An economist and a psychologist form a line: What can imperfect perception of length tell us about stochastic choice?

Standard choice experiments are hampered by the fact that utility is either unknown or imperfectly measured. By contrast, we design an induced-values choice experiment: objects are valued according to only a single attribute with a continuous measure and we can observe whether the choice was optimal. Subjects are given a choice set involving lines of various lengths and are told to select one. They are paid an amount that increases with the length of their choice. Line length is an easily understood measure that naturally serves as a proxy for utility. We find that the likelihood that subjects select the optimal line is decreasing in the number of lines in the choice set, the similarity of the line lengths, and the length of the longest line. We also find that response times are increasing in these same features of the choice sets. However, we find evidence that suboptimal choices are associated with longer response times than are optimal choices. This result appears to be consistent with Fudenberg et al. (Am Econ Rev 108(12):3651–3684, 2018). Errors in our data are better described as having a Gumbel distribution rather than a normal distribution. We find evidence consistent with the independence from irrelevant alternatives (IIA) property and we observe dynamic effects. We also observe effects consistent with (possibly endogenous) memory decay and attention. We hope our results can inform stochastic choice models and that our induced-values design is useful in other settings.