When Fairness Isn’t Fair: Understanding Choice Reversals Involving Social Preferences

In settings with uncertainty, tension exists between ex ante and ex post notions of fairness (e.g., equal opportunity versus equal outcomes). In a laboratory experiment, the most common behavioral pattern is for subjects to select the ex ante fair alternative ex ante, and switch to the ex post fair alternative ex post. One potential explanation embraces consequentialism and construes the reversals as manifestations of time inconsistency. Another abandons consequentialism, thereby avoiding the implication that revisions imply inconsistency. We test between these explanations by examining the demand for commitment, and contingent planning. The hypothesis of time-consistent non-consequentialism receives strong support.

Transcript

1. When Fairness Isn’t Fair Understanding Choice Anomalies Involving Social Preferences James Andreoni UCSD Deniz Aydin WashU Blake Barton Stanford Doug Bernheim Stanford Jeffrey Naecker Wesleyan
2. Introduction
3. Motivating Thought Exercise Allocate 10 lottery tickets between two people, Alice and Bob • One ticket is winner, pays $10 to holder
4. Motivating Thought Exercise Allocate 10 lottery tickets between two people, Alice and Bob • One ticket is winner, pays $10 to holder • How do you allocate?
5. Motivating Thought Exercise Allocate 10 lottery tickets between two people, Alice and Bob • One ticket is winner, pays $10 to holder • How do you allocate? Allocate 10 lottery tickets between two other people, Anthony and Barbara • 10 tickets have already been allocated to Anthony • You allocate additional 10 tickets • One ticket (from 20) is winner, pays $10 to holder
6. Motivating Thought Exercise Allocate 10 lottery tickets between two people, Alice and Bob • One ticket is winner, pays $10 to holder • How do you allocate? Allocate 10 lottery tickets between two other people, Anthony and Barbara • 10 tickets have already been allocated to Anthony • You allocate additional 10 tickets • One ticket (from 20) is winner, pays $10 to holder • How do you allocate?
7. Motivating Thought Exercise Allocate 10 lottery tickets between two people, Alice and Bob • One ticket is winner, pays $10 to holder • How do you allocate? Allocate 10 lottery tickets between two other people, Anthony and Barbara • 10 tickets have already been allocated to Anthony • You allocate additional 10 tickets • One ticket (from 20) is winner, pays $10 to holder • How do you allocate? • Now told that your set of 10 tickets definitely contains the winner • You can revise your allocation between Anthony and Barbara
8. Motivating Thought Exercise Allocate 10 lottery tickets between two people, Alice and Bob • One ticket is winner, pays $10 to holder • How do you allocate? Allocate 10 lottery tickets between two other people, Anthony and Barbara • 10 tickets have already been allocated to Anthony • You allocate additional 10 tickets • One ticket (from 20) is winner, pays $10 to holder • How do you allocate? • Now told that your set of 10 tickets definitely contains the winner • You can revise your allocation between Anthony and Barbara • How do you allocate?
