount effects on weighting functions are described by the authors as post hoc.

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Registry

Crossref · 10.1037/0033-2909.130.5.769

Cites

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Statistics

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Claims the paper makes

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  • Findingnone given
    § Abstract

    The same form of hyperbola-like function describes discounting of both delayed and probabilistic outcomes.

    “although the same form of hyperbola-like function describes discounting of both delayed and probabilistic outcomes, a variety of recent findings are inconsistent with a single-process account.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The subjective value of a reward is increasingly discounted from its nominal amount as the delay until or the odds against receiving the reward increase, and individuals choose the reward with the higher discounted subjective value.
  • Findingcitation
    § Abstract

    The finding that temporal discounting is better described by a hyperbola than by an exponential has been replicated in study after study.

    “The finding that temporal discounting is better described by a hyperbola than by an exponential has been replicated in study after study (e.g., Green, Myerson, & McFadden, 1997; Kirby, 1997; Kirby & Maraković, 1995; Kirby & Santiesteban, 2003; Rachlin et al., 1991; Simpson & Vuchinich, 2000).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Green, Myerson, & McFadden, 1997

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    • cites Kirby, 1997

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    • cites Kirby & Maraković, 1995

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  • Findingcitation
    § Abstract

    Studies of both human and nonhuman subjects have obtained evidence of preference reversals with procedures other than the one used by Green et al. (1981) and Green, Fristoe, and Myerson (1994).

    “studies of both human and nonhuman subjects have obtained evidence of preference reversals with other types of procedures (Ainslie & Haendel, 1983; Ainslie & Herrnstein, 1981; Green & Estle, 2003; Kirby & Herrnstein, 1995; Mazur, 1987; Rachlin & Green, 1972; Rodriguez & Logue, 1988).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Ainslie & Haendel, 1983

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    • cites Ainslie & Herrnstein, 1981

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    • cites Green & Estle, 2003

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  • Findingcitation
    § Abstract

    Adding an exponent produced a statistically significant increase in the proportion of variance accounted for in the group median data depicted in Figure 6.

    “With respect to the group median data depicted in Figure 6, Myerson and Green (1995) reported that adding an exponent produced a statistically significant increase in the proportion of variance accounted for.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Myerson and Green (1995)

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  • Findingown data
    § Abstract

    Equation 3 provided the best fit to the data in Figure 6 (R2 = .977).

    “It can be seen that Equation 3 (solid curve) provided the best fit to the data in Figure 6 (R2 = .977).”
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  • Classified as probably not a substantial claim. 28
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    Findingcitation
    § Abstract

    Equation 3 provided significantly better fits to individual discounting data from a majority of children (12-year-olds) as well as to individual data from a substantial proportion of older adults.

    “In addition, Green, Myerson, and Ostaszewski (1999b) showed that Equation 3 provided significantly better fits to individual discounting data from a majority of children (12-year-olds) as well as to individual data from a substantial proportion of older adults.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Green, Myerson, and Ostaszewski (1999b)

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    Findingcitation
    § Abstract

    In Green et al. (1981), pigeons offered a choice further in advance of the outcome period strongly preferred the larger, later reward, whereas when the choice was offered shortly before the outcome period, each pigeon reversed preference and strongly preferred the smaller, sooner reward.

    “when the choice was offered further in advance of the outcome period, analogous to Time 1 in Figures 1 and 2, each pigeon strongly preferred the larger, later reward. When the choice was offered shortly before the outcome period, analogous to Time 2, each pigeon showed a reversal in preference, now strongly preferring the smaller, sooner reward.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Green et al. (1981)

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    Findingown data
    § Abstract

    In Figure 6, the hyperbola (Equation 2) provided a much better fit than the exponential, although it also tended to systematically overpredict subjective values at briefer delays and underpredict subjective values at longer delays.

    “The hyperbola (Equation 2; dashed-and-dotted curve) provided a much better fit, although it, too, tended to systematically overpredict the subjective values at briefer delays and underpredict the subjective values at longer delays.”
    Quote in the paperNot a substantial claim

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    Findingcitation
    § Abstract

    With age, there was a developmental decrease in how steeply delayed rewards were discounted, as indicated by decreases in the value of the k parameter, as well as a systematic increase in the value of the s parameter.

    “With age, there was a developmental decrease in how steeply delayed rewards were discounted, as indicated by decreases in the value of the k parameter with age, as well as a systematic increase in the value of the s parameter with age, suggesting developmental changes in the way that time and amount are scaled.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Green et al. (1999b)

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    Findingown data
    § Abstract

    Both the exponential and simple hyperbola systematically overpredict subjective values at briefer delays and underpredict subjective values at longer delays, whereas the fits of Equation 3 reveal no such systematic bias.

    “In this regard, it should be noted that both the exponential and simple hyperbola systematically overpredict subjective values at briefer delays and underpredict subjective values at longer delays. In contrast, the fits of Equation 3 reveal no such systematic bias (see Figure 6 for an example).”
    Quote in the paperSubstantial claim

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    Findingown data
    § Abstract

    In Figure 6, the exponential (Equation 1) provided the poorest fit, systematically overpredicting subjective values at briefer delays and underpredicting subjective values at longer delays.

    “As may be seen, the exponential (Equation 1; dashed curve) provided the poorest fit, systematically overpredicting the subjective values at briefer delays and under-predicting the subjective values at longer delays.”
    Quote in the paperNot a substantial claim

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    Findingown data
    § Abstract

    In Figure 6, the exponential accounts for 81.5% of the variance, whereas the hyperbola accounts for 93.7%.

