Discounting of past outcomes.

Drug use, abuse, and addiction are common behavioral manifestations of impulsiveness. A useful and popular laboratory analogue of impulsiveness is temporal discounting. Temporal discounting refers to the reduction in the present, subjective value of outcomes that are temporally distant in the future. The extensive literature on temporal discounting indicates hyperbolic discounting, the magnitude effect, and the sign effect. It is possible that the same principles may apply to other dimensions of psychological distance, including past temporal distance. The purpose of the present study was to examine the possibility that outcomes in the past are discounted hyperbolically and at a similar rate to outcomes in the future. The magnitude and sign effects were also examined in past discounting. Indifference points of college students were determined from a paper-and-pencil questionnaire of future and past discounting. The results demonstrate that humans discount temporally distant past outcomes similarly to future outcomes. Discounting of the future and past are qualitatively and quantitatively similar; discounting of past outcomes is orderly, hyperbolic, and consistent with most empirical observations from studies of future discounting, including the magnitude and sign effects. The present study indicates that the discounting of past outcomes is a quantifiable phenomenon, and the results are similar to observations from the established future-discounting literature. Past discounting may be of use in the study of drug-dependent and other impulsive populations. Implications of a relationship between future and past discounting are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Discounting of hypothetical and potentially real outcomes in nicotine-dependent and nondependent samples.

Discounting is a behavioral phenomenon in which the value of an outcome diminishes as a function of its increased delay or decreased probability and is related to substance abuse research because of its theoretical ties with behavioral models of impulsive choice. Research to date suggests that hypothetical outcomes used in discounting research yield data that are indistinguishable from those using potentially real outcomes. However, the extant literature focuses primarily on delay discounting in non-drug-using humans and has not examined whether hypothetical outcomes yield disproportionate numbers of nonsystematic response patterns. In two experiments, we compared hypothetical and potentially real monetary outcomes in delay and probability discounting tasks in terms of rates of discounting and the frequency of nonsystematic response patterns. In Experiment 1, 61 adults reported no smoking, binge drinking, or illicit drug use in the past year. Experiment 2 included a community sample of nicotine-dependent adults (N = 36). In both experiments, discounting for hypothetical and potentially real outcomes yielded similar data, replicating and extending a growing literature pointing to the empirical equivalence of these outcomes. These findings are relevant to research on discounting that is frequently used in the study of substance use and other impulse-control behaviors. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Decision making with long-term consequences: Temporal discounting for single and multiple outcomes in the future.

Two experiments were conducted to investigate how individuals evaluate future outcomes. Normative decision models postulate that the value of future outcomes should be discounted as a function of time. The present research obtained discounted values for single outcomes in the future but did not obtain discounted values for outcomes presented in series. In Exp 1, students evaluated (1) college-funding programs that required students to work to obtain support and (2) loans that required payments after completing college. A ratio-discounting function described the value of future support and deferred payments. In Exp 2, students were asked to evaluate work-study programs that described variable support over 1–4 yrs. Temporal discounting did not occur for the series of outcomes; college support for the 4th yr of college was just as valuable as support during the 1st yr. Results are discussed in relation to a general model of temporal discounting. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Temporal discounting of rewards in patients with bipolar disorder and schizophrenia.

Patients with bipolar disorder (BD) and schizophrenia (SZ) often show decision-making deficits in everyday circumstances. A failure to appropriately weigh immediate versus future consequences of choices may contribute to these deficits. We used the delay discounting task in individuals with BD or SZ to investigate their temporal decision making. Twenty-two individuals with BD, 21 individuals with SZ, and 30 healthy individuals completed the delay discounting task along with neuropsychological measures of working memory and cognitive function. Both BD and SZ groups discounted delayed rewards more steeply than did the healthy group even after controlling for current substance use, age, gender, and employment. Hierarchical multiple regression analyses showed that discounting rate was associated with both diagnostic group and working memory or intelligence scores. In each group, working memory or intelligence scores negatively correlated with discounting rate. The results suggest that (a) both BD and SZ groups value smaller, immediate rewards more than larger, delayed rewards compared with the healthy group and (b) working memory or intelligence is related to temporal decision making in individuals with BD or SZ as well as in healthy individuals. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

The short of it: Abbreviating the temporal discounting procedure.

