This proposal requests a three-year grant to support a program of research in matching theory and experiments at the University of Michigan and Carnegie-Mellon University. Part of the proposed research will be conducted in China, in collaboration with Xiangdong Qin at Shanghai Jiao Tong University and Zongkai Shi at Tsinghua University. This program is an extension of work that has been supported by NSF grant SES-0720943 and university funds. The proposed research is likely to have direct impact on the school choice reform in the U.S. and college admissions reform in China.
(1) Intellectual merit: The PIs propose to conduct theoretical and experimental studies of a family of matching mechanisms applied to the school choice problem: the Boston mechanism, which is one of the most commonly used and prominent school choice algorithms in practice, and two alternatives which have superior theoretical properties--the Gale-Shapley mechanism and the modified Boston mechanism. Data from the experiment will provide a rigorous evaluation of the family of mechanisms in the school choice context. The PIs then propose experimental studies of the college admissions mechanisms, with variants used in China. Both the theoretical and the experimental studies of these mechanisms are essential to advancing knowledge. Mechanisms cannot be evaluated purely on theoretical grounds, because people may not use them as intended. Nor can they be evaluated as used in the real world, because we do not have access to people's true preferences. Experiments are vital to understanding how mechanisms will perform. It is important to note that the findings will guide both theory and practice regardless of whether the hypotheses are confirmed or rejected.
(2) Broader impacts: School choice has been one of the most important and most widely debated topics in the past twenty years. In the current debate on school reform, choice has moved to the top of the national agenda. The Boston mechanism is a prominent algorithm used in several cities pioneering the school choice program, but its performance has not been thoroughly evaluated. As more states have passed legislation mandating intra- or inter-district choice, it is urgent to evaluate this mechanism as well as alternative mechanisms in order to make meaningful policy recommendations. Similarly, college admissions mechanisms in China present a new class of matching problems which influence the education and labor market outcomes of more than 10 million high school seniors every year. The research proposal has the potential to benefit society by influencing the method by which students are matched with schools and colleges. The successful and timely completion of the proposed experimental program is only possible with the involvement of undergraduate and graduate students. Chen has been working with undergraduate students through the Undergraduate Research Opportunities Program at the University of Michigan since 1999 and the NSF REU program. The PIs will continue to include 1-2 undergraduate students in this research project every year. New undergraduate students will have the opportunity to become involved in most phases of the project, including literature review, assistance in conducting experiments and preliminary data analysis. Analysis of large data sets requires the hard work and dedication of graduate students. Therefore, the PIs plan to get one graduate student research assistant for each year of the project. Graduate students are encouraged to participate in conferences and workshops to present their research to the research community. Graduate students will learn the entire process of experimental research, from experimental design, execution, data analysis to writing and presentation.
This project studied, both theoretically and experimentally, the college and high school admissions systems in China. Much like in the USA, in China also college admissions is among the most debated topics and there appears to be no consensus among authorities in various provinces as to what might be the best way to assign students to colleges, as each province has been implementing a different system, often leading to dissatisfaction by many families. We have observed that all the various existing systems in China are hybrids of the assignment systems currently in use in the USA for public school admissions; namely hybrids between the Gale-Shapley student-proposing deffered acceptance and the Boston mechanisms. We have captured this entire class of admissions systems via a parametric assignment family and have theoretically shown that as one moves from one extreme member toward the other, systems become more stable, making more "fair" assignments and more incentive compatible, giving participants good incentives for truth-telling and eliminating gaming incentives. We have found that when welfare is evaluated before admissions are carried out, then these conclusions no longer hold. We conclude that the Chinese systems are able to offer a compromise among the extreme members of the family and may be useful for many practical assignment problems depending on the desideratum of the planner. We have also shown that much of the theoretical predictions are confirmed by our laboratory experiments.
