Game Theory :High School Selection Applications
Every year the New York City wide school district must allocate all of its eighth graders to different high schools. The student’s parents must preference their top five schools in order. The concern is there will be a greater concentration of bids for more highly rated schools, consequently making them more selective. Unfortunately, some schools are much better than others, so not every student gets their match. Some students were matched to one school, some even to multiple schools, but nearly half of them do not receive any match, most of these students coming from under performing middle and junior high schools.
Too many people want too few schools. School officials cannot simply raise the value of the higher bids to clear the market, so three academics Roth, Abdulkadiroglu and Pathak devised a more equitable strategy based off what’s called the “stable marriage” problem. The stable marriage problem effectively pairs multiple bachelors and bachelorettes together based on individual preference. First, the bachelor proposes to his first choice. Then, the bachelorette rejects all possible bachelors except for her favorites, however she has yet to formally choose her bachelor. The rejected bachelors then propose a second favorite bachelorette, and the rounds continue until all members are matched. Because the bachelorette does not have to give an immediate answer on a favorite, she has the option to accept a later proposal—a more stable option than previous proposals.
The “stable marriage” works for because students become the bachelors with hierarchical favorites, and the schools become the bachelorettes with delayed decision power. The only difference is that schools accept not one partner, but hundreds or thousands. Since the implementation of this method, the number of unmatched students decreased over ninety percent from about 31,000 to 3,000. Whereas before over half the students were unmatched, now over half get their first choice, and around a third get their second or third choice.
Tullis, Tracy. “How Game Theory Helped Improve New York City’s High School Application Process.” The New York Times. The New York Times, 06 Dec. 2014. Web. 22 Oct. 2015.