Catchment areas, stratification, and access to better schools

School Choice provides students with the opportunity to attend better schools than those in their neighborhood. This is crucial for students from disadvantaged areas where schools may be of lower quality. Our theoretical model and numerical simulations show that the widely used Deferred Acceptance (DA) algorithm has limitations in providing access to better schools (ABS). When schools have varying levels of quality and when there are priorities linked to neighborhood schools, the DA algorithm experiences significant limitations in providing ABS. Top Trading Cycles, when compared to DA, offers greater ABS, particularly for disadvantaged students.