    “In Figure 6, for example, the exponential (Equation 1) accounts for 81.5% of the variance, whereas the hyperbola (Equation 2) accounts for 93.7% (for another particularly striking example, see Rachlin et al., 1991, Figure 7).”
    Quote in the paperNot a substantial claim

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    Findingnone given
    § Abstract

    The results of studies with both humans and nonhuman animals clearly violate the stationarity assumption and are consistent with the discounting account.

    “The results of studies with both humans and nonhuman animals clearly violate the stationarity assumption and are consistent with the discounting account.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The subjective value of a reward is increasingly discounted from its nominal amount as the delay until or the odds against receiving the reward increase, and individuals choose the reward with the higher discounted subjective value.

  • May combine two claims.

    Findingcitation
    § Abstract

    In the two studies to compare fits of the three discounting functions to individual data, the hyperbola-like discounting function provided statistically adequate fits to the data from all participants, whereas both the exponential and the hyperbola failed to describe some of the individual data.

    “In the two studies to compare fits of the three discounting functions to individual data, the hyperbola-like discounting function provided statistically adequate fits to the data from all the participants, whereas both the exponential and the hyperbola failed to describe some of the individual data (Myerson & Green, 1995; Simpson & Vuchinich, 2000).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Myerson & Green, 1995

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    • cites Simpson & Vuchinich, 2000

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    Findingcitation
    § Abstract

    The 2 participants who were tested with the real rewards first showed very little discounting of either real or hypothetical rewards, suggesting the possibility of an order effect, although the sample size was too small to evaluate this statistically.

    “The 2 participants who were tested with the real rewards first, however, showed very little discounting of either real or hypothetical rewards, suggesting the possibility of an order effect (although the sample size was too small to evaluate this statistically).”
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    • cites Johnson and Bickel (2002)

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    Findingcitation
    § Abstract

    For the 4 participants who were tested with hypothetical rewards before real rewards, a hyperbolic discounting function (Equation 2) generally provided good fits, although 1 participant's data were better fit by the exponential function (Equation 1).

    “For the 4 participants who were tested with hypothetical rewards before real rewards, a hyperbolic discounting function (Equation 2) generally provided good fits (although 1 participant’s data were better fit by the exponential function, Equation 1).”
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    • cites Johnson and Bickel (2002)

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    Findingcitation
    § Abstract

    Johnson and Bickel (2002) reported that for 5 of the 6 participants, there were no systematic differences in discount rate between the real reward and hypothetical reward conditions, although 1 participant did show reliably steeper discounting of the real rewards.

    “Johnson and Bickel (2002) reported that for 5 of the 6 participants, there were no systematic differences in discount rate between the real reward and hypothetical reward conditions, although 1 participant did show reliably steeper discounting of the real rewards.”
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    • cites Johnson and Bickel (2002)

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    Findingown data
    § Abstract

    Our analysis of group median data for both real and hypothetical reward data revealed that the hyperbola-like discounting function accounted for more than 93% of the variance and provided a significantly better fit than a simple hyperbola.

    “Our analysis of the group median data for both the real and hypothetical reward data revealed that the hyperbola-like discounting function (solid curve in Figure 9) accounted for more than 93% of the variance and provided a significantly better fit than a simple hyperbola (dashed curve).”
    Quote in the paperSubstantial claim

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    Findingown data
    § Abstract

    The same form of two-parameter hyperbola-like function that describes the discounting of delayed and probabilistic gains (Equations 3 and 5) described the discounting of probabilistic losses, as well as delayed losses.

    “The same form of two-parameter hyperbola-like function that describes the discounting of delayed and probabilistic gains (Equations 3 and 5) described the discounting of probabilistic losses, as well as delayed losses.”
    Quote in the paperSubstantial claim

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    Findingown data
    § Abstract

    When the authors fit Equation 3 to the Murphy et al. data, it provided excellent descriptions of both the losses (R2 = .968) and the gains (R2 = .994), significantly better than the simple hyperbola, most notably for losses.

    “when we fit Equation 3 to the Murphy et al. data, it provided excellent descriptions of both the losses (R2 = .968) and the gains (R2 = .994), significantly better, in fact, than the simple hyperbola, most notably with respect to the data for losses.”
    Quote in the paperSubstantial claim

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    Findingown data
    § Abstract

    For delayed heroin rewards by participants with heroin addiction, Equation 3 accounted for R2 = .866, compared with .336 for Equation 1 and .771 for Equation 2.

    “In the case of the discounting of delayed heroin rewards by participants with heroin addiction, for example, the proportion of variance accounted for (R2) by the fit of Equation 3 was .866, compared with .336 and .771 for the fits of Equations 1 and 2, respectively.”
    Quote in the paperSubstantial claim

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    Findingcitation
    § Abstract

    There was a gain-loss asymmetry (probabilistic gains discounted more steeply than losses of equal amounts) when the probabilistic amounts were large, but statistically equivalent discounting of gains and losses was observed when the amounts were small.

    “There was a gain-loss asymmetry (i.e., probabilistic gains were discounted more steeply than losses of equal amounts) when the probabilistic amounts were large, but statistically equivalent discounting of gains and losses was observed when the amounts were small.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductcitation
    § Abstract

    These results must be interpreted cautiously because of the small sample sizes and the lack of independence in the estimates of the k and s parameters.

