Reexamining Education Fairness: An Experimental Study of College

Admission Policies in China

Yang ZhangMay 7, 2013

College Admission Policies in China

• College Entrance Exam (Gaokao)• A nation-wide comprehensive exam in every June• Universities only consider Gaokao scores in recruiting new students.

• College Admissions• Competition for college education is limited within each province because of the quota

system.• Local variations in college admission policies

• Immediate acceptance (most provinces) vs. deterred acceptance (e.g. Shanghai).• Exam content• Timing of application

Timing of Application

• Low information• Not knowing your own and others’ Gaokao scores.

• Private/asymmetric information• Estimating your own score based on the official answers, but not knowing others’

scores.

• Complete information• Knowing your rank among all students.

Gaokao Exam

Result Distribution

Research Questions

• How does timing of application affect students’ strategies in college application?

• How does timing of application affect the distribution of admission outcomes?

Three Games

1. Mimic Exams

2. College Entrance Exam• Randomly pick one mimic exam score.

Mimic 1 Mimic 2

A 71-79 91-100

B 51-60 81-90

C 41-50 61-70 1 1 2 1 2 2c b c a b a

Three Games Cont’d

3. College Application• Choose one university from Harvard and the UI.• Get 2 dollars from Harvard and 1 dollar from the UI.• Three games only differ in the timing of application.

4. College Admission• Each university only admits one student.

Defining Admission Fairness

• Expected Rank Distribution • Ideal Outcome Distribution

Rank A B C

1 0.75 0.25 0

2 0.25 0.5 0.25

3 0 0.25 0.75

A B C

Harvard 0.75 0.25 0

UI 0.25 0.5 0.25

None 0 0.25 0.75

Expected Utility 1.75 1 0.25

Available Information in College Choice (e.g Student A)

• Complete Information• Expected rank distribution (unnecessary)• A, B, and C’s Gaokao scores

• Private/asymmetric information• Expected rank distribution• A’s Gaokao score

• Low information• Expected rank distribution

Experiment

• Subjects• 10 groups and 30 subjects• 21 Chinese (15 experienced), 6 Americans, 1 Taiwanese, and 2 Koreans• 8 groups for each treatment (complete, private, and low information)

• Post-game discussion• Which games are fair and which are not fair? • What was your expectation of other players’ choices (belief)? • Does the experiment well reflect the reality?• Other thoughts?

Complete Information Game: Evaluating the Expected Strategies

• Nash Equilibrium(a) • Observed Strategy Distribution

Rank Strategy

1 Harvard

2 UI

3 Harvard or UI

Rank Strategy

Harvard UI

11(8)

0(0)

20(0)

1(8)

30.125(1)

0.875(7)

Complete Information Game: Evaluating the Expected Admission Outcomes• Expected outcome distribution

• Luck in getting a higher score

• Observed outcome distribution

• Adjusted outcome distribution

A B C

Harvard 0.75 0.25 0

UI 0.25 0.5 0.25

None 0 0.25 0.75

Expected Utility 1.75 1 0.25

A B C

Harvard 0.75 0.375 0

UI 0.25 0.375 0.5

None 0 0.25 0.5

Expected Utility 1.75 1.125 0.5

A B C

Harvard 0.75 0.25 0

UI 0.25 0.5 0.25

None 0 0.25 0.75

Expected Utility 1.75 1 0.25

High score Low score

A 0.7 0.3

B 0.3 0.7

C 0.5 0.5

Private Information Game: Evaluating the Expected Strategies

High score Low score Harvard UI Harvard UI

A0.75 0.25 0.75 0.25(3) (1) (3) (1)

B0.5 0.5 0.333 0.667(1) (1) (2) (4)

C0 1 0.25 0.75(0) (4) (1) (3)

High score Low scoreA Harvard HarvardB UI UIC UI Harvard

High score Low scoreA Harvard HarvardB UI UIC UI UI

High score Low scoreA Harvard HarvardB Harvard UIC UI UI

High score Low scoreA Harvard UIB Harvard HarvardC Harvard UI

High score Low scoreA Harvard UIB Harvard HarvardC UI UI

Private Information Game: Evaluating the Expected Admission Outcomes• Expected outcome distribution • Adjusted outcome distribution

A B CHarvard 0.828 0.099 0.018UI 0.109 0.443 0.383None 0.063 0.458 0.599ExpectedUtility 1.77 0.64 0.42

Low Information Game: Evaluating the Expected Strategies

• Bayesian Equilibrium • Observed Strategy Distribution

Strategy

A Harvard

B UI

C UI

Strategy

Harvard UI

A1(8)

0(0)

B0.875(7)

0.125(1)

C0(0)

1(8)

Low Information Game: Evaluating the Expected Admission Outcomes• Expected outcome distribution • Adjusted outcome distribution

A B CHarvard 1 0 0

UI 0 0.75 0.25None 0 0.25 0.75Expected Utility 2 0.75 0.25

A B CHarvard 0.781 0.219 0UI 0 0.094 0.906None 0.219 0.688 0.094Expected Utility 1.56 0.53 0.91

Conclusions

• Observed Strategies• Complete information: the experimental results perfectly fit the Nash equilibrium that A

chooses Harvard, B chooses the UI, and C is indifferent between the two.• Private information: A is more likely to choose Harvard, and B is more likely to choose

the UI no matter which score they pick. C chooses the UI most of the time. A bigger sample is needed to further evaluate the PBEs.

• Low information: As the Bayesian equilibrium suggests, A always chooses Harvard and C always chooses the UI. B is risk-seeking that she applies for Harvard most of the time.

• Adjusted Outcome Distributions• Complete information yields ideal outcome distribution.• Private information greatly favors C and slightly favors A at the cost of B.• Low information is biased against both A and B, but in favor of C, which contradicts the

Bayesian equilibrium.

Future Research Directions

• Under deterred acceptance algorithms, how will different levels of information affect college choices?• Two-sided matching game

• Statistically evaluate the theoretical predictions with agent quantal response equilibrium.• A problem of chi2 test.

• Policy innovation and diffusion in an authoritarian country.• “The adoption of a design is at least partly a political process. (Roth 2002: 1345)”

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