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.

When choosing between immediate and future rewards, how do people deal with uncertainty about the value of the future outcome or the delay until its occurrence? Skylark et al. (2020) suggested that people employ a delay-reward heuristic: the inferred value of an ambiguous future reward is a function of the stated delay, and vice-versa. The present paper investigates the role of this heuristic in choice behaviour. In Studies 1a–2b, participants inferred the value of an ambiguous future reward or delay before the true value was revealed and a choice made. Preference for the future option was predicted by the discrepancy between the estimated and true values: the more pleasantly surprising the delayed option, the greater the willingness to choose it. Studies 3a–3c examined the association between inference and preference when the ambiguous values remained unknown. As predicted by the use of a delay-reward heuristic, inferred delays and rewards were positively related to stated rewards and delays, respectively. More importantly, choices were associated with inferred rewards and, in some circumstances, delays. Critically, estimates and choices were both order-dependent: when estimates preceded choices, estimates were more optimistic (people inferred smaller delays and larger rewards) and were subsequently more likely to choose the delayed option than when choices were made before estimates. These order effects argue against a simple model in which people deal with ambiguity by first estimating the unknown value and then using their estimate as the basis for decision. Rather, it seems that inferences are partly constructed from choices, and the role of inference in choice depends on whether an explicit estimate is made prior to choosing. Finally, we also find that inferences about ambiguous delays depend on whether the estimate has to be made in “days” or in a self-selected temporal unit, and replicate previous findings that older participants make more pessimistic inferences than younger ones. We discuss the implications and possible mechanisms for these findings.