Central European Journal of Operations Research

, Volume 23, Issue 4, pp 727–741 | Cite as

College admissions with stable score-limits

  • Péter BiróEmail author
  • Sofya Kiselgof
Original Paper


A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that students apply for programmes and are ranked according to their scores. Students who apply for a programme with the same score are tied. Ties are broken by lottery in Ireland, by objective factors in Turkey (such as date of birth) and by 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 decision to make, 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 boundaries for any solution arising from a tie-breaking strategy. Finally we show that both the H-stable and the L-stable applicant-proposing score-limit algorithms are manipulable.


College admissions Stable matching Mechanism design 

JEL Classification

C78 I21 



We would like to thank Gábor Varjasy, the representative of Educatio Kht (the non-profit governmental organization which runs the higher education admission scheme in Hungary). Furthermore we acknowledge Tamás Fleiner, Rob Irving and the two referees for their useful comments and we also thank Jordi Masso and Antonio Romero-Medina for their help in understanding the Spanish higher education admissions system. Finally we would like to thank the participants of the Frontiers of Market Design: Matching Markets Conference, the 8th Spain-Italy-Netherlands Meeting on Game Theory, the Fourth Congress of the Game Theory Society, the 11th Meeting of Society of Social Choice and Welfare and the Fourth International Workshop on Computational Social Choice, for giving useful feedback.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Research Centre for Economic and Regional Studies, Institute of EconomicsHungarian Academy of SciencesBudapestHungary
  2. 2.Department of Operations Research and Actuarial SciencesCorvinus University of BudapestBudapestHungary
  3. 3.Laboratory of Decision Choice and Analysis (DecAn)NRU Higher School of EconomicsMoscowRussia

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