College admissions with stable score - limits

2013. No. 6.

Péter Biró, Kiselgof S. G.

A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that the students apply for programmes and they are ranked according  to their scores. Students who apply for a programme with the same score are in a tie. Ties  are broken by lottery in Ireland, by objective factors in Turkey (such as date of birth) and  other precisely defined rules in Spain. In Hungary, however, an equal treatment policy is  used, students applying for a programme with the same score are all accepted or rejected  together. In such a situation there is only one question to decide, whether or not to admit  the last group of applicants with the same score who are at the boundary of the quota. Both  concepts can be described in terms of stable score-limits. The strict rejection of the last  group with whom a quota would be violated corresponds to the concept of H-stable (i.e.  higher-stable) score-limits that is currently used in Hungary. We call the other solutions  based on the less strict admission policy as L-stable (i.e. lower-stable) score-limits. We show  that the natural extensions of the Gale-Shapley algorithms produce stable score-limits,  moreover, the applicant-oriented versions result in the lowest score-limits (thus optimal for  students) and the college-oriented versions result in the highest score-limits with regard to  each concept. When comparing the applicant-optimal H-stable and L-stable score-limits we prove that the former limits are always higher for every college. Furthermore, these two  solutions provide upper and lower bounds for any solution arising from a tie-breaking  strategy. Finally we show that both the H-stable and the L-stable applicant-proposing scorelimit algorithms are manipulable.

Keywords: matchings, обобщенные паросочетания

Publication based on the results of: An investigation of new methods of mathematical modelling and mechanism design in the social, economic and political sciences (2013)