Discounting of delayed and probabilistic losses over a wide range of amounts

Abstract

The present study examined delay and probability discounting of hypothetical monetary losses over a wide range of amounts (from $20 to $500,000) in order to determine how amount affects the parameters of the hyperboloid discounting function. In separate conditions, college students chose between immediate payments and larger, delayed payments and between certain payments and larger, probabilistic payments. The hyperboloid function accurately described both types of discounting, and amount of loss had little or no systematic effect on the degree of discounting. Importantly, the amount of loss also had little systematic effect on either the rate parameter or the exponent of the delay and probability discounting functions. The finding that the parameters of the hyperboloid function remain relatively constant across a wide range of amounts of delayed and probabilistic loss stands in contrast to the robust amount effects observed with delayed and probabilistic rewards. At the individual level, the degree to which delayed losses were discounted was uncorrelated with the degree to which probabilistic losses were discounted, and delay and probability loaded on two separate factors, similar to what is observed with delayed and probabilistic rewards. Taken together, these findings argue that although delay and probability discounting involve fundamentally different decision-making mechanisms, nevertheless the discounting of delayed and probabilistic losses share an insensitivity to amount that distinguishes it from the discounting of delayed and probabilistic gains. Keywords delay discounting; probability discounting; losses; amount; hyperboloid; behavioral economics; humans Many everyday situations involve choosing between outcomes that differ in amount as well as in the delay until their occurrence or the likelihood of their occurrence. Such choices are important not just because of their consequences for people's lives but also because of their theoretical implications. Perhaps in recognition of the important life consequences of individuals' choice behavior, there is a rapidly growing literature on differences in the degree to which various groups of people (e.g., substance abusers, the elderly) discount the value of delayed or probabilistic outcomes (Madden & Bickel, 2010). From an individualdifferences perspective, researchers are seeking to understand the extent to which an Address correspondence to: Leonard Green, Washington University, Department of Psychology, Campus Box 1125, St. Louis, MO 63130, Phone: (314) lgreen@wustl individual's tendency to discount the value of outcomes that are delayed or probabilistic reflects a single underlying trait (e.g., impulsivity) or whether multiple traits are involved. In addition, there is a growing interest in how individuals make such choices, perhaps in recognition that the processes involved reflect fundamental decision-making mechanisms (e.g., Green & Myerson, 2013;van den Bos & McClure, 2013). Of course, these different lines of research can have important ...

Effects of delay and probability combinations on discounting in humans

“…In contrast to previous research (e.g., Green et al, 2014), for delayed losses we found a significantly greater k as magnitude increased ( p = 0.001, t 62 = 3.35). However, consistent with previous research (Green et al, 2014), we did not observe a magnitude effect between probabilistic losses of $1000 and $10 ( p = 0.12, t 69 = 1.56).…”

“…In contrast to previous research (e.g., Green et al, 2014), for delayed losses we found a significantly greater k as magnitude increased ( p = 0.001, t 62 = 3.35). However, consistent with previous research (Green et al, 2014), we did not observe a magnitude effect between probabilistic losses of $1000 and $10 ( p = 0.12, t 69 = 1.56). Finally, and also consistent with previous research (e.g., Estle et al, 2006), we observed significantly greater h s for gains of $1000 compared to $10 ( p < 0.001, t 38 = 3.76).…”

“…In addition, magnitude effects consistent with previous research were obtained for gains and losses using 5-trial adjusting probability tasks. Inconsistent with previous research (Green et al, 2014), a magnitude effect was observed using 5-trial adjusting delay tasks involving monetary losses. However, this may have been an artifact of the smaller range of magnitudes assessed in Experiment 1 compared to previous research (Green et al, 2014).…”

“…Green et al (2014), however, examined a much wider, parametric range of magnitudes and found no systematic change in discounting. Although the k s differed at magnitudes similar to those used in the present study (i.e., $20 and $3000), there was no functional relation across the full range of magnitudes.…”

“…In contrast, probability discounting increases as magnitude increases (e.g., Green et al, 1999; Yi and Bickel, 2005). Unlike outcomes involving gains, however, researchers have not found a magnitude effect in delay or probability discounting when the outcomes are described as losses (Estle et al, 2006; Green et al, 2014). Although an integrated, theoretical account of these patterns has not been widely accepted, they nevertheless provide benchmarks to evaluate the validity of new methods to measure discounting.…”