A typical temporal discounting procedure determines the present, subjective value (indifference point) of a delayed outcome at 5 to 8 different delays to that outcome. These indifference points are used to determine a single index of discounting called a discounting rate. One concern that remains in the collection of this data is the high number of trials or choices, resulting in participant fatigue or other factors that may affect the validity of the data. In this report, we propose an abbreviated alternative to the more comprehensive and time-consuming discounting procedure. Specifically, we propose that fewer indifference points can be used to determine statistically equivalent discount rates with no loss in data sensitivity. We reanalyzed temporal discounting data obtained with 7 indifference points, and estimated discount rates from all combinations of 2, 3, and 4 of the 7 indifference points. Results indicate that valid and sensitive discounting indices can be obtained with fewer indifference points, and the most appropriate sets of indifference points are highlighted. The proposed abbreviated procedure is likely to be particularly useful when time constraints or participant fatigue is a concern as well as in repeated-measures contexts. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing signal-detection models of yes/no and two-alternative forced-choice recognition memory.

The current study compared 3 models of recognition memory in their ability to generalize across yes/no and 2-alternative forced-choice (2AFC) testing. The unequal-variance signal-detection model assumes a continuous memory strength process. The dual-process signal-detection model adds a thresholdlike recollection process to a continuous familiarity process. The mixture signal-detection model assumes a continuous memory strength process, but the old item distribution consists of a mixture of 2 distributions with different means. Prior efforts comparing the ability of the models to characterize data from both test formats did not consider the role of parameter reliability, which can be critical when comparing models that differ in flexibility. Parametric bootstrap simulations revealed that parameter regressions based on separate fits of each test type only served to identify the least flexible model. However, simultaneous fits of receiver-operating characteristic data from both test types with goodness-of-fit adjusted with Akaike’s information criterion (AIC) successfully recovered the true model that generated the data. With AIC and simultaneous fits to real data, the unequal-variance signal-detection model was found to provide the best account across yes/no and 2AFC testing. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A Discounting Framework for Choice With Delayed and Probabilistic Rewards.

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An algorithm for identifying nonsystematic delay-discounting data.

[Correction Notice: An erratum for this article was reported in Vol 16(4) of Experimental and Clinical Psychopharmacology (see record 2008-10619-006). Several misprints occurred and should read as follows: 1) Warren K. Bickel is with the University of Arkansas for Medical Sciences. 2) The first sentence in the abstract should read "Several discounting studies have used the R2 measure to identify data with poor fits to a mathematical discounting model as nonsystematic data to be eliminated." 3) In Table 2, the last row of column one should read "Madden opioid." 4) In the last line of the caption of Figure 2, "though" should read "through."] Several previous discounting studies have use the R2 measure to identify data sets with poor fits to a mathematical discounting model as nonsystematic data to be eliminated before further analyses are conducted. Data from three previous delay-discounting studies (six separate groups, with a total of 161 individuals) were used to demonstrate why using R2 to assess the fits of discounting data is problematic. A significant, positive correlation between discounting rate parameter and R2 was found in most groups, showing that R2 is more stringent as a measure of fit for low discounting rates than for high discounting rates. Furthermore, it is suggested that identifying nonsystematic data based on any measure of fit to a mathematical discounting model may be problematic because it confounds discounting rate comparison with the issue of discounting model assessment. Therefore, a model-free method to identify nonsystematic data is needed. An algorithm for identifying nonsystematic data is presented that is based on the expectation of a monotonically decreasing discounting function. This algorithm identified 13 cases out of the 161 reanalyzed data sets as nonsystematic. These nonsystematic data are presented, along with examples of data not identified as nonsystematic. This algorithm, or modifications of it, may be useful in a variety of human and nonhuman animal discounting studies (e.g., delay discounting, probability discounting) as an alternative to the R2 measure for identifying nonsystematic data. The algorithm may be used in empirical investigations to improve discounting methodology, and may be used to identify outliers to be removed from analyses. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Further evidence for temporal decay in working memory: Reply to Lewandowsky and Oberauer (2009).

The sources of forgetting in working memory (WM) are a matter of intense debate: Is there a time-related decay of memory traces, or is forgetting uniquely due to representation-based interference? In a previous study, we claimed to have provided evidence supporting the temporal decay hypothesis (S. Portrat, P. Barrouillet, & V. Camos, 2008). However, reanalyzing our data, S. Lewandowsky and K. Oberauer (2009) demonstrated that they do not provide compelling evidence for temporal decay and suggested a class of alternative models favoring a representation-based interference account. In this article, we develop from the most recent proposals made by Lewandowsky and Oberauer 2 of the most plausible extensions of these alternative models. We show that neither of these extensions can account for recent findings related to between-domain WM performance and that both lead to predictions that are contradicted by new empirical evidence. Finally, we show that recent studies that have been claimed to rule out the temporal decay hypothesis do not resist close scrutiny. We conclude that the time-based resource-sharing model remains the most parsimonious way to account for forgetting and restoration of memory traces in WM. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Age differences in temporal discounting: The role of dispositional affect and anticipated emotions.

