A psychologist and an economist form a line

A psychologist and an economist form a line: What can imperfect perception of length tell us about stochastic Sean Duffy John Smith choice? Rutgers-Camden Psychology Economics

Choice experiment 2

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Assessment 4

Choice experiment We infer that U(Pringles) ≥ U(Coke) But what if the choice was a mistake? Or utility is random or imperfect? True preferences are not observable 5

An economist and a psychologist walk into a bar n Objective reality is perceived imperfectly n How long is this line? q q Comparison Reproduction Psychologists study imperfect perception n q q Judgments of length, weight, shades, loudness, etc. Weber-Fechner Law (1860) 6

Our choice experiment n Using this insight, we design n An “idealized” choice experiment where: n Can observe “true” preferences of subjects q n Preferences are stable and objective But subjects have imperfect perception of their preferences 7

Experimental Design n Objects of choice are lines n Paid an increasing amount in the q length of line selected n Length is a proxy for utility n Does this help us better understand random choice? q Yes? 8

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Experimental Design n Between 2 and 6 lines n Varied the length of the longest line from q 160 pixels (8. 0 cm) n q n And 304 pixels (15. 1 cm) Varied the difficulty of the treatment q Lines of n n n very similar lengths kinda similar lengths very different lengths 16

Response times! n Unlike the paper in Getafe n We give subjects up to 60 seconds to make the selection 17

Choice is random (no table) n n Probability longest line is selected is decreasing in q q Number of lines in choice set Difficulty of choice n q (similarity of the lengths) Length of the lines n Economists: Wealth effects q n Richer, so expend less effort Psychologists: Weber’s law q Larger stimulus, reduced absolute sensitivity 18

Response times (no table) n n Response times are increasing in q q Number of lines in choice set Difficulty of choice n q (similarity of the lengths) Length of the lines n Suggests subjects are expending more effort on longer lines 19

Response times n More difficult decisions q n n Longer response times Fudenberg, Strack, and Strzalecki (AER, 2018) Uncertain utility in a choice Constant cost of gathering information Incorrect decisions will have longer response times than q correct decisions 20

Correct faster than incorrect? n n n Pooled Correct: 12. 25 s Incorrect: 15. 730 s q n M-W: p<0. 001 Same result when restricted to q q q number of lines difficulty treatment line lengths 21

But… n n Maybe subjects who take longer on task Are also worse at the task 22

Response times Suboptimal decisions take longer Optimal decisions are faster 23

Random choice models n 24

Gumbel errors? ? ? n Gumbel distribution q q Type 1 extreme-value Double exponential F(ε)=e Normal -ε -e Gumbel 25

Multinomial Discrete Choice n Estimate: n (1, 3, 5) Gumbel errors, identically distributed (2, 4, 6) Normal errors, identically distributed n n (1, 2) Linear: Lengthi (3, 4) Log: log (Lengthi) (5, 6) Power: (Lengthi)1. 04 n Compare AICs n n 26

Gumbel vs. Normal AIC smaller for Gumbel than normal Errors appear to be Gumbel 27

Conclusions n In our idealized choice setting q Where we know the true preferences n Choice is random n Longer response times for more difficult choices n Suboptimal choices have longer response times than optimal choices q n Fudenberg, Strack, and Strzalecki correct? Errors Gumbel distribution 28

Random choice n Random choice is due to many things q q q Attention sets Private information Etc. n But even controlling for these random choice occurs because of imperfect perception of our own preferences n And we can study this in the lab n n 29

Bad science in psychology n. Ask me about the very bad science q Later 30

Thanks! n n n John Smith Rutgers University-Camden smithj@camden. rutgers. edu 31