Game Theory in School Applications
This article is about the algorithm designed to pair incoming high school freshman in New York City with their best match high school. In the previous admissions process, students ranked their top 5 schools, who then reviewed the students and accepted their picks. This system created a plethora of unintended consequences. For example, some schools would only accept students who had listed them first on their list, meaning that students who applied to multiple schools using that system were highly disadvantaged if their top school did not accept them, regardless of their qualifications. Even more significantly, schools acting independently of each other maximized their own interests rather than the students’- top students received acceptances from multiple schools while masses of less highly achieving students received no acceptances at all and were instead matched with schools they did not list.
The new system utilizes “deferred acceptance,” a system which emphasized mutual interest. Both students and schools create ordered lists of their top preferences, and then a computer program runs down the list of students’ preferences and tentatively matches them with schools that also listed them, able to change that matching if another student is ranked higher on the schools list. This system maximizes the efficiency of the application system, ensuring that the best “strategy” is simply to list schools in order of true preference, and that as many students as possible are matched with a school from their lists. In the first year the new system was implemented, the number of students who did not get a school on their lists dropped from 31,000 to 3,000.
As discussed in class, any actor in a game will follow the strategy which best maximizes his or her interests. In the previous system, the best strategy for each individual school was therefore to accept the most qualified students, often overlapping with other schools’ picks and not maximizing acceptance. The strange details of a school’s decision, such as how a school is ranked on a student’s list, distorted students’ strategies and prevented them from simply applying to schools which they liked. The equilibrium in a game like this is not necessarily that which benefits society the most, and the new algorithm somewhat corrects that issue.