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.
We propose to conduct theoretical and experimental studies of a family of matching mechanisms applied to the school choice and college admissions 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 Chinese parallel mechanisms. Within the last decade, many Chinese provinces have transitioned from the `sequential' to the `parallel' college admissions mechanisms. We show that all of the provinces that have abandoned the sequential mechanism have moved towards less manipulable and more stable mechanisms. Furthermore, Tibet implements the least manipulable parallel mechanism, whereas Beijing, Gansu and Shangdong have adopted the most manipulable versions. In the laboratory, participants are most likely to reveal their preferences truthfully under the DA mechanism, followed by the parallel and then the sequential mechanisms. While stability comparisons follow the same order, efficiency comparisons vary across environments. Results from our study will inform policy makers of the efficacy of various matching mechanisms used in school choice and college admissions. (Chen and Kesten 2014) To evaluate the external validity of laboratory matching experiments, we propose to study canonical matching mechanisms in the large, to systematically assess how scale affects the performance of these mechanisms. Specifically, we study the performance of two canonical matching mechanisms, the Boston and the Deferred Acceptance (DA) mechanism, when the scale of the market increases. We find that, when the number of students per match increases from 4 to 40, the proportion of truth-telling significantly increases under the DA but decreases under the Boston mechanism. Furthermore, this increase in scale significantly decreases both efficiency and stability under the Boston mechanism. However, further increasing the scale to 4,000 students per match has no effect on the performance of either mechanism. Our results indicate that ``large" might be much smaller than predicted in the theoretical literature. (Chen, Jiang, Kesten, Robin and Zhu, 2014)