We examined age differences in temporal discounting, the tendency to devalue delayed outcomes relative to immediate ones, with particular emphasis on the role of affective responses. A life-span sample completed an incentive-compatible temporal discounting task involving both monetary gains and losses. Covariates included demographic characteristics, cognitive functioning, personality traits, affective responses, and subjective health. Advanced age was associated with a lower tendency to discount the future, but this effect reached statistical significance only for the discounting of delayed gains. An examination of covariates suggested that age effects were associated with age differences in mental health and affective responses rather than demographic or cognitive variables. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

"An algorithm for identifying nonsystematic delay-discounting data": Correction to Johnson and Bickel (2008).

Reports an error in "An algorithm for identifying nonsystematic delay-discounting data" by Matthew W. Johnson and Warren K. Bickel (Experimental and Clinical Psychopharmacology, 2008[Jun], Vol 16[3], 264-274). Several misprints occurred and should read as follows: 1) Warren K. Bickel is with the University of Arkansas for Medical Sciences. It appears correctly in this erratum. 2) The first sentence in the abstract should read "Several discounting studies have used the R2 measure to identify data with poor fits to a mathematical discounting model as nonsystematic data to be eliminated." 3) In Table 2, the last row of column one should read "Madden opioid". 4) In the last line of the caption of Figure 2, "though" should read "through". (The following abstract of the original article appeared in record 2008-06716-009.) Several previous discounting studies have use the R2 measure to identify data sets with poor fits to a mathematical discounting model as nonsystematic data to be eliminated before further analyses are conducted. Data from three previous delay-discounting studies (six separate groups, with a total of 161 individuals) were used to demonstrate why using R2 to assess the fits of discounting data is problematic. A significant, positive correlation between discounting rate parameter and R2 was found in most groups, showing that R2 is more stringent as a measure of fit for low discounting rates than for high discounting rates. Furthermore, it is suggested that identifying nonsystematic data based on any measure of fit to a mathematical discounting model may be problematic because it confounds discounting rate comparison with the issue of discounting model assessment. Therefore, a model-free method to identify nonsystematic data is needed. An algorithm for identifying nonsystematic data is presented that is based on the expectation of a monotonically decreasing discounting function. This algorithm identified 13 cases out of the 161 reanalyzed data sets as nonsystematic. These nonsystematic data are presented, along with examples of data not identified as nonsystematic. This algorithm, or modifications of it, may be useful in a variety of human and nonhuman animal discounting studies (e.g., delay discounting, probability discounting) as an alternative to the R2 measure for identifying nonsystematic data. The algorithm may be used in empirical investigations to improve discounting methodology, and may be used to identify outliers to be removed from analyses. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A theory of criterion setting with an application to sequential dependencies.

Describes 3 models (the linear additive learning model, the exponential additive learning model, and the independent trace model) of sequential effects in psychophysical tasks. These models were tested using data from a study by W. S. Verplack et al (see record 1953-04864-001). The models appear to be most consistent with the independent trace model in which the momentary value of the criterion is modified by memory traces, an independent trace being retained for each relevant past event. On this basis, a theory of criterion setting is developed: A long-term process determines an initial value for the criterion, and 2 short-term processes adjust the criterion to match current changes in the expected probabilities of signals and to maximize the information transmitted by the S's responses. The theory is applied to results in the literature. (65 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effect of memory decay on predictions from changing categories.

In contrast to the static categories assumed in most categorization experiments, many real-world categories undergo gradual and systematic change in their definitions over time. Four experiments were carried out to study such category change. In these studies, participants successfully adjusted as category change occurred, but also showed a lingering and cumulative effect of past observations. The participants' performance was closely modeled by incorporating memory decay for past observations into J. R. Anderson's (1990, 1991) rational categorization algorithm and into a version of R. M. Nosofsky's (1986) exemplar categorization model. The resulting models suggest that the decay function is closer to a power law than to an exponential and that decay occurs both by item and by time, with the item decay being stronger than the time decay. The finding of power law decay gives additional support to claims that exemplar memories are used in categorization. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

In search of reliable persuasion effects: III. The sleeper effect is dead: Long live the sleeper effect.