    “Although these results must be interpreted cautiously because of the small sample sizes and the lack of independence in the estimates of the k and s parameters (Myerson, Green, & Warusawitharana, 2001), these systematic (and meaningful) changes in the parameters with age suggest that across this age range, differences in temporal discounting are primarily quantitative in nature and do not reflect”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Myerson, Green, & Warusawitharana, 2001

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  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationcitation
    § Abstract

    The parameter s may represent the nonlinear scaling of amount and/or time and is generally equal to or less than 1.0.

    “The parameter s may represent the nonlinear scaling of amount and/or time and is generally equal to or less than 1.0 (Myerson & Green, 1995).”
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    • cites Myerson & Green, 1995

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    Interpretationcitation
    § Abstract

    If Equations 2 or 3 provide the best description, such findings are consistent with the view that choices between rewards available at different times are really choices between different rates of reward.

    “Alternatively, if Equations 2 or 3 were to provide the best description, such findings would be consistent with the view that choices between rewards available at different times are really choices between different rates of reward.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Abstract

    Both Equations 2 and 3 are consistent with the view that choices between rewards available at different times are really choices between different rates of reward.

    “Thus, both Equations 2 and 3 are consistent with the view that choices between rewards available at different times are really choices between different rates of reward.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § Abstract

    Economists and researchers in decision analysis typically assume that temporal discounting is exponential.

    “Economists and researchers in decision analysis typically assume that temporal discounting is exponential (i.e., subjective value decreases by a constant percentage per unit time).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Abstract

    A major alternative proposal is that the temporal discounting function is a hyperbola.

    “One major alternative proposal is that the discounting function is a hyperbola (e.g., Mazur, 1987):”
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    • cites Mazur, 1987

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    Interpretationreasoning
    § Abstract

    According to the discounting account, preference reversals occur because the subjective value of the larger, later reward decreases more slowly as its receipt becomes more delayed than does the subjective value of the smaller, sooner reward.

    “According to the discounting account represented in Figure 1, preference reversals occur because the subjective value of the larger, later reward decreases more slowly as its receipt becomes more delayed than does the subjective value of the smaller, sooner reward.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The subjective value of a reward is increasingly discounted from its nominal amount as the delay until or the odds against receiving the reward increase, and individuals choose the reward with the higher discounted subjective value.

  • May combine two claims.

    Interpretationreasoning
    § Abstract

    It follows mathematically that the amount of an immediate reward judged equal in value to a delayed reward is given by Ad/(1 + D/m)^(q/r), which is equivalent to Equation 3.

    “It follows mathematically that the amount of an immediate reward that is judged equal in value to a delayed reward is given by the expression Ad/(1 + D/m)q/r. This is equivalent to Equation 3 with k = 1/m and s = qlr (Myerson & Green, 1995).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Myerson & Green, 1995

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    • The authors state this as an assumption: The perceived rate equals the perceived amount divided by the perceived delay, where the perceived magnitude of each variable (amount and delay) is a power function of the actual magnitude.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Abstract

    A hyperbola-like discounting function in which the denominator of the hyperbola is raised to a power, s, has been proposed.

    “A hyperbola-like discounting function in which the denominator of the hyperbola is raised to a power, s, has also been proposed (Green, Fry, & Myerson, 1994):”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Green, Fry, & Myerson, 1994

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    Interpretationreasoning
    § Abstract

    The finding that the same hyperbola-like function describes temporal discounting in all individual participants suggests that individual differences in discounting are primarily quantitative and may reflect variations on fundamentally similar choice processes.

    “The finding that the same hyperbola-like function, Equation 3, describes temporal discounting in all individual participants is theoretically significant because it suggests that individual differences in discounting are primarily quantitative and may reflect variations on fundamentally similar choice processes.”
    Quote in the paperSubstantial claim

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    Premisecitation
    § Abstract

    Rachlin et al. (1991) proposed that the value of probabilistic rewards may be described by a hyperbola discounting function of the same form as that used for delayed rewards.

    “Rachlin et al. (1991) proposed that the value of probabilistic rewards may be described by a discounting function of the same form (i.e., a hyperbola) as that which they used to describe delayed rewards:”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Rachlin et al. (1991)

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    Interpretationreasoning
    § Abstract

    Thus, a hyperbola-like discounting function describes the discounting of different commodities as well as discounting of monetary rewards by different age groups.

    “Thus, a hyperbola-like discounting function describes the discounting of different commodities as well as discounting of monetary rewards by different age groups.”
    Quote in the paperSubstantial claim

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    Interpretationcitation
    § Abstract

    This finding is predicted by prospect theory and by the hyperbola-like form of the probability discounting function when the exponent is less than 1.0.

    “This finding, which is predicted by prospect theory (Kahneman & Tversky, 1979), is also predicted by the hyperbola-like form of the probability discounting function when the exponent is less than 1.0.”
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    • cites Kahneman & Tversky, 1979

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    Premisecitation
    § Abstract

    Myerson et al. (2003) found that amount of reward had no significant effect on the exponent of the temporal discounting function in either of two relatively large samples, but the exponent of the probability discounting function increased significantly with amount in both samples.

    “Amount of reward had no significant effect on the exponent of the temporal discounting function in either of two relatively large samples (both Ns > 100). In contrast, the exponent of the probability discounting function increased significantly with the amount of reward in both samples.”
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    • cites Myerson et al., 2003

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    Premisecitation
    § Abstract

    Ostaszewski et al. (1998) showed that including an exponent in the discounting function significantly improved the fit, with Equation 5 accounting for significantly more variance than Equation 4.

