Prediction and optimization in school choice

Abstract

In this thesis, I study how data-driven optimization can be used to improve school choice. In a typical school choice system, each student receives a set of school options, called the student's menu. Based on his/her menu, each student submits a preference ranking of schools in the menu. Based on the submitted preferences, a centralized algorithm determines the assignment. In Boston, New York City, Chicago, Denver, New Orleans,Washington DC, among other cities, the assignment algorithm is the student-proposing deferred acceptance (DA) algorithm, which can also incorporate a priority for each student at each school. These priorities may contain a deterministic as well as a random component. An advantage of this algorithm is incentive-compatibility, meaning that no student has incentives to misreport his/her preferences. The first research question of this thesis is how to optimize the menus and priorities so that students have equitable chances to go to the schools they want, while the city's school busing costs are controlled. The second question is how the assignment algorithm can be modified to keep the same assignment probability of every student to every school, while improving neighbors' chances of going to the same school. To answer these questions, I build a multinomial logit (MNL) model to predict how students will rank schools under new menus, and validate the predictive accuracy of this model out of sample. I also propose a simple plan for menus and priorities, called the Home-Based plan, and compare with other proposals using the MNL model. (As a result of this analysis, the Home-Based plan was adopted by Boston in 2013.) I then show how one can further optimize the menus and priorities under the MNL model, by developing a new theoretical connection between stable matching and assortment planning, as well as methodologies on solving a new type of assortment planning problem, in which the objective is social welfare rather than revenue. Finally, I show how to further optimize the correlations between students' assignments to improve neighbors' chances of going to the same school.