An Economist and a Psychologist Form a Line: What Can Imperfect Perception of Length Tell Us About Stochastic Choice?

Abstract

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 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 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 …nd a negative relationship between the demanding nature of the choice problems and the likelihood that subjects select the optimal lines. We also …nd a positive relationship between the demanding nature of the choice problems and the response times. However, we …nd 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 e¤ects consistent with memory decay and attention. Finally, we …nd evidence that choices in our experiment exhibit the independence from irrelevant alternatives (IIA) property.

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

“…Consistent with these predictions, we …nd evidence that suboptimal decisions are associated 1 7 For instance, see Henmon (1911), Volkmann (1934, Mosteller and Nogee (1951), Hey (1995), Mo¤att (2005), Woodford (2014), Alós-Ferrer, Granić, Kern, andWagner (2016), Echenique and Saito (2017), Konovalov and Krajbich (2019), Alós-Ferrer, Fehr, and Netzer (2021), Du¤y, Gussman, and Smith (2021), Alós-Ferrer and Garagnani (2022a), and Du¤y and Smith (2022).…”

“…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.…”