School choice under transferable capacities

ended

"Public schools are the largest providers of education in many countries. In the vast majority of the OECD countries, more than two third of secondary students were educated in public schools in 2016. The ""non-market"" feature of admissions to this type of schools calls for a careful design of how to allocate seats to students. In recent decades, school choice has appeared as a promising alternative. Centralized public school choice is a system that allocates public school seats to students by taking into account their preferences over various schools. Each school has a fixed capacity and a priority order that is determined by law. Stability --- essentially about respecting priorities --- and efficiency --- maximizing students' welfare --- have been the guiding principles for public school choice design. Yet, it is impossible to satisfy both principles. However, the Gale-Shapley student proposing deferred acceptance is a second best solution, being the student-optimal stable (constraint) matching mechanism. Nevertheless, the welfare loss is considerable. I observed that this is in part due to the fact that capacities are assumed to be rigid. I interpret them as (class size) ideal capacities because, in practice, schools are flexible so that they can add a few seats to their reported capacities. In theory, this flexibility can be exploited to mitigate the welfare loss in deferred acceptance. The flexibility is subjected to not adding more seat to the whole system, so it is a transfer of capacities. This project aims at designing a student-optimal stable matching mechanism under transferable capacities. More specifically, I will study such a mechanism and empirically evaluate the welfare gains of transferable capacities. I will also study the feasibility of stability and full efficiency. Such a mechanism will help improve the assignment of public school seats to students in many cities around the world, including Boston, many cities in England and Hungary."