High School Selective System & The Matching Market
In the article “School-Choice Expert Has Unique Take on Brooklyn District’s New Admissions System”, the author talks about how the high school system in Brooklyn’s District 15 is changing from grade-selective system to a lottery type. The aim of this transformation is to maximize general welfare for all students and to promote the development of integrated schools with high qualities. Through changing the selective system, more students can receive education, the gap between schools’ education qualities will be reduced, and more integrated schools will be developed. As the author mentioned at the end of the article, under this situation, “everybody wins.”
This article is related to the idea of matching market. In the matching market, resources are allocated to people based on their preference. The situation can be depicted by the bipartite graph by illustrating students as L nodes and schools as R nodes. However, as mentioned in the article, previously, top students got into several schools at the same time, leaving no empty spot for other students.
To explain this problem, for instance, there are two students A, B, and two schools a, b. A was the top student and got into both a and b. Therefore, although B’s ability matches the requirement of b (shown as an edge from B to b), B could not get into b due to lack of spots. This would lead to a utility of zero for the student b with poorer academic performance. Through the transformation, as mentioned in the article, students will rank schools based on their preference and schools will also rank their applicants. The result of the ranking can be viewed as the valuations towards different schools. The ideal result that the officials are trying to achieve is the maximization of the total valuations of all students. Based on the previous example, A will get a value of 6 for a and value of 3 for b. Therefore, A will choose a. In this way, B can get into b and A can get into a at the same time.