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

Abstract

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 e¤ort. 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 …nd that both choices and the allocation of e¤ort are a¤ected by the material incentives in the choice problem and the available cognitive resources. We …nd evidence that optimal choices have shorter deliberation times than suboptimal choices, which is consistent with previous theoretical predictions. The distribution of errors can have signi…cant implications for the speci…cation of stochastic choice models. Speci…cations where errors have a Gumbel distribution appear to provide a better …t than those with a normal distribution. Despite that the cognitive load manipulation a¤ects 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 a¤ected by the available cognitive resources. This perhaps suggests that these results are general and persistent features of choice.

Stochastic Choice and Imperfect Judgments of Line Lengths: What Is Hiding in the Noise?

“…McFadden (1974) and Yellot (1977) demonstrate that if choice errors have a Gumbel 10 (not normal) distribution then this implies the Luce (1959) logistic stochastic choice rule. 11 Despite the signi…cance of the stochastic distribution of the noise, to our knowledge, the only papers to investigate this in a setting where incentivized choice is an increasing function of a single, objective measure are Du¤y, Gussman, and Smith (2021) and Du¤y and Smith (2022). Similar to these previous e¤orts, we …nd that the errors are better described as having a Gumbel distribution rather than a normal distribution.…”

“…As previously noted, Du¤y, Gussman, and Smith (2021) and Du¤y and Smith (2022) also describe incentivized judgments of length. These previous e¤orts had choice sets that varied in size (2-6 items), rather than the binary choice we study here.…”

“…Caplin and Dean (2015), Dean and Neligh (2019), Dewan andNeligh (2020), andCaplin, Csaba, Leahy, andNov (2020) incentivize judgments of countable stimuli to test models of rational inattention. Du¤y, Gussman, and Smith (2021) and Du¤y and Smith (2022) incentivize judgments of line length to better understand stochastic choice. Other authors incentivize judgments of static or dynamic dots to test models of decision making.…”

“…7 Speci…cally, we can observe both the response times and the number of instances within a trial that the subject clicked to reveal a line, which we refer to as View clicks. Du¤y, Gussman, and Smith (2021) and Du¤y and Smith (2022) also employ incentivized line judgment tasks, but with choice sets that ranged between 2 and 6 items. However, our binary choice design here permits us to address a di¤erent set of questions.…”

The Future of Decisions From Experience: Connecting Real-World Decision Problems to Cognitive Processes

“…Nonsymbolic numerosity information could lead to less precise representations than symbolic numerosity information. Thus, modeling number perception explicitly and understanding how numeric cognition might differ between symbolic and nonsymbolic presentations ( Duffy et al, 2021 ; Garcia et al, 2022 ; Zeigenfuse et al, 2014 ) can help us to better understand preferential behavior from experiences.…”