Speed, Accuracy, and Complexity

This paper re-examines the validity of using response time to infer problem complexity. It revisits a canonical Wald model of optimal stopping, taking signal-to-noise ratio as a measure of problem complexity. While choice quality is monotone in problem complexity, expected stopping time is inverse U-shaped. Indeed decisions are fast in both very simple and very complex problems: in simple problems it is quick to understand which alternative is best, while in complex problems it would be too costly – an insight which extends to general costly information acquisition models. This non-monotonicity also underlies an ambiguous relationship between response time and ability, whereby higher ability entails slower decisions in very complex problems, but faster decisions in simple problems. Finally, this paper proposes a new method to correctly infer problem complexity based on the finding that choices react more to changes in incentives in more complex problems.