    “Ostaszewski et al. (1998) evaluated Equations 4 and 5, and they showed that including an exponent in the discounting function significantly improved the fit (i.e., Equation 5 accounted for significantly more of the variance than Equation 4).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Ostaszewski et al. (1998)

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    Premisecitation
    § Abstract

    Ostaszewski et al. (1998) suggested that the discounting of probabilistic rewards may be better described by a hyperbola-like form analogous to Equation 3.

    “Alternatively, Ostaszewski et al. (1998) suggested that the discounting of probabilistic rewards may be better described by a hyperbola-like form analogous to that for delayed rewards (i.e., Equation 3):”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Ostaszewski et al. (1998)

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    Premisecitation
    § Abstract

    When Equation 5 was fit to individual data from the 68 participants in Experiment 1, the estimated value of s was less than 1.0 in 87% of cases, significantly more than expected by chance if the exponent were 1.0.

    “When Equation 5 was fit to the individual data from the 68 participants in Experiment 1, the estimated value of 5 was less than 1.0 in 87% of the cases, significantly more than would be expected by chance if the exponent were actually 1.0”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Green et al. (1999a)

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  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationreasoning
    § Abstract

    Preference reversals with probabilistic rewards might be explained by assuming that the subjective value of the smaller, less risky reward decreases more than the subjective value of the larger, more risky reward if the probabilities of winning decrease.

    “Similarly, preference reversals with probabilistic rewards might be explained by assuming that the subjective value of the smaller, less risky reward decreases more than the subjective value of the larger, more risky reward if the probabilities of winning decrease.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § Abstract

    Behavior is risk averse when the odds against receiving a reward are low (probability high) but not when the odds against are high (probability low).

    “Second, the nature of the deviation is such that behavior is risk averse when the odds against receiving a reward are low (i.e., when the probability of reward is high) but not when the odds against are high (i.e., when the probability of reward is low).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § Abstract

    Preference reversals with delayed rewards occur because the subjective value of the smaller, sooner reward increases more than the subjective value of the larger, later reward as delays to both are decreased equally.

    “Recall that it was argued previously that preference reversals with delayed rewards occur because the subjective value of the smaller, sooner reward increases more than the subjective value of the larger, later reward as the delays to both are decreased equally.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationcitation
    § Abstract

    The finding that the same form of mathematical function describes both temporal and probability discounting raises the possibility, but does not prove, that they both reflect a single discounting process.

    “The finding that the same form of mathematical function describes both temporal and probability discounting raises the possibility (although it does not prove) that they both reflect a single discounting process”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Green & Myerson, 1996

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    • cites Rachlin et al., 1986, 1994

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    • cites Stevenson, 1986

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    Premisecitation
    § Abstract

    Green et al. (1999a) showed that as amount increased from $200 to $100,000, probabilistic rewards were discounted more and more steeply, whereas for delayed rewards, the degree of discounting decreased from $200 to $10,000, with little systematic change when amount increased further.

    “Green et al. (1999a) also examined discounting of three other hypothetical reward amounts and showed that as amount increased from $200 to $100,000, probabilistic rewards were discounted more and more steeply, whereas for delayed rewards, the degree of discounting decreased from $200 to $10,000, with little systematic change when amount was increased further.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Green et al. (1999a)

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    Interpretationcitation
    § Abstract

    Ostaszewski et al.'s findings are inconsistent with both forms of single-process accounts.

    “Thus, Ostaszewski et al.’s (1998) findings are inconsistent with both forms of single-process accounts.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Ostaszewski et al.’s (1998)

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  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract

    Reynolds et al. (2004) reported that how steeply an individual discounted delayed rewards was a significantly better predictor of whether he or she was a smoker than how steeply the individual discounted probabilistic rewards.

    “Reynolds et al. (2004) reported that how steeply an individual discounted delayed rewards was a significantly better predictor of whether he or she was a smoker than how steeply the individual discounted probabilistic rewards.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Reynolds et al. (2004)

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  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning
    § Abstract

    These problems may be avoided by localizing magnitude effects not in the value function but in the weighting functions for probabilistic and delayed outcomes and by assuming that amount affects these weighting functions in different ways.

    “These problems may be avoided by localizing magnitude effects, not in the value function, but rather in the weighting functions for probabilistic and delayed outcomes and by assuming that amount affects these weighting functions in different ways.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Individuals making choices involving delayed rewards are actually evaluating rates of reward.

  • May combine two claims.

    Premisecitation
    § Abstract

    Ostaszewski (1997) found that with hypothetical probabilistic rewards, rate of discounting did not differ between extraverts and introverts or between high and low impulsive groups.

    “with hypothetical probabilistic rewards, the rate of discounting did not differ between extraverts and introverts or between high and low impulsive groups”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Ostaszewski (1997)

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  • May combine two claims.

    Premisecitation
    § Abstract

    Ostaszewski et al. (1998) showed that inflation affects temporal discounting but does not affect probability discounting.

    “For example, Ostaszewski et al. (1998) showed that inflation affects temporal discounting but does not affect probability discounting.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Ostaszewski et al. (1998)

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation
    § Abstract

    These results suggest that temporal and probability discounting are dissociable by cultural processes, contrary to the predictions of single-process theories.

    “These results suggest that temporal and probability discounting are dissociable by cultural processes, contrary to the predictions of single-process theories.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premiseown data
    § Abstract

    Despite cultural differences, Equations 3 and 5 provided accurate descriptions of the discounting of all three groups, with median proportion of variance accounted for by fits to individual data greater than .930 on both tasks.

