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 experimenters. As a consequence, the inferences available to researchers are limited. By contrast, we design a choice experiment where the objects are valued according to only a single attribute with a continuous measure and we can observe the true preferences of subjects. Subjects have an imperfect perception of the choice objects but can improve the precision of their perception with cognitive effort. Subjects are given a choice set involving several lines of various lengths and are told to select one of them. They strive to select the longest line because they are paid an amount that increases with the length of their choice. Our design allows us to observe the search history, the response times, and make unambiguous conclusions about the optimality of choices. We find a negative relationship between the demanding nature of the choice problems and the likelihood that subjects select the optimal lines. We also find a positive relationship between the demanding nature of the choice problems and the response times. 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, Strack, and Strzalecki (2018). Additionally, our experimental design permits a multinomial discrete choice analysis. Our results suggest that the errors in our data are better described as having a Gumbel distribution rather than a normal distribution. We also observe effects consistent with memory decay and attention. Finally, we find evidence that choices in our experiment exhibit the independence from irrelevant alternatives (IIA) property.