9. Our Findings 1. Across decision tasks: a. Subjects split tickets evenly in ex post frame – ie allocation (5, 5) b. Subjects offset built-in inequality in ex ante frame – ie allocation (0, 10)
10. Our Findings 1. Across decision tasks: a. Subjects split tickets evenly in ex post frame – ie allocation (5, 5) b. Subjects offset built-in inequality in ex ante frame – ie allocation (0, 10) 2. Within decision task: tension between ex ante and ex post → choice reversals
11. Our Findings 1. Across decision tasks: a. Subjects split tickets evenly in ex post frame – ie allocation (5, 5) b. Subjects offset built-in inequality in ex ante frame – ie allocation (0, 10) 2. Within decision task: tension between ex ante and ex post → choice reversals • Implications for theory • Frame-dependence and reversals inconsistent with expected utility • Run additional treatments to separate possible explanations
12. Our Findings 1. Across decision tasks: a. Subjects split tickets evenly in ex post frame – ie allocation (5, 5) b. Subjects offset built-in inequality in ex ante frame – ie allocation (0, 10) 2. Within decision task: tension between ex ante and ex post → choice reversals • Implications for theory • Frame-dependence and reversals inconsistent with expected utility • Run additional treatments to separate possible explanations 3. Reversals driven by non-consequentialist preferences
13. Implications • What is “fair” depends on context • We focus on timing of the allocation decision • Equal opportunity, ie ex ante fairness • Equal outcomes, ie ex post fairness
14. Implications • What is “fair” depends on context • We focus on timing of the allocation decision • Equal opportunity, ie ex ante fairness • Equal outcomes, ie ex post fairness • Relevant for any decision involving economic shocks with unequal effects
15. Introduction Result 1: Framing Effects Result 2: Reversals Theory Result 3: Separating Theories Conclusion
16. Result 1: Framing Effects
17. The Basic Task • 20 lottery tickets allocated between two recipients • Distribution of tickets 1-10 fixed ahead of time (“computer’s tickets”) • Varies between rounds • Known by subject • Subject chooses distributions of tickets 11-20
18. The Basic Task • 20 lottery tickets allocated between two recipients • Distribution of tickets 1-10 fixed ahead of time (“computer’s tickets”) • Varies between rounds • Known by subject • Subject chooses distributions of tickets 11-20 • One of the 20 tickets drawn at random • Recipient allocated that ticket gets $10
19. Allocating Tickets
20. Recipient Households • All recipients are poor households in Kenya listed on GiveDirectly • Household composition varies across rounds, but is similar within rounds • Why use GiveDirectly households instead of other lab participants? • Reduce image concerns • Larger impact of lottery payment
21. Households
22. Types of Decision Task • Ex ante task (A) • Allocates tickets without knowing if winning ticket is in her group • Subject knows computer’s allocation when she makes decision
23. Types of Decision Task • Ex ante task (A) • Allocates tickets without knowing if winning ticket is in her group • Subject knows computer’s allocation when she makes decision • Ex post task (P) • First reveal whether winning ticket is among computer’s tickets or among subject’s tickets • If among subject’s tickets, subject makes allocation as in task above
24. Ex Ante Task
25. Ex Post Task
26. Rounds • Subjects face 8 decision tasks of varying types • Each household appears only once across all 8 rounds • One round chosen at random and implemented • Each round had a different computer ticket allocation or “fingerprint” Round 1 2 3 4 5 6 7 8 Household A 7 2 10 1 8 3 9 0 Household B 3 8 0 9 2 7 1 10
27. Decision Categories Assume computer allocates 8 tickets to A (and 2 to B): Subject’s allocation to A Category 0 1 2 3 4 5 6 7 8 9 10
28. Decision Categories Assume computer allocates 8 tickets to A (and 2 to B): Subject’s allocation to A Category 0 1 2 3 4 5 ← Ex Post Equalizing (no offsetting) 6 7 8 9 10
29. Decision Categories Assume computer allocates 8 tickets to A (and 2 to B): Subject’s allocation to A Category 0 1 2 ← Ex Ante Equalizing (fully offsetting) 3 4 5 ← Ex Post Equalizing (no offsetting) 6 7 8 9 10
30. Decision Categories Assume computer allocates 8 tickets to A (and 2 to B): Subject’s allocation to A Category 0 1 2 ← Ex Ante Equalizing (fully offsetting) 3 Mixed (partial offsetting) 4 5 ← Ex Post Equalizing (no offsetting) 6 7 8 9 10
31. Decision Categories Assume computer allocates 8 tickets to A (and 2 to B): Subject’s allocation to A Category 0 Overcompensating (excessive offsetting) 1 2 ← Ex Ante Equalizing (fully offsetting) 3 Mixed (partial offsetting) 4 5 ← Ex Post Equalizing (no offsetting) 6 7 8 9 10
32. Decision Categories Assume computer allocates 8 tickets to A (and 2 to B): Subject’s allocation to A Category 0 Overcompensating (excessive offsetting) 1 2 ← Ex Ante Equalizing (fully offsetting) 3 Mixed (partial offsetting) 4 5 ← Ex Post Equalizing (no offsetting) 6 Reinforcing 7 8 9 10