    “It also is noteworthy that despite the cultural differences, Equations 3 and 5 provided accurate descriptions of the discounting of all three groups: For each group, the median proportion of variance accounted for by fits to individual data was greater than .930 on both tasks.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Du et al., 2002

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Bickel et al. (1999) found that current cigarette smokers, who discounted delayed monetary rewards more steeply than nonsmokers, tended to discount hypothetical amounts of cigarettes even more steeply than money.

    “Bickel et al. (1999) found that current cigarette smokers, who discounted delayed monetary rewards more steeply than nonsmokers, tended to discount hypothetical amounts of cigarettes even more steeply than money”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Bickel et al. (1999)

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract

    Bickel et al. (1999) found steeper discounting by current smokers than by those who had never smoked cigarettes.

    “although Bickel et al. (1999) found steeper discounting by current smokers than by those who had never smoked cigarettes”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Bickel et al. (1999)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing).

    Interpretationcitation
    § Abstract

    Given that larger delayed amounts are discounted less steeply than smaller amounts, it would seem to follow that low-income individuals would discount a given amount less steeply than high-income individuals.

    “Given that larger delayed amounts are discounted less steeply than smaller amounts (e.g., Green et al., 1997), it would seem to follow that low-income individuals would discount a given amount less steeply than high-income individuals.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Green et al., 1997

      Not checked in the free run.

    • The authors state this as an assumption: The same nominal amount of money would be worth more to a low-income individual than to a high-income individual.

  • May combine two claims.

    Premisecitation
    § Abstract

    Petry (2001b) reported that individuals with a primary diagnosis of pathological gambling with a history of substance abuse discounted delayed rewards more steeply than pathological gamblers without a history of substance abuse, who in turn showed steeper discounting than controls.

    “individuals with a primary diagnosis of pathological gambling with a history of substance abuse discounted delayed rewards more steeply than pathological gamblers without a history of substance abuse, who in turn, showed steeper discounting than controls (Petry, 2001b).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Petry, 2001b

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Madden et al. (1997) found that people addicted to heroin, who were more impulsive than controls with respect to monetary rewards, tended to discount hypothetical delayed amounts of heroin even more steeply than they discounted money.

    “Madden et al. (1997) found that people addicted to heroin, who were more impulsive than controls with respect to monetary rewards, tended to discount hypothetical delayed amounts of heroin even more steeply than they discounted money”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Madden et al. (1997)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationcitation
    § Abstract

    Petry's (2001a) finding that currently abstinent alcoholics show rates of discounting intermediate between currently drinking alcoholics and nonalcoholic controls is consistent with the idea that discounting rates may predict success at giving up cigarettes and alcohol.

    “Petry’s (2001 a) finding that currently abstinent alcoholics show rates of discounting intermediate between those of currently drinking alcoholics and nonalcoholic controls is also consistent with the idea that discounting rates may predict success at giving up cigarettes and alcohol”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Petry (2001 a)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Pathological gambling is typically associated with financial problems as well as with other psychiatric disorders.

    “pathological gambling is typically associated with financial problems as well as with other psychiatric disorders (e.g., Ibáñez et al., 2001 ).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Ibáñez et al., 2001

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract

    Mitchell (1999) observed no differences between smokers and nonsmokers in the discounting of probabilistic rewards.

    “Interestingly, Mitchell (1999) observed no differences between smokers and nonsmokers in the discounting of probabilistic rewards”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Mitchell (1999)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    In Du et al. (2002), the Chinese discounted delayed rewards more steeply than the Japanese, but the Japanese discounted probabilistic rewards more steeply than the Chinese.

    “More relevant to the question of whether a single process is involved in both, the Chinese discounted delayed rewards more steeply than the Japanese, but the Japanese discounted probabilistic rewards more steeply than the Chinese.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Du et al., 2002

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation
    § Abstract

    Petry and Casarella (1999) reported that substance abusers who were also problem gamblers discounted delayed monetary rewards more steeply than those with only substance abuse problems, who in turn showed steeper temporal discounting than those with neither substance abuse nor gambling problems.

    “They reported that substance abusers who were also problem gamblers discounted delayed monetary rewards more steeply than those who had only substance abuse problems, who in turn, showed steeper temporal discounting than those with neither substance abuse nor gambling problems.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Petry and Casarella (1999)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Abstract

    Reynolds et al. (2004) found that smokers discounted probabilistic rewards more steeply than nonsmokers.

    “although Reynolds et al. (2004) did find that smokers discounted probabilistic rewards more steeply than nonsmokers.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Reynolds et al. (2004)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Holt, Green, and Myerson (2003) reported no statistically significant differences in temporal discounting between college students categorized as gamblers and nongamblers on the SOGS, although group differences in probability discounting were observed.

    “Holt, Green, and Myerson (2003), however, reported no statistically significant differences in temporal discounting between college students categorized as gamblers and nongamblers on the basis of their scores on the South Oaks Gambling Screen (SOGS; Lesieur & Bloom, 1987), although group differences in probability discounting were observed.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Holt, Green, and Myerson (2003)

      Not checked in the free run.

    • cites Lesieur & Bloom, 1987

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Madden et al. (1997) obtained significant correlations between EPQ Impulsivity scores and behavioral discounting measures: for hypothetical monetary rewards, correlations between k-parameter values and Impulsivity scores were .40 for the addiction group and .39 for the control group.

    “For hypothetical monetary rewards, the correlations between k-parameter values and Impulsivity scores were .40 for the addiction group and .39 for the control group.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Madden et al. (1997)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Murphy et al. (2001) found that gains were discounted more steeply than losses, and this difference was observed at the individual level as well as at the group level.

