The Economics of Education: Controlled School Choice in Matching Theory

Scholars in economics have long attempted to quantify the most philosophically intangible concepts such as fairness and equity. In the United States, fairness of affirmative action in higher education has become one of the most controversial social issues. The Economist covered this issue as their cover story in April 2013 in a controversial assessment of the need for governments to abolish affirmative action policies. Fairness of these policies has also been questioned publicly by several recent Supreme Court cases including Fisher v. University of Texas-Austin (where Abigail Fisher sued the University of Texas-Austin for reverse discrimination against her “white” race), and the recent case Schuette v. Coalition to Defend Affirmative Action (which questions whether states should ban schools from using affirmative action and involved the Michigan school system—the ruling is discussed in depth in this Slate Magazine article). Using mathematical theories, economists have already worked on assessing fairness in affirmative action policies for more than a decade. Controlled school choice literature, as I’ll discuss today, is a relatively recent development in the field of economics. The goal of this academic inquiry is to study mechanisms related to matching students to schools while maintaining a balance of diversity. But in this field of inquiry, how is fairness measured? Is the current system fair? If so, why are there so many social concerns arising from the existing system?

First, it’s critical to understand that for the purposes of studying this balance, fairness is measured on whether or not a market matches students with schools, and that every student and school is assigned with deserved matching. In other words, there should be no matching of a student and/or a school that deviates from the current state and makes the current matching better without making anyone else worse off. This requires that we know the preference of schools for the applicants and therefore raises another question: if we do not know their true preferences and only know what people record on paper, then can we assess whether it’s beneficial for applicants to lie about their preferences? Will stating their true preference ensure a better outcome? This concept is called “strategy-proofness” and is discussed in this paper, “Matching Markets: Theory and Practice.”

With these two concepts in mind—fairness and strategy-proofness—what are the current systems used? Are they fair? Are they strategy-proof? Currently, the most prevalent mechanisms used are the quota and reserve system. Quota puts an upper numerical bound on the number of students admitted. Reserve requires schools to admit certain numbers of minority students; it sets a lower bar for the number of minority students admitted. For example, under the quota system, a school cannot admit more than 70 percent male students. Under a reserve system, a school has to admit at least 15 percent Asian students. Reserve has been proven to be more beneficial to minority students than quota, as cited in the paper, “Effective Affirmative Action in School Choice.” Professor Kojima from Stanford University in this Games and Economic Behavior paper concludes that affirmative action policies based on majority quotas may in fact hurt minority students.

Despite the quota system’s shortcomings, both of these systems can result in a matching that is simultaneously fair and strategy-proof (students and schools have no incentive to lie about their preference) if a student is only identified with one diversity attribute. For example, a student can only be either Asian or female—but not both. The industry paper,“How to Control Controlled School Choice”, by Professor Echnique from Cal Tech and Professor Yenmez from Carnegie Mellon University further proves this point. Yet despite this, it is my assessment that assumptions in this hypothesis should be adjusted in future research so a student can be allowed to be identified with multiple diversity attributes.

These unrealistic assumptions in the current model helps explain why so many social concerns have arisen—we cannot yet measure how fair affirmative action policy truly is. At the same time, through the lens of mathematical theory, scholars such as Isa E. Hafalir and Bumin M. Yenmez from Carnegie Mellon University are working on relaxing unrealistic assumptions that a student can be identified with only one diversity attribute. If such a mechanism with more realistic assumptions can be found then true progress could be made in creating a fruitful system for fair and equitable school choice and enrollment policies.

Further Reading:

Stable matching: Theory, evidence, and practical design. Some of the theories and algorithms introduced in the paper are being used in the real world, especially theories about topics such as school matching as well as kidney exchange.

Image credit: Lauren Manning via flickr