Judgments of extent in the economics laboratory: Are there brains in choice? Sean Duffy Steven Gussman John Smith Rutgers-Camden Rutgers-Camden Rutgers-Camden Psychology Digital Studies Economics

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

Choice experiment

Assessment

Assessment

 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

After choosing (unhealthy) Pringles   0.5 0.5 Attributes of previous choices might interact with current choice 0.5 0.5

Our choice experiment An “idealized” choice experiment where: Goods are attribute-free Can observe “true” preferences of subjects Preferences are stable and objective But subjects have imperfect perception of their preferences

Experimental Design Objects of choice are lines Paid an increasing amount in the length of line selected

Experimental Design Can only view one line at a time Memory is crucial in choice Can also observe the search history Similar to Mouselab

Experimental Design Why pick the longest line? Paid an amount that increases in length of selected line $1 per 240 pixels $0.004167 per pixel If time expires without a choice Assumed that selected line had zero length

Experimental Design Between 2 and 6 lines Each occurred with prob 0.2 Varied the length of the longest line from 160 pixels (8.0 cm) And 304 pixels (15.1 cm)

Experimental Design Easy treatment Medium treatment Longest line relatively obvious Medium treatment Longest line somewhat obvious Difficult treatment Longest line not obvious Each occurred with prob 1/3

Cognitive resources and choice Do the available cognitive resources affect choice in our idealized choice setting?

How to manipulate cognitive resources? Cognitive Load Task that occupies cognitive resources Unable to devote to deliberation Observe behavior Require subjects to memorize a number Big number Small number Differences in behavior?

Cognitive load 100 trials 50 high load treatment 525809 3 6-digit number to remember 50 low load treatment 1-digit number to remember Cognitive load treatment randomly determined 525809 3

Experimental Design Strongly incentivized memorization task Performance in memorization task unrelated to payment for line selection in that period Paid for 30 randomly selected line selection if 100 memorization tasks correct Paid for 29 if 99 correct … Paid for 1 if 71 correct Paid for none if 70 or fewer correct

Experimental Design Timing within each period: Given new number to remember 5 seconds Line selection task 15 seconds Asked for number Repeat

Details 92 Subjects 9200 line selections E-prime Earned average $26 Response times in microseconds! (6 decimal places) Earned average $26 From $5 to $35

DV: Selected the longest line-Logit Selected longest line DV: Selected the longest line-Logit High Load -0.1570 (p=0.004) -0.1616 -0.1532 (p=0.01) Longest line size “normalized” -0.0032 (p<0.001) -0.0033 -0.0031 Number of lines “normalized” -0.3154 -0.3267 -0.3111 Repeated Measures No Fixed Effects Random Effects Difficulty dummies Yes Less accuracy with longer lines Less accuracy with more lines High load, less likely longest line selected Weber’s Law

High load and selected line Similar analysis holds for the variable: Longest - Selected Subjects in High load treatment are making worse line selections

DV: Unique lines viewed High Load -0.02677 (p<0.001) -0.02669 -0.02670 Longest line size “normalized” -0.0002 (p=0.02) (p=0.01) -0.00020 Number of lines “normalized” 0.9812 0.9818 0.9817 Repeated Measures No Fixed Effects Random Effects Difficulty dummies Yes High load, fewer unique lines viewed Fewer unique lines viewed with longer lines More unique views with more lines

High load and search High load also: spends less time viewing longest line fewer view clicks

But… Bad searches are not causing most of the bad choices 97% of suboptimal choices occurred where subjects viewed the longest line

Random choice models Objects {1, 2,…, N} Values {v1, v2,…, vN} Probability of selecting object i from set: Pr 𝑖 = 𝑒 𝜆𝑣𝑖 𝑗=1 𝑁 𝑒 𝜆𝑣𝑗 Usually v’s are not known But in our setting they are known

One more interesting thing A B C D E F Percent selected longest line given that the longest line is letter

One more interesting thing 50.8% 52.8% 50.0% 60.2% 64.5% 78.7% Percent selected longest line given that the longest line is letter

One more interesting thing 64.1% 58.0% 62.8% 70.8% 66.0% - Percent selected longest line given that the longest line is letter

One more interesting thing 64.8% 62.0% 71.6% 79.3% - - Percent selected longest line given that the longest line is letter

One more interesting thing 72.5% 72.5% 78.7% - - - Percent selected longest line given that the longest line is letter

One more interesting thing 76.9% 79.9% - - - - Percent selected longest line given that the longest line is letter

Conclusions In our idealized choice setting Available cognitive resources Negatively affects optimality of choices Negatively affects searches

What can visual judgments do for you? Real decisions first Involve a judgment Own willingness to pay Probability of event Effect of announcement on value of asset Then a decision You think a way to incorporate these into an experimental interface

Thanks! John Smith smithj@camden.rutgers.edu