    “Gains were discounted more steeply than losses, and this difference was observed at the individual level as well as at the group level”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Murphy et al. (2001)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisenone given
    § Abstract

    The sample sizes in studies involving individuals addicted to heroin tended to be larger than those involving smokers and drinkers.

    “the sample sizes in the studies involving individuals addicted to heroin tended to be larger than those involving smokers and drinkers.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § Abstract

    Petry (2001a) found a significant correlation between a psychometric measure of impulsivity and k-parameter values when hypothetical delayed monetary rewards were studied but not when hypothetical delayed alcohol rewards were studied.

    “Petry (2001a) found a significant correlation between a psychometric measure of impulsivity (Eysenck, Pearson, Easting, & Allsopp, 1985) and k-parameter values when hypothetical delayed monetary rewards were studied but not when hypothetical delayed alcohol rewards were studied.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Petry (2001a)

      Not checked in the free run.

    • cites Eysenck, Pearson, Easting, & Allsopp, 1985

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation
    § Abstract

    Chapman (1996; Chapman & Elstein, 1995) reported that discount rates for delayed health and monetary outcomes are poorly correlated, providing further evidence against a unitary impulsivity construct.

    “In addition, Chapman (1996 ; Chapman & Elstein, 1995) has reported that discount rates for delayed health and monetary outcomes are poorly correlated, providing further evidence against a unitary impulsivity construct.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Chapman (1996 ; Chapman & Elstein, 1995)

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation
    § Abstract

    Holt et al. (2003) found that gamblers discounted probabilistic rewards less steeply than nongamblers, suggesting that gamblers are impulsive in the sense that they are less affected by risk than nongamblers.

    “Gamblers discounted probabilistic rewards less steeply than nongamblers, suggesting that gamblers are impulsive in the sense that they are less affected by risk than nongamblers.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Holt et al. (2003)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S1 (asserted). May combine two claims.

    Interpretationreasoning
    § Abstract

    If temporal and probability discounting both reflect impulsivity, then a negative correlation is predicted.

    “If temporal and probability discounting both reflect impulsivity, then a negative correlation is predicted.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Abstract

    Mitchell (1999) reported that smokers were significantly more impulsive than individuals who had never smoked on 19 of 28 personality measures linked to impulsivity.

    “Mitchell (1999) reported that smokers were significantly more impulsive than individuals who had never smoked on 19 of 28 personality measures that have been linked to impulsivity in the literature.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Mitchell (1999)

      Not checked in the free run.

  • May combine two claims. The quote only partly states this claim.

    Premisecitation
    § Abstract

    Odum and Rainaud (2003) found that using participants who reported no problems with food, alcohol, or money, there was no difference in the rates at which hypothetical amounts of food and alcohol were discounted, although both types of reward were discounted more steeply than money.

    “Odum and Rainaud found that there was no difference in the rates at which hypothetical amounts of food and alcohol were discounted, although both types of reward were discounted more steeply than money.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Odum and Rainaud (2003)

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation
    § Abstract

    The finding that alcoholics discount alcohol more steeply than money is similar to findings with heroin and cigarette smokers and provides further evidence that abused substances are discounted more steeply than money, at least by substance abusers.

    “This finding is similar to that observed with participants addicted to heroin (Madden et al., 1997) and cigarette smoking participants (Bickel et al., 1999), and it provides further evidence that abused substances are discounted more steeply than money, at least by the substance abusers.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Madden et al., 1997

      Not checked in the free run.

    • cites Bickel et al., 1999

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Holt et al. (2003) found that both gambling and nongambling groups discounted large delayed amounts more steeply than small delayed amounts, whereas both groups discounted large probabilistic amounts less steeply than small probabilistic amounts.

    “Both groups discounted large delayed amounts more steeply than small delayed amounts, whereas both groups discounted large probabilistic amounts less steeply than small probabilistic amounts.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Holt et al. (2003)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Petry (2001a) found that both alcoholics and nonalcoholics discounted alcohol more steeply than money.

    “alcoholics and nonalcoholics both discounted alcohol more steeply than money.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Petry (2001a)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Conclusion

    With probabilistic rewards, amount did not affect the value of the discount rate parameter h but was directly related to the value of the exponent.

    “whereas with probabilistic rewards, amount did not affect the value of the discount rate parameter h but was directly related to the value of the exponent (Myerson et al., 2003).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Myerson et al., 2003

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Conclusion

    Although individuals generally prefer larger to smaller, sooner to later, and certain to probabilistic rewards, these basic facts are not sufficient to predict choice when these attributes are combined.

    “For example, although individuals generally prefer larger to smaller, sooner to later, and certain to probabilistic rewards, these basic facts are not sufficient to predict choice when these attributes are combined.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § Conclusion

    The prediction that the exponent should not be influenced by amount was confirmed for delayed rewards, but it was not supported in the case of probabilistic rewards where larger amounts were associated with larger exponents.

    “Although this prediction was confirmed for delayed rewards, it was not supported in the case of probabilistic rewards where larger amounts were associated with larger exponents (Myerson et al., 2003).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Myerson et al., 2003

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation
    § Abstract

    The difference between discounting rates for gains and losses depends on the amounts involved and does so in opposite ways for the two types of discounting.

    “Estle et al. ’s (2003) finding that the difference between discounting rates for gains and losses depends on the amounts involved and does so in opposite ways for the two types of discounting.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Estle et al. (2003)

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Conclusion

    These and other dissociations are inconsistent with the claim that one type of discounting is more fundamental, and they imply that there may be at least two distinct discounting processes.