33. Treatments Do allocation decisions depend on the frame?
34. Treatments Do allocation decisions depend on the frame? Treatment Rounds 1-4 Participants 1 Ex-ante 71 2 Ex-post 72
35. Treatments Do allocation decisions depend on the frame? Treatment Rounds 1-4 Participants 1 Ex-ante 71 2 Ex-post 72 Details: • All sessions run at UCSD • Subjects paid flat rate of $10 for participating
36. Allocations are Frame-Sensitive Ex Ante Frame Ex Post Frame 0.0 0.2 0.4 0.6 Frequency Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Continuous Consistency Strictness
37. Allocations are Frame-Sensitive Ex Ante Frame Ex Post Frame 0.0 0.2 0.4 0.6 Frequency Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Continuous Consistency Strictness
38. Persistence of Initial Framing • Does exposure to both frames change sensitivity to frame?
39. Persistence of Initial Framing • Does exposure to both frames change sensitivity to frame? • Expand set of treatments: Treatment Rds 1-2 Rds 3-4 Rds 5-8 Participants 1 Ex-ante Ex-ante Ex-ante 71 2 Ex-post Ex-post “ 72 3 Ex-ante Ex-post “ 48 4 Ex-post Ex-ante “ 48
40. Experience Has No Effect on Frame-Sensitivity EA EP EA EP EA EP EP EA EA EA EA EA Rounds 1−2 Rounds 3−4 Rounds 5−8 1 2 3 4 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Frequency Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Consistency
41. Experience Has No Effect on Frame-Sensitivity EA EP EA EP EA EP EP EA EA EA EA EA Rounds 1−2 Rounds 3−4 Rounds 5−8 1 2 3 4 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Frequency Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Consistency
42. Experience Has No Effect on Frame-Sensitivity EA EP EA EP EA EP EP EA EA EA EA EA Rounds 1−2 Rounds 3−4 Rounds 5−8 1 2 3 4 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Frequency Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Consistency
43. Result 2: Reversals
44. New Type of Decision Task • Ex ante task with surprise ex post revision (AR) • After making ex ante choice, subject learns whether or not one of her tickets was chosen • If one of her tickets was chosen, asked to confirm/revise • Does not know in advance that she will have this opportunity
45. New Type of Decision Task • Ex ante task with surprise ex post revision (AR) • After making ex ante choice, subject learns whether or not one of her tickets was chosen • If one of her tickets was chosen, asked to confirm/revise • Does not know in advance that she will have this opportunity Full treatment specification: Treatment Rds 1-2 Rds 3-4 Rds 5-8 1 Ex-ante Ex-ante Ex-ante w/surprise revision 2 Ex-post Ex-post “ 3 Ex-ante Ex-post “ 4 Ex-post Ex-ante “
46. New Type of Decision Task • Ex ante task with surprise ex post revision (AR) • After making ex ante choice, subject learns whether or not one of her tickets was chosen • If one of her tickets was chosen, asked to confirm/revise • Does not know in advance that she will have this opportunity Full treatment specification: Treatment Rds 1-2 Rds 3-4 Rds 5-8 Shorthand 1 Ex-ante Ex-ante Ex-ante w/surprise revision 4A_4AR 2 Ex-post Ex-post “ 4P_4AR 3 Ex-ante Ex-post “ 2A2P_4AR 4 Ex-post Ex-ante “ 2P2A_4AR
47. Generating Choice Reversals • Do competing fairness motivations generate choice reversals? • Look at initial ex-ante vs surprise ex-post revision choices for same round • Focus on last four rounds of Treatment 1 (4A_4AR) • 68.3% of choices revised • 78.9% of subjects revise at least once • 71% of Revisions were to exactly 50-50 division of tickets
48. Choice Reversals are Prevalent Initial Final Final (changes only) 0.0 0.2 0.4 0.6 0.8 Frequency Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Intensity
49. Joint Distribution of Initial and Final Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing 0.0 0.1 0.2 0.3 0.4 Frequency Revised_Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing
