Research on Improving Middle School Choice Lottery System from the Perspective of Preference Utilitarianism

This study analyzes the results of the middle school allocation in Region A for the 2023 academic year and proposes a new allocation method that can significantly improve the results. We analyze the middle school application data for Region A and find that some schools have more first-choice applicants than seats, while others have fewer first-choice applicants than seats. However, the application rates for second-choice schools exceeded 100% of the capacity for all schools, indicating that there were no universally unpopular schools. Nevertheless, 113 students were not assigned to either their first or second-choice schools in the 2023 academic year in Reagion A. This study proposes a new assignment method that maximizes student satisfaction by efficiently assigning students to their first-choice schools while taking into account the characteristics of regions where there is a herding effect toward applying to their first-choice schools, but where there are no universally unpopular schools that students would avoid when considering their second-choice schools. The new assignment method effectively reduces random assignments by finding the optimal assignment for students from a preference utilitarian perspective. Simulations show that the new assignment method we propose assigns all students in Region A to their first- and second-choice schools. Furthermore, when we improve the apply method to allow students to apply to multiple schools with the same ranking, the new assignment method can also assign all students to their first-choice school if more than 80% of students apply to two schools in their first choice.