Fairness Under Uncertainty

Fairness Rating
Major Findings of Study I
People judge fairness under uncertainty
ቤተ መጻሕፍቲ ባይዱ
based on both the value of the chances and the final outcomes;
Fairness perception of chances depends on
Fairness under UncertaintyTheoretical Solutions
Mainly in Economics literature


Yager and Kreinovich (2000) - fair division under interval uncertainty (the division weights of agents cannot be uniquely determined) Boiney (2001) - choice under uncertainty when fairness involves heterogeneous preferences. Chavas and Coggins (2003) - Resource allocation when policy makers have imperfect information on agents.
whether people are sharing or receiving them. People tend to have a bias towards selfinterest .
Study II: Purposes
X% chance vs. X% pie, assuming a
neutral role
Insight on Responders by using the
minimal acceptance offers (MAO)
Exclusive vs. independent chances
3 Games in Study II
DUG SUG-e (as in Study 1) with exclusive chance in
SUG with Independent Chances
Proposer’s offer: X% for Responder, 100%-X% for Proposer Responder’s Minimum Acceptable Offer (MAO): Y%
Study I: DUG and SUG
Deterministic Ultimatum Game (DUG) Splitting 100 beans (worth $5) The Stochastic Ultimatum Game (SUG) Two players determine their chances of winning 100 beans The proposer makes an offer on how large a chance he is willing to give the responder for winning 100 beans. The responder decides to accept or to reject the offer. If the offer is accepted, a random number will be generated to decide whether the proposer or the responder gets 100 beans. The other person will get nothing. If the offer is rejected, then the game is over, and nobody gets any beans.

Why Study Fairness under Uncertainty?
Resources vs. Goals: resources
increase the chances of reaching goals, not guarantee it. Sharing resource sharing chances of reaching individual goals. E.g. Pollution regulation, Health investment, Education resource, Safety equipment, etc.
Study I: Experimental Design
Design

112 subjects (56 pairs) One-Shot game Fairness Rating: after Responders make a decision, both Proposers and Responders rate how fair the offer is on a scale of 0-100, where 0 represents “not fair at all” and 100 represents “very fair”.
Stochastic Ultimatum Game
Proposer’s offer: X% for Responder, 100%-X% for Proposer Responder’s Minimum Acceptable Offer (MAO): Y%
X≥Y
X<Y
Random number ≦ 100-X
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30% of $100
30% Chance
of Wining $100
John
Jane
Key Findings
When taking a neutral perspective, people
Three conditions (Between Subject)

DUG: Fairness rating of offers SUG-Ex ante: fairness rating before the uncertainty is resolved ) SUG-Ex post: fairness rating after the uncertainty is resolved
Is 30% Chance More or Less Fair Than 30% Pie?
--Fairness Under Uncertainty
Min Gong Jonathan Baron Howard Kunreuther
Is 30% Chance More or Less Fair Than 30% Pie?
Interaction between Roles and Uncertainty
Average Offers in the SUG (37% of 100 beans) and DUG
(36% chance of winning 100 beans) are n.s., but the fairness ratings are.
Fairness under UncertaintyDescriptive Studies
Mainly in Psychology Literature



Ubel and Loewenstein, 1996; Ubel, Baron, and Asch 1999- people are willing to trade efficiency for fairness. See (2009) –the role of knowledge in fairness judgment with uncertainty (Prediction vs. Procedure) Bone and Sucking (2004) – People favor ex ante efficiency over ex post equality in a simple design, and the opposite in more complicated treatments
Random number > 100-X
Proposer gets 0 beans Responder gets 0 beans
Proposer gets 100 beans Responder gets 0 beans
Proposer gets 0 beans Responder gets100 beans
view X% of the exclusive chance fairer than X% of the independent chance, which is in turn fairer than X% of pie; When taking roles as givers or receiver of chances, people have self-interest bias; Fairness of chances are judged on both the value of chances and final outcomes.
which only one player gets 100 beans SUG-i with independent chances

Similar to Sgame in Study 1 that two players’ chances add up to 100% But two players have independent chances the outcome can be: both get 100, nobody gets anything, or one gets 100.
Fairness Rating of Offers in 3 Conditions (with offers being statistically the same )
100 80 60 40 20 0 DUG SUG-ex ante Games SUG -ex post 87 67 66 56 46 69 Proposer Responder
Regression Results

Fairness depends on



Offers (β1 =1.85, p<0.01) Outcomes (β2 =0.14, p<0.05) People judge fairness not only by the intention and probabilities, but also by the actual outcomes. Consistent with recent finding in Cushman et al. (2009) Interaction b/w Roles and Uncertainty (β4 =25, p<0.01) Responders: x% chance is less fair than x% (β3 =-16, p<0.01) Proposer: x% chance is fairer than x% (β3 +β4 =9) Compared to a 1% increase in the offer increasing the fairness rating by only 1.85, roughly speaking, for the Proposer, offering 35% of the chance is as fair as offering 40% of the beans. But for the Responder, receiving 35% of the chance is only as fair as receiving 26% of the beans.