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College admissions with stable score-limits

Author

Listed:
  • Peter Biro

    () (Institute of Economics Research Centre for Economic and Regional Studies Hungarian Academy of Sciences)

  • Sofya Kiselgof

    () (Postgraduate Student, Lecturer Laboratory of Decision Choice and Analysis (DecAn), NRU Higher School of Economics, Moscow, Russia)

Abstract

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 score-limit algorithms are manipulable.

Suggested Citation

  • Peter Biro & Sofya Kiselgof, 2013. "College admissions with stable score-limits," IEHAS Discussion Papers 1306, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  • Handle: RePEc:has:discpr:1306
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    Other versions of this item:

    • Péter Biró & Sofya Kiselgof, 2015. "College admissions with stable score-limits," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 727-741, December.

    References listed on IDEAS

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    Citations

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    Cited by:

    1. Kolos Csaba Agoston & Peter Biro & Iain McBride, 2016. "Integer programming methods for special college admissions problems," IEHAS Discussion Papers 1632, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    2. Peter Biro & Tamas Fleiner & Rob Irving, 2013. "Matching Couples with Scarf's Algorithm," IEHAS Discussion Papers 1330, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    3. Katarína Cechlárová & Tamás Fleiner & David Manlove & Iain McBride & Eva Potpinková, 2015. "Modelling practical placement of trainee teachers to schools," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 547-562, September.
    4. Ferenc Forgó & László Kóczy & Miklós Pintér, 2015. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 723-725, December.

    More about this item

    Keywords

    college admissions; stable matching; mechanism design;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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