  This paper re-examines the use of 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 distorting incentives in
favour of an alternative has a greater effect on choices in more complex
problems.
