Notes on discounting

In general, if a variable can be expressed as a function of its own maximum value, that function may be called a discount function. Delay discounting and probability discounting are commonly studied in psychology, but memory, matching, and economic utility also may be viewed as discounting processes. When they are so viewed, the discount function obtained is hyperbolic in form. In some cases the effective discounting variable is proportional to the physical variable on which it is based. For example, in delay discounting, the physical variable, delay (D), may enter into the hyperbolic equation as kD. In many cases, however, the discounting data are not well described with a single-parameter discount function. A much better fit is obtained when the effective variable is a power function of the physical variable (kDS in the case of delay discounting). This power-function form fits the data of delay, probability, and memory discounting as well as other two-parameter discount functions and is consistent with both the generalized matching law and maximization of a constant-elasticity-of-substitution utility     

Rate, Probability and Matching: Comments on ��The Identities Hidden in the Matching Laws, and Their Uses�� by David Thorne

David Thorne's (2010) article, “The Identities Hidden In The Matching Laws, And Their Uses” performs a valuable service in pointing out alternative expressions of matching. However, some identities tend to obscure rather than illuminate empirical relationships. Three such problematic instances are discussed: interresponse time as a function of interval and ratio schedule parameters; probability equality as implying rate matching; the apparent simplicity of probabilistic functions, as opposed to response rate functions, of reinforcement rate.     

Comparing Delay Discounting Rates When Using the Fill-in-the-Blank and Multiple-Choice Methods

Several methods have been devised to measure delay discounting. The present study recruited university students to complete a delay-discounting task involving five different outcomes (finding a dating partner, free cigarettes, winning $100,000, being owed $100,000, and obtaining one's ideal body image) that was administered using either the fill-in-the blank (FITB) or multiple-choice (MC) method. Results showed that the different administration methods sometimes produced significantly different rates of discounting, the direction of which differed by outcome. Hyperbolic discounting and the area under the discounting curve were nearly always significantly correlated when the FITB method was used but were never significantly correlated when the MC method was used. Discounting across the five outcomes produced a two-factor solution when the FITB data were factor analyzed. The MC data were described by a one-factor solution. The present results illustrate that procedural variables have a potentially profound impact on delay-discounting data, and generalizing from studies on delay discounting should be done with caution until those variables are fully understood.     

Delay Discounting as a Function of Intrinsic/Extrinsic Religiousness,Religious Fundamentalism,and Regular Church Attendance

Delay discounting occurs when the subjective value of an outcome decreases because its delivery is delayed. Previous research has suggested that the rate at which some, but not all, outcomes are discounted varies as a function of regular church attendance. In the present study, 509 participants completed measures of intrinsic religiousness, extrinsic religiousness, religious fundamentalism, and whether they regularly attended church services. They then completed a delay-discounting task involving five outcomes. Although religiousness was not a significant predictor of discounting for all outcomes, participants scoring high in intrinsic religiousness tended to display less delay discounting than participants scoring low. Likewise, participants scoring high in religious fundamentalism tended to display more delay discounting than participants scoring low. These results partially replicate previous ones in showing that the process of discounting may vary as a function of religiousness. The results also provide some direction for those interested in altering how individuals discount.     

Sex differences in the effects of disinhibition,perceived peer drinking,and delay discounting on drinking among Japanese college students

Disinhibition, perceived peer drinking, and delay discounting are considered significant predictors of drinking in young adults. This study examined whether perceived peer drinking and delay discounting mediate the association between disinhibition and drinking for young men and women. In this study, 258 Japanese college students (109 men and 149 women, mean age 19.17 (SD = 1.20) years old) completed a self-administered questionnaire that included four measures—the disinhibition subscale of the Sensation Seeking Scale for Japanese Adolescents, the proportion of friends who drink as an index of perceived peer drinking behaviors, the Monetary Choice Questionnaire, and participants’ own drinking behavior. In the multiple mediator models analyzed using structural equation modeling, for both sexes, perceived peer drinking had the largest direct effect on participants’ drinking, followed by disinhibition and delay discounting. However, the results of mediation analyses indicated that perceived peer drinking mediated the association between disinhibition and drinking for only women. The results of this study imply that it is important to consider sex differences in the association between personality traits and peer influence to develop programs aiming to reduce drinking among young adults in Japan.     

Good or Bad,We Want it Now: Fixed‐cost Present Bias for Gains and Losses Explains Magnitude Asymmetries in Intertemporal Choice

Intertemporal tradeoffs are ubiquitous in decision making, yet preferences for current versus future losses are rarely explored in empirical research. Whereas rational‐economic theory posits that neither outcome sign (gains vs. losses) nor outcome magnitude (small vs. large) should affect delay discount rates, both do, and moreover, they interact: in three studies, we show that whereas large gains are discounted less than small gains, large losses are discounted more than small losses. This interaction can be understood through a reconceptualization of fixed‐cost present bias, which has traditionally described a psychological preference for immediate rewards. First, our results establish present bias for losses—a psychological preference to have losses over with now. Present bias thus predicts increased discounting of future gains but decreased (or even negative) discounting of future losses. Second, because present bias preferences do not scale with the magnitude of possible gains or losses, they play a larger role, relative to other motivations for discounting, for small magnitude intertemporal decisions than for large magnitude intertemporal decisions. Present bias thus predicts less discounting of large gains than small gains but more discounting of large losses than small losses. The present research is the first to demonstrate that the effect of outcome magnitude on discount rates may be opposite for gains and losses and also the first to offer a theory (an extension of present bias) and process data to explain this interaction. The results suggest that policy efforts to encourage future‐oriented choices should frame outcomes as large gains or small losses. Copyright © 2012 John Wiley & Sons, Ltd.     

Decision Making with Uncertain Reinforcement in Children with Attention Deficit/Hyperactivity Disorder (ADHD)

Reward-related processes are impaired in children with ADHD. Whether these deficits can be ascribed to an aversion to delay or to an altered responsiveness to magnitude, frequency, valence, or the probability of rewards still needs to be explored. In the present study, children with ADHD and normal controls aged 7 to 10 years performed a simple probabilistic discounting task. They had to choose between alternatives where the magnitude of rewards was inversely related to the probability of outcomes. As a result, children with ADHD opted more frequently for less likely but larger rewards than normal controls. Shifts of the response category after positive or negative feedback, however, occurred as often in children with ADHD as in control children. In children with ADHD, the frequency of risky choices was correlated with neuropsychological measures of response time variability but unrelated to measures of inhibitory control. It is concluded that the tendency to select less likely but larger rewards possibly represents a separate facet of dysfunctional reward processing, independent of delay aversion or altered responsiveness to feedback.     

Imprecise Epistemic Values and Imprecise Credences

A number of recent arguments purport to show that imprecise credences are incompatible with accuracy-first epistemology. If correct, this conclusion suggests a conflict between evidential and alethic epistemic norms. In the first part of the paper, I claim that these arguments fail if we understand imprecise credences as indeterminate credences. In the second part, I explore why agents with entirely alethic epistemic values can end up in an indeterminate credal state. Following William James, I argue that there are many distinct alethic values that a rational agent can have. Furthermore, such an agent is rationally permitted not to have settled on one fully precise value function. This indeterminacy in value will sometimes result in indeterminacy in epistemic behaviour—that is, because the agent’s values aren’t settled, what she believes might not be.