Choice bundling, unpacked: Observed and predicted effects on intertemporal choice in an additive model of hyperbolic delay discounting

Abstract

One method known to increase preference for larger, later rewards (LLRs) over smaller, sooner rewards (SSRs) is choice bundling, in which a single choice produces a series of repeating consequences over time. The present study examined whether effects of choice bundling on preference for LLRs: (1) increase with the number of rewards in the bundle (i.e., bundle size); (2) are independent of differences in reward magnitude between conditions; and (3) accord with predictions of an additive model of hyperbolic delay discounting, in which the value of a bundle of rewards can be expressed as the summed discounted value of all rewards in that bundle. Participants (N = 252) completed a choice task to assess valuation of monetary LLRs at bundle sizes of 1 (control), 3, and 9 rewards per choice (ascending/descending order counterbalanced). To control for the magnitude effect, the total reward amounts were held constant across conditions. Choice bundling significantly increased LLR preference (p < .001), with the largest effect observed at the largest bundle size. The descending bundle-size order produced significantly greater LLR preference than the ascending order (p < .05), although order did not significantly interact with bundle size. Difference scores between observed measures and those predicted by an additive model of hyperbolic discounting were small and not significantly different than zero, but were not equivalent to zero. Future research should investigate the clinical utility of choice bundling for reducing the maladaptive health behavior (e.g., substance use) with which delay discounting is associated.

Choice Bundling Increases Valuation of Delayed Losses More Than Gains in Cigarette Smokers

“…This value was divided equally among all gains/losses in the bundle (see Figure 2 ) in order to hold the amounts constant across bundle-size conditions. This procedure controlled for the “magnitude effect” in delay discounting research, in which degree of discounting is inversely related to amount (e.g., Estle et al, 2006 ; for further discussion relevant to choice bundling, see Stein and Madden, 2021 ).…”

“…Neither the six-trial, adjusting-delay task nor the use of the adjusting-amount task in this study allowed application of standardized criteria to detect nonsystematic responding ( Johnson and Bickel, 2008 ). To mitigate this concern, data quality in the choice bundling assessment was monitored by inclusion of three quality control questions, similar to methods used previously ( Stein et al, 2018a ; Stein and Madden, 2021 ). Specifically, after the sixth trial in each of three adjusting-amount conditions, a seventh trial asked participants to choose between $450 now and $900 now.…”

“…Specifically, after the sixth trial in each of three adjusting-amount conditions, a seventh trial asked participants to choose between $450 now and $900 now. In the bundle-size 3 and 9 conditions, these monetary amounts were framed as separate rewards, as described above for these conditions; however, all delays were removed (e.g., $300 now, $300 now, and $300 now; Stein and Madden, 2021 ). Choice of the smaller option in these questions was interpreted as inattention or atypical valuation of monetary rewards.…”

“…Several studies have offered empirical support for this predicted effect of choice bundling (for review, see Ashe and Wilson, 2020 ), showing that bundling increases preference for LL gains (money and/or food) in both humans ( Kirby and Guastello, 2001 ; Hofmeyr et al, 2011 ) and nonhumans ( Ainslie and Monterosso, 2003 ; Stein et al, 2013 ). These include a recent study from our group ( Stein and Madden, 2021 ) showing in an online sample from the general population ( N = 252) that the efficacy of choice bundling is enhanced by increasing the number of rewards in the choice bundle (for a similar finding in rats, see Stein et al, 2013 ). Observed effects in this online study also approximated those predicted by the additive model of hyperbolic discounting (Equation 2).…”

“…This is due to the non-constant rate of devaluation in hyperbolic discounting in which value is lost quickly at short delays and more slowly at long delays. When a single choice produces repeating outcomes, the relatively stable subjective values of individual LL outcomes sum to a larger value than the sum of individual SS outcomes (for further discussion, see Ainslie, 2001 ; Ashe and Wilson, 2020 ; Stein and Madden, 2021 ).…”