50. Awareness of Both Frames • Does exposure to both frames reduce prevalence of choice reversals? • Compare revision behavior in last 4 rounds of all treatments • First four rounds: varying experience with ex ante and ex post tasks • Second four rounds: all face ex ante with surprise revision
51. Experience Has No Effect on Reversals Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing 1 2 3 4 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 Frequency Revised_Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing
52. Experience Has No Effect on Reversals Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing 1 2 3 4 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 Frequency Revised_Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing
53. Theory
54. Time-Consistency and Uncertainty • Decision maker forms complete contingent plan • Time-consistent DM follows through with plan at each node • Otherwise, time-inconsistent
55. Time-Consistency and Uncertainty • Decision maker forms complete contingent plan • Time-consistent DM follows through with plan at each node • Otherwise, time-inconsistent • Classic result: EU =⇒ time-consistent • (Markowitz 1959, Raiffa 1968, Machina 1989)
56. Time-Consistency and Uncertainty • Decision maker forms complete contingent plan • Time-consistent DM follows through with plan at each node • Otherwise, time-inconsistent • Classic result: EU =⇒ time-consistent • (Markowitz 1959, Raiffa 1968, Machina 1989) • Does non-EU =⇒ time-inconsistency? • Yes, if we assume DM is consequentialist
57. Time-Consistency and Uncertainty • Decision maker forms complete contingent plan • Time-consistent DM follows through with plan at each node • Otherwise, time-inconsistent • Classic result: EU =⇒ time-consistent • (Markowitz 1959, Raiffa 1968, Machina 1989) • Does non-EU =⇒ time-inconsistency? • Yes, if we assume DM is consequentialist • Can also have non-consequentialist DM who is time-consistent • Example: Machina’s Mom
58. Differentiating the Theories Two explanations for choice reversals: 1. Time-inconsistent consequentialists 2. Non-consequentialists
59. Differentiating the Theories Two explanations for choice reversals: 1. Time-inconsistent consequentialists 2. Non-consequentialists Two ways of differentiating these explanations: 1. Commitment device 2. Contingent revision plan
60. Result 3: Separating Theories
61. Adding Commitment • New type of decision task: Ex ante with commitment (AC ) • Same as AR, but subject knows she will have ex-post revision option • After submitting ex ante choice (but before learning about ticket), subject is offered three costless options • “I definitely want the chance to revise" • “I definitely do no want the chance to revise" • “I do not care about having an opportunity to revise"
62. Adding Commitment • New type of decision task: Ex ante with commitment (AC ) • Same as AR, but subject knows she will have ex-post revision option • After submitting ex ante choice (but before learning about ticket), subject is offered three costless options • “I definitely want the chance to revise" • “I definitely do no want the chance to revise" • “I do not care about having an opportunity to revise" • New treatment: Rds 1-4 Rds 5-8 Participants Ex-ante w/surprise revision Ex-ante w/commitment 72
63. Adding Commitment • New type of decision task: Ex ante with commitment (AC ) • Same as AR, but subject knows she will have ex-post revision option • After submitting ex ante choice (but before learning about ticket), subject is offered three costless options • “I definitely want the chance to revise" • “I definitely do no want the chance to revise" • “I do not care about having an opportunity to revise" • New treatment: Rds 1-4 Rds 5-8 Participants Shorthand Ex-ante w/surprise revision Ex-ante w/commitment 72 4AR_4AC
64. Aggregate Commitment Results • Preference for commitment: 40.6% of choices • Preference for flexibility: 30.2% of choices • Indifference: 29.2% of choices • Availability of commitment reduces revisions to 36.8% of choices • Compare to 68.3% in last four rounds of 4A_4AR
