Visual judgments of length in the economics laboratory : Are there brains in stochastic choice?

We design an induced value choice experiment where the objects are valued according to only a single attribute with a continuous measure. Subjects have an imperfect perception of the choice objects but they can reduce their imperfect 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 is increasing in the length of their selection. This "idealized" choice experiment produces a dataset that is uniquely suited to study apparently random choice. We also manipulate the available cognitive resources of the subjects by imposing either a high or low cognitive load. We find that both choices and the allocation of effort are affected by the material incentives in the choice problem and the available cognitive resources. In particular, we find that subjects in the high load treatment make inferior line selections and perform worse searches. When we restrict attention to the set of viewed lines, we find evidence that subjects in the high load treatment make worse choices. Therefore, the low quality searches do not fully explain the low quality choices. We find evidence that optimal choices have shorter deliberation times than suboptimal choices, which is consistent with previous theoretical predictions. The distribution of errors can have significant implications for the specification of stochastic choice models. Our results suggest that errors are better described as having a Gumbel distribution rather than a normal distribution. We hope that this can inform the selection of stochastic choice models