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 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. 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. Specifications where errors have a Gumbel distribution appear to provide a better fit than those with a normal distribution. Despite that the cognitive load manipulation affects both choice and search, it is notable that neither the Gumbel distribution results nor the relationship between optimal choice and deliberation time appear to be affected by the available cognitive resources. This perhaps suggests that these results are general and persistent features of choice.