Speed, Accuracy, and the Optimal Timing of Choices∗

We model the joint distribution of choice probabilities and decision times in binary decisions as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant cost per unit time for gathering information. We show that choices are more likely to be correct when the agent chooses to decide quickly provided that the agent’s prior beliefs are correct. This better matches the observed correlation between decision time and choice probability than does the classical drift-diffusion model (DDM), where the agent knows the utility difference between the choices. ∗This paper was submitted to the AER on June 8, 2015 under the title “Stochastic Choice and Optimal Sequential Sampling.” We thank Stefano DellaVigna and Antonio Rangel for very stimulating conversations, a co-editor, three anonymous referees, as well as Jerome Busemeyer, Jan Drugowitsch, Arash Khodadadi, Josh Tenenbaum and Gonzalo Cisternas for helpful comments, Ian Krajbich, Carriel Armel and Antonio Rangel for sharing their experimental data with us, Kevin Kainan Li, In Young Cho and Jonathan Libgober for expert research assistance, and the Sloan Foundation and NSF grants SES-0954162, SES-1123729, SES1258665 and CAREER grant SES-1255062 for support. †Department of Economics, MIT ‡Department of Economics, University of California, Berkeley §Department of Economics, Harvard University