1. Reexamining Education Fairness: An Experimental Study of College Admission Policies in China Yang Zhang May 7, 2013

2. 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

3. 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

4. Research Questions How does timing of application affect students’ strategies in college application? How does timing of application affect the distribution of admission outcomes?

5. Three Games 1. Mimic Exams 2. College Entrance Exam Randomly pick one mimic exam score. Mimic 1Mimic 2 A71-7991-100 B51-6081-90 C41-5061-70

6. 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.

7. Defining Admission Fairness Expected Rank Distribution Ideal Outcome Distribution RankABC 10.750.250 2 0.50.25 30 0.75 ABC Harvard0.750.250 UI0.250.50.25 None00.250.75 Expected Utility1.7510.25

8. 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

9. 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?

10. Complete Information Game: Evaluating the Expected Strategies Nash Equilibrium(a) Observed Strategy Distribution RankStrategy 1Harvard 2UI 3Harvard or UI Rank Strategy HarvardUI 1 1 (8) 0 (0) 2 0 (0) 1 (8) 3 0.125 (1) 0.875 (7)

11. Complete Information Game: Evaluating the Expected Admission Outcomes Expected outcome distribution Luck in getting a higher score Observed outcome distribution Adjusted outcome distribution ABC Harvard0.750.250 UI0.250.50.25 None00.250.75 Expected Utility1.7510.25 ABC Harvard0.750.3750 UI0.250.3750.5 None00.250.5 Expected Utility1.751.1250.5 ABC Harvard0.750.250 UI0.250.50.25 None00.250.75 Expected Utility1.7510.25 High scoreLow score A0.70.3 B 0.7 C0.5

12. Private Information Game: Evaluating the Expected Strategies High scoreLow score HarvardUIHarvardUI A 0.750.250.750.25 (3)(1)(3)(1) B 0.5 0.3330.667 (1) (2)(4) C 010.250.75 (0)(4)(1)(3) High scoreLow score AHarvard BUI C Harvard High scoreLow score AHarvard BUI C High scoreLow score AHarvard B UI C High scoreLow score AHarvardUI BHarvard C UI High scoreLow score AHarvardUI BHarvard CUI

13. Private Information Game: Evaluating the Expected Admission Outcomes Expected outcome distribution Adjusted outcome distribution ABC Harvard 0.5-10-0.50-0.125 UI 0-0.50-0.750.25-0.75 None 0-0.250.25-0.625 Expected Utility 1.5-20.75-10.25-0.75 ABC Harvard 0.8280.0990.018 UI 0.1090.4430.383 None 0.0630.4580.599 Expected Utility 1.770.640.42

14. Low Information Game: Evaluating the Expected Strategies Bayesian Equilibrium Observed Strategy Distribution Strategy AHarvard BUI C Strategy HarvardUI A 1 (8) 0 (0) B 0.875 (7) 0.125 (1) C 0 (0) 1 (8)

15. Low Information Game: Evaluating the Expected Admission Outcomes Expected outcome distribution Adjusted outcome distribution ABC Harvard100 UI00.750.25 None00.250.75 Expected Utility20.750.25 ABC Harvard 0.7810.2190 UI 00.0940.906 None 0.2190.6880.094 Expected Utility1.560.530.91

16. 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.

17. 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)”