1. 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

2. 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)

3. perceived = truth + ε Thurstone (1927) Luce (1959, 1977)
McFadden (1974, 1976, 1981)
Ui = Vi + εi
Choice i is selected from K if:
Vi + εi ≥ Vk + εk for every kK

4. Random Utility/Random Choice
Tversky (1969), Yellott (1977), Falmagne (1978), Loomes, Starmer, and Sugden (1989), Sopher and Gigliotti (1993), Loomes and Sugden (1995), Sopher and Narramore (2000), Gul and Pesendorfer (2006), Rubinstein and Salant (2006), Tyson (2008), Caplin, Dean, and Martin (2011), Gul, Natenzon, and Pesendorfer (2014), Loomes and Pogrebna (2014), Caplin and Dean (2015), Caplin and Martin (2015), Cubitt, Navarro-Martinez, and Starmer (2015), Fudenberg, Iijima, and Strzalecki (2015), Lu (2016), Apesteguia, Ballester, and Lu (2017), Agranov and Ortoleva (2017), Dean and Neligh (2017), Navarro-Martinez, Loomes, Isoni, Butler, and Alaoui (2017), Natenzon (2018), Apesteguia and Ballester (2018), Caplin, Dean, and Leahy (2018), Echenique, Saito, and Tserenjigmid (2018), Koida (2018), and Kovach and Tserenjigmid (2018).

5. and εi has Gumbel distribution
Random choice models
McFadden (1974) and Yellott (1977):
Ui = Vi + εi
and εi has Gumbel distribution
Imply the Luce model:
Probability of selecting object i from set K:
Pr 𝑖,𝐾 = 𝑒 𝑉𝑖 kK 𝑒 𝑉𝑘

6. F(ε)=e-e-ε Gumbel errors??? Gumbel distribution Type 1 extreme-value
Double exponential
F(ε)=e-e-ε
Normal
Gumbel

7. Choice experiment

8. Assessment

9. Assessment

10.  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

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

12. Our choice experiment An “idealized” choice experiment where:
Attributes will not interact in a way that is not observable
Can observe “true” preferences of subjects
Preferences are stable and objective
But subjects have imperfect perception of their preferences

13. Experimental Design Objects of choice are lines
Paid an increasing amount in the
length of line selected
Length is a proxy for utility

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

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

23. 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)

24. 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

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

26. 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?

27. 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

28. 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

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

30. 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

31. DV: Selected the longest line-Logit
Selected longest line
DV: Selected the longest line-Logit
High Load
(p=0.004)
(p=0.01)
Longest line size “normalized”
(p<0.001)
Number of lines “normalized”
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?
Choice overload?

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

33. DV: Unique lines viewed
High Load
(p<0.001)
Longest line size “normalized”
(p=0.02)
(p=0.01)
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

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

35. But… Bad searches are not causing
most of the bad choices
97% of suboptimal choices occurred where
subjects viewed the longest line
Analyze
Selected longest line viewed
Not consideration set effects

36. and εi Gumbel distributed:
Random choice models
McFadden (1974) and Yellot (1977):
Ui = Vi + εi
and εi Gumbel distributed:
Vi not typically observable
Vi =  xi
Where xi is a vector of observables
Vi =  Lengthi

37. Multinomial Discrete Choice
Estimate the following
(1) Gumbel errors, identically distributed
(2) Normal errors, identically distributed
(3) Gumbel errors, non-identically distributed
HEV model of Bhat (1995)
(4) Normal errors, non-identically distributed
Compare AICs

38. Multinomal Discrete Choice
AIC smaller for Gumbel than normal
Estimates of  varies V

39. Restrict to =0.1 Errors seem to have a Gumbel distribution
Except for one specification
AIC smaller for Gumbel than normal
Errors seem to have a Gumbel distribution

40. Position dependence A B C D E F Percent selected longest line
given that the longest line is letter

41. Position dependence 50.8% 52.8% 50.0% 60.2% 64.5% 78.7%
Percent selected longest line
given that the longest line is letter

42. Position dependence 64.1% 58.0% 62.8% 70.8% 66.0% -
Percent selected longest line
given that the longest line is letter

43. Position dependence 64.8% 62.0% 71.6% 79.3% - -
Percent selected longest line
given that the longest line is letter

44. Position dependence 72.5% 72.5% 78.7% - - -
Percent selected longest line
given that the longest line is letter

45. Position dependence 76.9% 79.9% - - - - Percent selected longest line
given that the longest line is letter

46. Reutskaja et al. (2011, AER) Eye tracking choice experiment Real goods
Forgetting
Effect of attention
Clicks seen longest
Time since seen longest

47. Conclusions In our idealized choice setting
Available cognitive resources
Negatively affects optimality of choices
Negatively affects searches
Errors Gumbel distribution

48. 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

49. Matějka and McKay (2015, AER)
Rational inattention foundation for discrete choice models
Agents can reduce the Shannon entropy
by incurring costs associated with attention
implies a random choice specification
similar to Luce (1959a)
In our experiment
subjects devote cognitive effort
in order to better judge the line lengths

50. What next?
No cognitive load
No time pressure
Observe response times

51. Thanks!
John Smith