TITLE:  Prediction and Optimzation in School Choice

ABSTRACT:

In public school choice, students are not assigned to a designated school based on home location, but submit preference rankings for a given set of schools to the school board, which takes into account everyone’s choices to compute the assignment. Such systems exist in Boston, Chicago, Denver, Miami, Minneapolis, New York City, New Orleans, and San Francisco. An important policy lever is what choice options to offer to each neighborhood, and how to prioritize between students. A key tradeoff is between giving students equitable chances to go to the schools they want and controlling the city’s school busing costs.

We study the optimization problem of choosing the choice menus and priorities for each neighborhood in order to maximize the sum of utilitarian and max-min welfare, subject to capacity and transportation constraints. The optimization is built on-top of a predictive model of how students will choose given new choice menus, which we validate using both out-of-sample testing and a field experiment. We show that under a fluid approximation, the optimization reduces to an assortment planning problem in which the objective is social-welfare rather than revenue. We show how to efficiently solve this sub-problem under MNL, Nested-Logit and Markov Chain choice models, and use this to produce better menus and priorities for Boston, which we evaluate by discrete simulations while taking into account possible errors in parameters.