During the pandemic, school districts have adopted hybrid schedules to continue the education of the students while maintaining social distance. In a hybrid schedule, students in the same classroom are usually divided into two groups and students only in the same group can physically attend...

This paper analyzes the properties of the Taiwan mechanism, used for high school placement nationwide starting in 2014. In the Taiwan mechanism, points are deducted from an applicant's score with larger penalties for lower ranked choices. Deduction makes the mechanism a new hybrid between the...