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?

John

Jane

30% of $100 30% Chance

of Wining $100

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Key Findings

When taking a neutral perspective, people 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.

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.

Fairness under Uncertainty- Theoretical 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.

Fairness under Uncertainty- Descriptive 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

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.

Stochastic Ultimatum Game

Proposer’s offer: X% for Responder, 100%-X% for ProposerResponder’s Minimum Acceptable Offer (MAO): Y%

X≥Y X<Y

Random number ≦ 100-X

Random number > 100-X

Proposer gets 0 beansResponder gets 0 beans

Proposer gets 100 beansResponder gets 0 beans

Proposer gets 0 beansResponder gets100 beans

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”.

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

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 f

airness 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.

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.

Fai rness Rat i ng of Off ers i n 3 Condi t i ons(wi th off ers bei ng stat i st i cal l y the same)

67

87

69

6656

46

0

20

40

60

80

100

DUG SUG-ex ante SUG -ex postGames

Fair

ness

Rat

ing

ProposerResponder

Major Findings of Study I

People judge fairness under uncertainty based on both the value of the chances and the final outcomes;

Fairness perception of chances depends on whether people are sharing or receiving them. People tend to have a bias towards self-interest .

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 whic

h 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 anythi

ng, or one gets 100.

SUG with Independent Chances

Proposer’s offer: X% for Responder, 100%-X% for Proposer Responder’s Minimum Acceptable Offer (MAO): Y%

X≥ Y X<Y

Proposer’s Random Number ≦ 100-X

Responder’s Random Number > 100-X

Proposer gets 0 beans Responder gets 0 beans

Proposer gets 100 beans

Responder gets100 beans

Experimental Design

152 subjects in between-subject (3 games) design Each subject makes a pre-committed offer and a

minimum acceptable offer (MAO), with counter balanced order

Half the players are randomly assigned to be Proposers, the other half Responders

Each Proposer’s offer is matched to the MAO of a random Responder to determine whether or not the resource is split or both players receive nothing.

Question: what is the lowest offer to be considered fair in the current game?

Pre-committed Offers, MAO, and Fair Offers of “Neutral” Players Judged fair offers are the highest in the DUG, followed by

SUG-i, and the lowest in SUG-e. All significant at 5%. Implication: x% of exclusive chance has the highest fairness,

followed by x% of independent chance, and x% of the beans is the least fair.

4440

3542

3834

28 26 25

0

20

40

60

DUG SUG- I ndependent SUG- Excl usi ve

Games

Perc

enta

ge o

f Be

ans

or C

hanc

es

J udged Fai r Off erPre- bi ndi ng Off erPre- bi ndi ng MAO

How do People Decide What to Offer?

Pre-committed offers depends on: MAO (t(139)=2.98, p<0.01) Judged fair offers (t(139)=3.58, p<0.01)

People consider both Rejection of lower offers Fairness the offer carries

Conclusions

When taking a neutral perspective, people 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.

Notes and Help

News stories about resources and chances Implications of the findings in term of real life

situations and public policy Missing literature?