Limits...
Cumulative Weighing of Time in Intertemporal Tradeoffs

View Article: PubMed Central - PubMed

ABSTRACT

We examine preferences for sequences of delayed monetary gains. In the experimental literature, two prominent models have been advanced as psychological descriptions of preferences for sequences. In one model, the instantaneous utilities of the outcomes in a sequence are discounted as a function of their delays, and assembled into a discounted utility of the sequence. In the other model, the accumulated utility of the outcomes in a sequence is considered along with utility or disutility from improvement in outcome utilities and utility or disutility from the spreading of outcome utilities. Drawing on three threads of evidence concerning preferences for sequences of monetary gains, we propose that the accumulated utility of the outcomes in a sequence is traded off against the duration of utility accumulation. In our first experiment, aggregate choice behavior provides qualitative support for the tradeoff model. In three subsequent experiments, one of which incentivized, disaggregate choice behavior provides quantitative support for the tradeoff model in Bayesian model contests. One thread of evidence motivating the tradeoff model is that, when, in the choice between two single dated outcomes, it is conveyed that receiving less sooner means receiving nothing later, preference for receiving more later increases, but when it is conveyed that receiving more later means receiving nothing sooner, preference is left unchanged. Our results show that this asymmetric hidden-zero effect is indeed driven by those supporting the tradeoff model. The tradeoff model also accommodates all remaining evidence on preferences for sequences of monetary gains.

No MeSH data available.


The effect of zero outcomes among those providing anecdotal support for the candidate models (top panel), and among those providing increasingly stronger support for the Tradeoff Model (bottom panel), in Experiment 3. TM = Tradeoff Model; DIUM = Discounted Instantaneous Utility Model; SMNZ = No-Zero Sequences Model; SMZ = Zero Sequences Model.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4998108&req=5

fig5: The effect of zero outcomes among those providing anecdotal support for the candidate models (top panel), and among those providing increasingly stronger support for the Tradeoff Model (bottom panel), in Experiment 3. TM = Tradeoff Model; DIUM = Discounted Instantaneous Utility Model; SMNZ = No-Zero Sequences Model; SMZ = Zero Sequences Model.

Mentions: Concerning the three hidden-zero tasks, we computed, for each participant, the proportion of choices favoring the larger-later outcome (a measure of patience). The top panel of Figure 5 shows the results for those providing anecdotal support for the respective models. As expected, DIUM supporters are not affected by zero outcomes. In contrast, those supporting TM, SMNZ, and SMZ are affected by them, but more so by the later zero than by the sooner one. Let pL, pS, and pN be the average proportions of patient choices in the later-zero, sooner-zero, and no-zero conditions, respectively. A measure of the asymmetry of the hidden-zero effect is then (pL − pN) − (pS − pN) = pL − pS, where a strictly asymmetric hidden-zero effect is pL − pN > 0 and pS − pN = 0. The asymmetry is more pronounced among those supporting TM, pL − pS = .18, 95% CI [.08; .28], than among those supporting SMNZ, pL − pS = .08, 95% CI [−.13; .29], and SMZ, pL − pS = .15, 95% CI [−.13; .43], but those supporting TM do seem to be affected somewhat by the sooner zero, pS − pN = .09, 95% CI [−.02; .19]. We must realize, however, that we are including all participants who provide anecdotal support for a model, several of whom do not lend convincing support to it. The bottom panel of Figure 5 therefore shows the results among those lending progressively more convincing support to TM. We see the asymmetric hidden-zero effect that we expected: An effect of the later zero, but no effect of the sooner one, among those lending substantial support, pL − pN = .27, 95% CI [.16; .38], pS − pN = .06, 95% CI [−.06; .19], among those lending strong support, pL − pN = .19, 95% CI [.06; .32], pS − pN = .02, 95% CI [−.13; .17], among those lending very strong support, pL − pN = .24, 95% CI [.09; .39], pS − pN = .01, 95% CI [−.17; .18], and among those lending decisive support, pL − pN = .24, 95% CI [.05; .43], pS − pN = −.05, 95% CI [−.27; .16].