    “These and other dissociations are inconsistent with the claim that one type of discounting is more fundamental, and they imply that there may be at least two distinct discounting processes.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Inflation appears to affect how steeply delayed rewards are discounted but does not affect the discounting of probabilistic rewards.
    • Rests on an assumption: Amount of reward has opposite effects on the rates of temporal and probability discounting.

  • May combine two claims.

    Interpretationreasoning
    § Conclusion

    In the present case, temporal and probability discounting data were both analyzed using discounting functions of the same mathematical form, and the different patterns of results obtained strongly suggest that different processes are involved.

    “In the present case, temporal and probability discounting data were both analyzed using discounting functions of the same mathematical form, and the different patterns of results obtained strongly suggest that different processes are involved.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Conclusion

    The findings provide some support for the mathematical model proposed by Myerson and Green (1995), but the model does not predict the entire pattern of results.

    “These findings provide some support for the mathematical model proposed by Myerson and Green (1995), but the model does not predict the entire pattern of results.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Myerson and Green (1995)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Chapman (1996) failed to observe a sign by magnitude interaction, although magnitude and sign effects were observed for both delayed health and money outcomes.

    “In contrast, Chapman (1996), in a study examining discounting of hypothetical gains and losses of health and money outcomes, failed to observe a sign by magnitude interaction, although magnitude and sign effects were observed for both delayed health and money outcomes.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Chapman (1996)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract

    Baker et al. (2003) reported that discounting of delayed gains is more affected by magnitude than is discounting of delayed losses, such that the difference between discounting rates for gains and losses was lower at higher amounts.

    “Baker et al. (2003) also have reported that discounting of delayed gains is more affected by magnitude than is discounting of delayed losses, such that the difference between discounting rates for gains and losses was lower at higher amounts.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Baker et al. (2003)

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Conclusion

    Neither the Myerson and Green (1995) nor the Prelec and Loewenstein model can account for the pattern of results in both the delayed and probabilistic domains.

    “Thus, neither the Myerson and Green (1995) nor the Prelec and Loewenstein model can account for the pattern of results in both the delayed and probabilistic domains.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Myerson and Green (1995)

      Not checked in the free run.

    • cites Prelec and Loewenstein

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning
    § Conclusion

    The pattern of domain differences revealed by the discounting framework illustrates the value of this approach in uncovering important empirical constraints that must be taken into account by future theoretical models.

    “Nevertheless, the pattern of domain differences revealed by the discounting framework illustrates the value of this approach in uncovering important empirical constraints that must be taken into account by future theoretical models.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationreasoning
    § Abstract

    If the gain-loss asymmetry increases with amount in one choice domain, then it would be predicted that the asymmetry would also increase with amount in the other domain.

    “Thus, if the gain-loss asymmetry increases with amount in one choice domain (e.g., probability discounting), then it would be predicted that the asymmetry would also increase with amount in the other domain (e.g., temporal discounting).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Conclusion

    The finding that temporal and probability discounting functions have the same mathematical form suggests that there may be similarities in the underlying decision-making processes, and could even indicate that the same process is involved in the discounting of both delayed and probabilistic rewards.

    “The finding that temporal and probability discounting functions have the same mathematical form suggests that there may be similarities in the underlying decision-making processes—and could even indicate that the same process is involved in the discounting of both delayed and probabilistic rewards.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § Conclusion

    With delayed rewards, amount was inversely related to the value of the discount rate parameter k but had no effect on the value of the exponent s.

    “Recall that with delayed rewards, amount was inversely related to the value of the discount rate parameter k but had no effect on the value of the exponent s (e.g., Myerson & Green, 1995)”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Myerson & Green, 1995

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Conclusion

    The exponents for temporal and probability discounting may well differ, but within each choice domain, the exponent should not be influenced by the amount of the reward.

    “Therefore, the exponents for temporal and probability discounting may well differ, but within each choice domain, the exponent should not be influenced by the amount of the reward.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationcitation
    § Conclusion

    The finding that for delayed rewards, exponents are independent of amount as well as the finding that the exponents for delayed and probabilistic rewards are different are both consistent with the view that the process of estimating the subjective value of a delayed reward involves fundamental psychophysical scaling processes and that such scaling is captured by the exponent parameter.

    “That is, the finding that for delayed rewards, exponents are independent of amount as well as the finding that the exponents for delayed and probabilistic rewards are different (Myerson et al., 2003) are both consistent with the view that the process of estimating the subjective value of a delayed reward involves fundamental psychophysical scaling processes and that such scaling is captured by the”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Myerson et al., 2003

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Interpretationreasoning
    § Conclusion

    Such findings raise the possibility that differences in impulsivity may underlie these behavioral problems and that assessment based on behavioral discounting measures may be able to predict who is at risk and who is most likely to benefit from interventions.

    “Such findings raise the possibility that differences in impulsivity may underlie these behavioral problems and that assessment based on behavioral discounting measures may be able to predict who is at risk and who is most likely to benefit from interventions.”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: Groups of individuals with certain kinds of behavioral problems (e.g., substance abusers) discount delayed rewards more steeply than controls.

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationreasoning
    § Abstract

    Because the value function describes the effect of amount on the value of both delayed and probabilistic outcomes, changes in amount will have similar effects on both temporal and probability discounting.

    “Because the value function describes the effect of amount on the value of both delayed and probabilistic outcomes, this implies that changes in amount will have similar effects on both temporal and probability discounting.”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: Prospect theory locates the source of gain-loss asymmetries in the value function.
88 of 88

  • The authors state this as an assumption.

    The subjective value of a reward is increasingly discounted from its nominal amount as the delay until or the odds against receiving the reward increase, and individuals choose the reward with the higher discounted subjective value.

