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Cumulative Weighing of Time in Intertemporal Tradeoffs

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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.


Observed proportions of participants choosing the high NPV option among those lending anecdotal support to the respective models (horizontal), plotted against the average predicted probabilities of choosing the high NPV option generated by the models (vertical), in Experiment 3. TM = Tradeoff Model; DIUM = Discounted Instantaneous Utility Model; SMNZ = No-Zero Sequences Model; SMZ = Zero Sequences Model.
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fig4: Observed proportions of participants choosing the high NPV option among those lending anecdotal support to the respective models (horizontal), plotted against the average predicted probabilities of choosing the high NPV option generated by the models (vertical), in Experiment 3. TM = Tradeoff Model; DIUM = Discounted Instantaneous Utility Model; SMNZ = No-Zero Sequences Model; SMZ = Zero Sequences Model.

Mentions: We identified three candidate models for describing preferences for sequences: The Discounted Instantaneous Utility Model (DIUM), in Equation (1), the Sequences Model (SM), in Equations (2a) and (2b), as previously applied by Loewenstein and Prelec (1993) and Guyse et al. (2002), and the Tradeoff Model (TM), in Equations (3a) and (3b). Although Loewenstein and Prelec (1993) applied Equations (2a) and (2b) in their empirical test of SM, they also showed how discounting of individual outcome utilities could be incorporated into their model. As evident from their simulations (Loewenstein & Prelec, 1993, Figure 4), discounting interacts with the “gestalt” properties of sequence when a sequence starts in (or close to) the present (e.g., 0, 1, and 2) or when time periods are noncontiguous (e.g., 1, 2, and 10). Similar to Loewenstein and Prelec (1993), who used contiguous 1-week intervals starting in one week, we use contiguous 1-year intervals starting in one year (i.e., 1, 2, and 3). And, as Loewenstein and Prelec (1993) did, we compare the performance of SM with that of DIUM. The novelty is that we introduce TM, with its cumulative weighing of time, as a candidate model, and that we apply the candidate models to sequences of unlabeled monetary gains rather than consumption experiences.


Cumulative Weighing of Time in Intertemporal Tradeoffs
Observed proportions of participants choosing the high NPV option among those lending anecdotal support to the respective models (horizontal), plotted against the average predicted probabilities of choosing the high NPV option generated by the models (vertical), 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

fig4: Observed proportions of participants choosing the high NPV option among those lending anecdotal support to the respective models (horizontal), plotted against the average predicted probabilities of choosing the high NPV option generated by the models (vertical), in Experiment 3. TM = Tradeoff Model; DIUM = Discounted Instantaneous Utility Model; SMNZ = No-Zero Sequences Model; SMZ = Zero Sequences Model.
Mentions: We identified three candidate models for describing preferences for sequences: The Discounted Instantaneous Utility Model (DIUM), in Equation (1), the Sequences Model (SM), in Equations (2a) and (2b), as previously applied by Loewenstein and Prelec (1993) and Guyse et al. (2002), and the Tradeoff Model (TM), in Equations (3a) and (3b). Although Loewenstein and Prelec (1993) applied Equations (2a) and (2b) in their empirical test of SM, they also showed how discounting of individual outcome utilities could be incorporated into their model. As evident from their simulations (Loewenstein & Prelec, 1993, Figure 4), discounting interacts with the “gestalt” properties of sequence when a sequence starts in (or close to) the present (e.g., 0, 1, and 2) or when time periods are noncontiguous (e.g., 1, 2, and 10). Similar to Loewenstein and Prelec (1993), who used contiguous 1-week intervals starting in one week, we use contiguous 1-year intervals starting in one year (i.e., 1, 2, and 3). And, as Loewenstein and Prelec (1993) did, we compare the performance of SM with that of DIUM. The novelty is that we introduce TM, with its cumulative weighing of time, as a candidate model, and that we apply the candidate models to sequences of unlabeled monetary gains rather than consumption experiences.

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.