Cumulative Weighing of Time in Intertemporal Tradeoffs
The effect of zero outcomes among those providing anecdotal support for the candidate models (top panel), and among those providing increasingly stronger support for the Tradeoff Model (bottom panel), in Experiment 3. TM = Tradeoff Model; DIUM = Discounted Instantaneous Utility Model; SMNZ = No-Zero Sequences Model; SMZ = Zero Sequences Model.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4998108&req=5

fig5: The effect of zero outcomes among those providing anecdotal support for the candidate models (top panel), and among those providing increasingly stronger support for the Tradeoff Model (bottom panel), in Experiment 3. TM = Tradeoff Model; DIUM = Discounted Instantaneous Utility Model; SMNZ = No-Zero Sequences Model; SMZ = Zero Sequences Model.
Mentions: Concerning the three hidden-zero tasks, we computed, for each participant, the proportion of choices favoring the larger-later outcome (a measure of patience). The top panel of Figure 5 shows the results for those providing anecdotal support for the respective models. As expected, DIUM supporters are not affected by zero outcomes. In contrast, those supporting TM, SMNZ, and SMZ are affected by them, but more so by the later zero than by the sooner one. Let pL, pS, and pN be the average proportions of patient choices in the later-zero, sooner-zero, and no-zero conditions, respectively. A measure of the asymmetry of the hidden-zero effect is then (pL − pN) − (pS − pN) = pL − pS, where a strictly asymmetric hidden-zero effect is pL − pN > 0 and pS − pN = 0. The asymmetry is more pronounced among those supporting TM, pL − pS = .18, 95% CI [.08; .28], than among those supporting SMNZ, pL − pS = .08, 95% CI [−.13; .29], and SMZ, pL − pS = .15, 95% CI [−.13; .43], but those supporting TM do seem to be affected somewhat by the sooner zero, pS − pN = .09, 95% CI [−.02; .19]. We must realize, however, that we are including all participants who provide anecdotal support for a model, several of whom do not lend convincing support to it. The bottom panel of Figure 5 therefore shows the results among those lending progressively more convincing support to TM. We see the asymmetric hidden-zero effect that we expected: An effect of the later zero, but no effect of the sooner one, among those lending substantial support, pL − pN = .27, 95% CI [.16; .38], pS − pN = .06, 95% CI [−.06; .19], among those lending strong support, pL − pN = .19, 95% CI [.06; .32], pS − pN = .02, 95% CI [−.13; .17], among those lending very strong support, pL − pN = .24, 95% CI [.09; .39], pS − pN = .01, 95% CI [−.17; .18], and among those lending decisive support, pL − pN = .24, 95% CI [.05; .43], pS − pN = −.05, 95% CI [−.27; .16].

View Article: PubMed Central - PubMed

ABSTRACT

We examine preferences for sequences of delayed monetary gains. In the experimental literature, two prominent models have been advanced as psychological descriptions of preferences for sequences. In one model, the instantaneous utilities of the outcomes in a sequence are discounted as a function of their delays, and assembled into a discounted utility of the sequence. In the other model, the accumulated utility of the outcomes in a sequence is considered along with utility or disutility from improvement in outcome utilities and utility or disutility from the spreading of outcome utilities. Drawing on three threads of evidence concerning preferences for sequences of monetary gains, we propose that the accumulated utility of the outcomes in a sequence is traded off against the duration of utility accumulation. In our first experiment, aggregate choice behavior provides qualitative support for the tradeoff model. In three subsequent experiments, one of which incentivized, disaggregate choice behavior provides quantitative support for the tradeoff model in Bayesian model contests. One thread of evidence motivating the tradeoff model is that, when, in the choice between two single dated outcomes, it is conveyed that receiving less sooner means receiving nothing later, preference for receiving more later increases, but when it is conveyed that receiving more later means receiving nothing sooner, preference is left unchanged. Our results show that this asymmetric hidden-zero effect is indeed driven by those supporting the tradeoff model. The tradeoff model also accommodates all remaining evidence on preferences for sequences of monetary gains.

No MeSH data available.