The delay-reward heuristic: What do people expect in intertemporal choice tasks?

Abstract

Recent research has shown that risk and reward are positively correlated in many environments, and that people have internalized this association as a "risk-reward heuristic": when making choices based on incomplete information, people infer probabilities from payoffs and vice-versa, and these inferences shape their decisions. We extend this work by examining people's expectations about another fundamental trade-off-that between monetary reward and delay. In 2 experiments (total N = 670), we adapted a paradigm previously used to demonstrate the risk-reward heuristic. We presented participants with intertemporal choice tasks in which either the delayed reward or the length of the delay was obscured. Participants inferred larger rewards for longer stated delays, and longer delays for larger stated rewards; these inferences also predicted people's willingness to take the delayed option. In exploratory analyses, we found that older participants inferred longer delays and smaller rewards than did younger ones. All of these results replicated in 2 large-scale pre-registered studies with participants from a different population (total N = 2138). Our results suggest that people expect intertemporal choice tasks to offer a trade-off between delay and reward, and differ in their expectations about this trade-off. This "delay-reward heuristic" offers a new perspective on existing models of intertemporal choice and provides new insights into unexplained and systematic individual differences in the willingness to delay gratification.

Keywords: decision-making; delay discounting; delay-reward heuristic; intertemporal choice; risk-reward heuristic.

Figure 1. Unique responses in each experiment. In all studies, participants tend to use just a handful of response values when inferring rewards or delays, although this is against a background of more idiosyncratic estimates. The numbers below the x-axis label the most popular values, along with the smallest and largest estimate in each study. Note that the x-axis is ordinal: the values are simply arranged from smallest to largest.

Figure 2. Estimated rewards as a function of stated delays, and estimated delays as a function of rewards. The plot shows log ₁₀(estimate + 1) against condition, with the y-axis tick marks exponentiated to improve clarity. Values have been jittered to reduce over-plotting. The right-hand panels show the same data with a logarithmic x-axis.

Figure 3. Figure 2 re-plotted without the raw data points. Error bars show confidence intervals (95% for Studies 1A and 1B, 99% for Studies 2A and 2B).

Figure 4. Choice of delayed option as a function of stated delay and stated reward. Error bars are Wilson confidence intervals (95% for Studies 1A and 1B; 99% for Studies 2A and 2B). The dotted line indicates indifference.

Figure 5. Trade-offs between money and time in typical experiments of intertemporal choice.