Stochastic choice and imperfect judgments of line lengths: What is hiding in the noise?

Noise is a pervasive feature of economic choice. However, standard economics experiments are not well equipped to study the noise because experiments are constrained: preferences are often either unknown or only imperfectly measured by experimenters. As a result of these designs – where the optimal choice is not observable to the analyst – many important questions about the noise in apparently random choice cannot be addressed. There is a long tradition in psychology of studying settings where subjects make choices about objectively measurable, but imperfectly perceived objects. We simply supplement this design with material incentives in a way that resembles economic choice. In our design, subjects make incentivized binary choices between lines and are paid a function of the length of the selected line. We find a gradual (not sudden) relationship between the difference in the lengths of the lines and the optimal choice. Our analysis suggests that the errors are better described as having a Gumbel distribution rather than a normal distribution, and our simulated data increase our confidence in this inference. We find evidence that suboptimal choices are associated with longer response times than optimal choices.