We study the allocation of time across decision problems. If a decision-maker (1) has noisy estimates of value, (2) improves those estimates the longer he or she analyzes a choice problem, and (3) allocates time optimally, then the decision-maker should spend less time choosing when the difference in value between two options is relatively large. To test this prediction we ask subjects to make 27 binary incentive-compatible intertemporal choices, and measure response time for each decision. Our time allocation model explains 54% of the variance in average decision time. These results support the view that decisionmaking is a cognitively costly activity that uses time as an input allocated according to cost-benefit principles.  Agents should allocate time according to cost-benefit tradeoffs. Such tradeoffs should also influence the amount of time that agents allocate to decision-making itself. It is natural to assume that agents have expected utility estimates that are noisy and that these noisy estimates can be improved by thinking longer about a choice problem. In this case, agents should allocate more decision time to choices between options of similar expected utility than to choices between options of dissimilar expected utility. Intuitively, if an agent's estimate of the value of the best option is close to her estimate of the next best alternative, then it is optimal to take more time to refine her estimates since this extra time has a good chance of leading her to change her choice. In contrast, if an agent has a noisy estimate of the value of an option but the option almost surely dominates its alternatives, then it is not worth taking the time to refine her estimates, because additional thinking is unlikely to change her choice. These intuitions generalize, predicting an inverse relationship between average decision time and the difference in expected value between rewards in a binary choice set (Gabaix and Laibson, 2005; Gabaix et al., 2006) . The current paper tests these predictions. Psychologists have studied the amount of time that subjects take to make comparative judgments since the work of Henmon (1906) . In perception, Johnson (1939) had subjects decide which of two simultaneously presented lines was longer, and found that response time (RT) was longer the more similar the lines: RT was a negative linear function of the logarithm of the difference in length. This pattern has been found with other perceptual quantities like area and luminance, with the size of visualized objects, and even with the magnitudes of abstract numbers (Moyer and Landauer, 1967) . Brain imaging studies suggest that all of these comparison tasks invoke a common cognitive process localized in the parietal lobes (e.g., Pinel et al., 2004) . In the experiments reported in the current paper, we find that response times are longer the more similar the discounted values of the rewards in a binary choice set. We ask laboratory subjects to make 27 binary intertemporal choices. We measure intertemporal preferences using data from these choices. We find that the average RT for each of the choices is predicted by the implied difference in discounted expected value. Choices with relatively large differences in discounted value have low average RTs. Differences in discounted value account for 54.1% of the variance in average RT. When we estimate different discount rates for different reward size categories, differences in discounted value account for 69.9% of the RT variance.
In a study of the cognitive costs associated with decision making, REF show that users allocate time for a decision-making task according to cost-benefit principles.
The allocation of time in decision-making *
Journal of the European Economic Association
Journal of the European Economic Association
Economics Medicine