65. Separating Theories Among subjects who tend to switch in first half of experiment: • Time-inconsistent consequentialists should prefer to commit so as not to be tempted to switch to ex post fairness • Non-consequentialists should choose flexibility
66. Revision Predicts Preference for Flexibility Never Revised 19.4% of subjects Revised once, always EA to EP 16.7% of subjects Revised once, never EA to EP 13.9% of subjects Revised twice, one time EA to EP 12.5% of subjects Revised twice, never EA to EP 15.3% of subjects Revised twice, always EA to EP 22.2% of subjects 0.00 0.25 0.50 0.75 1.00 Percentage Revision behavior in first four rounds Response Committment Indifference Flexibility Strictness
67. Planned Revisions • New type of decision task: Ex ante allocations with planned revisions (AP) • Participant allocates tickets as in ex ante task • Once all allocation decisions have been entered, asked whether she would like to provide instructions for the case where the winning ticket is definitely in her set of 10
68. Planned Revisions • New type of decision task: Ex ante allocations with planned revisions (AP) • Participant allocates tickets as in ex ante task • Once all allocation decisions have been entered, asked whether she would like to provide instructions for the case where the winning ticket is definitely in her set of 10 • New treatment: Rds 1-4 Rds 5-8 Participants Ex-ante Ex-ante w/planned revisions 46
69. Planned Revisions • New type of decision task: Ex ante allocations with planned revisions (AP) • Participant allocates tickets as in ex ante task • Once all allocation decisions have been entered, asked whether she would like to provide instructions for the case where the winning ticket is definitely in her set of 10 • New treatment: Rds 1-4 Rds 5-8 Participants Shorthand Ex-ante Ex-ante w/planned revisions 46 4A_4AP
70. Separating Theories • Time-inconsistent consequentialist: planned revision same as ex ante allocation • Non-consequentialist: planned revision same as ex post allocation
71. Planned Revisions Anticipate Reversals Initial Planned Revision 0.0 0.2 0.4 0.6 Frequency Category Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing
72. Conclusion
73. Key Empirical Results • Allocations are sensitive only to the current frame • Within decision tasks, choice reversals are very common • Subjects who reverse are more likely to demand commitment later • Subjects make contingent plan to change allocations
74. Takeaways • Implications: • Evidence supports non-consequentialism over time-inconsistency • If individuals shift allocations, what about entire society?
75. Takeaways • Implications: • Evidence supports non-consequentialism over time-inconsistency • If individuals shift allocations, what about entire society? • Future work: • Theories of procedural/deontological fairness • Different context, eg one with self-serving motivation • Political beliefs and demographics predict behavior?
76. Appendix
77. 4A_4AR 4P_4AR −2 −1 0 1 2 −2 −1 0 1 2 0.0 0.5 1.0 1.5 2.0 alpha density Back
78. Ex Ante Frame Ex Post Frame Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing 0.0 0.2 0.4 0.6 Frequency Intensity 0.25 0.5 0.75 1 Back
79. EA EP EA EP EP EA EA EP EA EA EA EA Rounds 1−2 Rounds 3−4 Rounds 5−8 2A2P_4AR 2P2A_4AR 4A_4AR 4P_4AR Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Frequency Intensity 0.25 0.5 0.75 1 Back
80. Strictness of Allocation Decisions 0.2 0.4 0.6 0 1 2 3 4 5 ‘Prize Amount Deviation From 10‘ Demand Strictness of Final Allocation Strictness of Initial Allocation Strictness of Initial vs Final Allocation Back
81. Initial Final Final (changes only) Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing Overcompensating Ex Ante Equalizing Mixed Ex Post Equalizing Reinforcing 0.0 0.2 0.4 0.6 0.8 Frequency Intensity 0.25 0.5 0.75 1 Back
82. Strictness of Commitment Preferences 0.3 0.4 0.5 0.6 0.7 0.8 1 2 3 4 5 ‘Prize Amount Deviation From 10‘ Demand Committed Flexible Back