Constrained College Admission Problem: Manipulability of Truncated College-optimal Stable Mechanism

Abstract

A central issue in college admission problems is their vulnerability to manipulation by students. Students can often falsely report their preferences and get into more preferred colleges. This paper first shows that the college admission mechanisms in South Korea and the US, where students are limited in the number of schools that they can apply to, are equivalent to truncated college-optimal stable mechanism (TCOSM). Then, by adopting the framework proposed by Pathak and Sönmez (2013), it proves that the type space which is vulnerable under TCOSM is equivalent to that incurs different matching under TCOSM and student-optimal stable mechanism (SOSM). The result implies that TCOSM becomes less manipulable as the truncation quota (the limited number of each student's applications) increases, considering the type space which is vulnerable under TCOSM with the lower truncation quota. The analysis on manipulability of TCOSM supports policy reforms that increase the truncation quota to enhance students' satisfaction in college admission.