    “This perspective assumes that the subjective value of a reward is increasingly discounted from its nominal amount as the delay until or the odds against receiving the reward increase and that individuals choose the reward with the higher (discounted) subjective value (e.g., Ainslie, 1992; Green & Myerson, 1993; Kagel, Battalio, & Green, 1995; Loewenstein & Elster, 1992; Rachlin, 1989).”

  • The authors state this as an assumption.

    Value is directly proportional to rate of reward.

    “if one assumes that value is directly proportional to rate of reward (Rachlin, 1971), then discounting will have the form of Equation 2.”

  • The authors state this as an assumption.

    Even an immediate reward involves some minimal delay, m, such that t = D + m, where D is the stated or programmed delay.

    “We assume first, that V = bA/t, where b is the proportionality constant and; is the actual delay, and second, that even an immediate reward involves some minimal delay, m, such that t = D + m, where D is the stated or programmed delay.”

  • The authors state this as an assumption.

    The perceived rate equals the perceived amount divided by the perceived delay, where the perceived magnitude of each variable (amount and delay) is a power function of the actual magnitude.

    “Myerson and Green (1995), therefore, assumed that the perceived rate would be equal to the perceived amount divided by the perceived delay, where the perceived magnitude of each variable (amount and delay) would be a power function of the actual magnitude.”

  • The authors state this as an assumption.

    Individuals making choices involving delayed rewards are actually evaluating rates of reward.

    “Because this derivation is based on the assumption that individuals making choices involving delayed rewards are actually evaluating rates of reward”

  • The paper relies on this without support.

    The same value function applies in both temporal and probability discounting.

    “Because the same value function applies in both temporal and probability discounting”

  • The authors state this as an assumption.

    The same nominal amount of money would be worth more to a low-income individual than to a high-income individual.

    “It might be assumed that the same nominal amount would be worth more to a low-income individual.”

  • The paper relies on this without support.

    Prospect theory locates the source of gain-loss asymmetries in the value function.

    “prospect theory locates the source of gain-loss asymmetries in the value function”

  • The paper relies on this without support.

    There is no evidence as to whether negative outcomes are discounted less steeply than positive outcomes when both are present in the same choice situation.

    “There is no evidence, however, as to whether negative outcomes are discounted less steeply than positive outcomes when both are present in the same choice situation.”

  • The paper relies on this without support.

    One such anomaly is the reversal in preference that may occur when the point in time at which choices between smaller, sooner and larger, later rewards is varied.

    “One such anomaly is the reversal in preference that may occur when the point in time at which choices between smaller, sooner and larger, later rewards is varied.”

  • The paper relies on this without support.

    The other anomaly is the observation that preference may reverse when the probabilities of smaller, more certain and larger, less certain rewards are both reduced.

    “The other anomaly is the observation that preference may reverse when the probabilities of smaller, more certain and larger, less certain rewards are both reduced.”

  • The paper relies on this without support.

    Inflation appears to affect how steeply delayed rewards are discounted but does not affect the discounting of probabilistic rewards.

    “For example, inflation appears to affect how steeply delayed rewards are discounted but does not affect the discounting of probabilistic rewards.”

  • The paper relies on this without support.

    Amount of reward has opposite effects on the rates of temporal and probability discounting.

    “More striking, amount of reward has opposite effects on the rates of temporal and probability discounting.”

  • The paper relies on this without support.

    Groups of individuals with certain kinds of behavioral problems (e.g., substance abusers) discount delayed rewards more steeply than controls.

    “A number of studies have shown that groups of individuals with certain kinds of behavioral problems (e.g., substance abusers) discount delayed rewards more steeply than controls.”
14 of 14

Claims other papers make about this one

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Cites

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Research works printed but not linked: 4

  1. Ainslie, 1983, The motives of the will., 119
  2. Barratt, 1985, Impulsiveness defined within a systems model of personality., Vol. 5, 113
  3. Barratt, 1995, Impulsiveness., 91
  4. Houston, 1982, Some learning rules for acquiring information., 140

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Related

Authors
Green, L., & Myerson, J.
Affiliations
Washington University in St. Louis (US)
ORCID
Venue
Psychological Bulletin
Publisher
American Psychological Association (APA)
Published
2004
Volume
130
Issue
5
Pages
769-792
ISSN
  • 0033-2909 (ISSN-L)
  • 1939-1455
DOI
10.1037/0033-2909.130.5.769
PMC
PMC1382186
OpenAlex
W1994077204
Semantic Scholar
5cd41d64265acb80c97db49684e1811561631c98
Cited by
1,676
References
136
Citations by year
2026: 51 · 2025: 74 · 2024: 73 · 2023: 64 · 2022: 68 · 2021: 95 · 2020: 141 · 2019: 94 · 2018: 86 · 2017: 113 · 2016: 108 · 2015: 109 · 2014: 94 · 2013: 92 · 2012: 86
FWCI
1.83
Type
journal article
Language
en
Open access
Locations
  • Psychological Bulletin (publishedVersion)
  • PubMed (publishedVersion)
  • PubMed Central (acceptedVersion)
Funders
National Institute of Mental Health (R01MH055308, MH55308)
Topics
  • Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
  • Social Sciences › Safety Research › Experimental Behavioral Economics Studies
Keywords
delay discounting, probabilistic discounting, expected delay, hyperbolic discounting, individual differences, decision making under uncertainty
MeSH terms
Choice Behavior, Humans, Reward, Time Factors, Models, Statistical

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-09.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-09.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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