The sleeper effect in persuasion is a delayed increase in the impact of a message that is accompanied by a discounting cue. Despite a long history, the sleeper effect has been notoriously difficult to obtain or to replicate, with the exception of a pair of studies by Gruder et al (1978). We conducted 16 computer-controlled experiments and a replication of the Gruder et al study to demonstrate that a sleeper effect can be obtained reliably when Ss (a) note the important arguments in a message, (b) receive a discounting cue after the message, and (c) rate the trustworthiness of the message communicator immediately after receiving the discounting cue. These operations are sufficiently different from those used in earlier studies to justify a new differential decay interpretation of the sleeper effect, in place of the dissociation hypothesis favored by most previous sleeper effect researchers. According to the differential decay interpretation, a sleeper effect occurs when message and discounting cue have opposite and near-equal immediate impacts that are not well-integrated in memory. The effect occurs, then, if the impact of the discounting cue decays faster than that of the message. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Hyperbolic temporal discounting in social drinkers and problem drinkers.

Two studies compared participants, distinguished by their typical alcohol consumption, on the degree to which they discounted the value of delayed, hypothetical amounts of money. Heavy social drinkers in Study 1 and problem drinkers in Study 2 both showed greater temporal discounting than light social drinkers; this difference was stronger in Study 2. Both studies found that a hyperbolic function described temporal discounting more accurately than an exponential function. These results are consistent with extending behavioral theories of intertemporal choice to characterize the determinants of alcohol consumption. The discounting differences also are consistent with more general behavioral economic and economic theories of addiction, although the hyperbolic functional form is inconsistent with the exponential discounting function in economic theory. The drinker groups also differed on impulsiveness and time orientation questionnaires, with light drinkers being less impulsive and more future oriented; however, these measures were not strongly correlated with the measure of temporal discounting. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Resource Slack and Propensity to Discount Delayed Investments of Time Versus Money.

The authors demonstrate that people discount delayed outcomes as a result of perceived changes over time in supplies of slack. Slack is the perceived surplus of a given resource available to complete a focal task. The present research shows that, in general, people expect slack for time to be greater in the future than in the present. Typically, this expectation of growth of slack in the future is more pronounced for time than for money. In 7 experiments, the authors demonstrate that systematic temporal shifts of perceived slack determine the extent and the pattern of delay discounting, including hyperbolic discounting. They use this framework to explain differential propensity to delay investments and receipts of time and money. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Error discounting in probabilistic category learning.

The assumption in some current theories of probabilistic categorization is that people gradually attenuate their learning in response to unavoidable error. However, existing evidence for this error discounting is sparse and open to alternative interpretations. We report 2 probabilistic–categorization experiments in which we investigated error discounting by shifting feedback probabilities to new values after different amounts of training. In both experiments, responding gradually became less responsive to errors, and learning was slowed for some time after the feedback shift. Both results were indicative of error discounting. Quantitative modeling of the data revealed that adding a mechanism for error discounting significantly improved the fits of an exemplar-based and a rule-based associative learning model, as well as of a recency-based model of categorization. We conclude that error discounting is an important component of probabilistic learning. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

The Sleeper Effect in Persuasion: A Meta-Analytic Review.

A meta-analysis of the available judgment and memory data on the sleeper effect in persuasion is presented. According to this effect, when people receive a communication associated with a discounting cue, such as a noncredible source, they are less persuaded immediately after exposure than they are later in time. Findings from this meta-analysis indicate that recipients of discounting cues were more persuaded over time when the message arguments and the cue had a strong initial impact. In addition, the increase in persuasion was stronger when recipients of discounting cues had higher ability or motivation to think about the message and received the discounting cue after the message. These results are discussed in light of classic and contemporary models of attitudes and persuasion. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Temporal Discounting When the Choice Is Between Two Delayed Rewards.

The present experiments extend the temporal discounting paradigm from choice between an immediate and a delayed reward to choice between 2 delayed rewards: a smaller amount of money available sooner and a larger amount available later. Across different amounts and delays, the data were consistently well described by a hyperbola-like discounting function, and the degree of discounting decreased systematically as the delay to the sooner reward increased. Three theoretical models (the elimination-by-aspects, present-value comparison, and common-aspect attenuation hypotheses) were evaluated. The best account of the data was provided by the common-aspect attenuation hypothesis, according to which the common aspect of the choice alternatives (i.e., the time until the sooner reward is available) receives less weight in the decision-making process. (PsycINFO Database Record (c) 2010 APA, all rights reserved)