Central European Journal of Operations Research

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

College admissions with stable score-limits

Original Paper

Abstract

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.

Keywords

College admissions Stable matching Mechanism design 

JEL Classification

C78 I21 

Notes

Acknowledgments

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.

References

  1. Abdulkadiroğlu A, Pathak PA, Roth AE (2005a) The New York City high school match. Am Econ Rev Pap Proc 95(2):364–367CrossRefGoogle Scholar
  2. Abdulkadiroğlu A, Pathak PA, Roth AE, Sönmez T (2005b) The Boston public school match. Am Econ Rev Pap Proc 95(2):368–371CrossRefGoogle Scholar
  3. Abdulkadiroğlu A, Pathak PA, Roth AE (2009) Strategy-proofness versus efficiency in matching with indifferences: redesigning the NYC high school match. Am Econ Rev 99(5):1954–1978CrossRefGoogle Scholar
  4. Al Roth’s market designer blog (2012) http://marketdesigner.blogspot.com
  5. Azevedo E, Leshno J (2011) A supply and demand framework for two-sided matching markets. Working paperGoogle Scholar
  6. Balinski M, Sönmez T (1999) A tale of two mechanisms: student placement. J Econ Theory 84(1):73–94MATHCrossRefGoogle Scholar
  7. Biró P (2008) Student admissions in Hungary as Gale and Shapley envisaged. Technical Report no. TR-2008-291 of the Computing Science Department of Glasgow UniversityGoogle Scholar
  8. Biró P (2012) University admission practices—Hungary. matching-in-practice.eu. Accessed 23 May 2012Google Scholar
  9. Biró P, Fleiner T, Irving RW, Manlove DF (2010) College admissions with lower and common quotas. Theor Comput Sci 411:3136–3153MATHCrossRefGoogle Scholar
  10. Blair C (1988) The lattice structure of the set of stable marriages with multiple partners. Math Oper Res 13(4):619–628MATHMathSciNetCrossRefGoogle Scholar
  11. Braun S, Dwenger N, Kübler D (2010) Telling the truth may not pay off: an empirical study of centralised university admission in Germany. 2010. B E J Econ Anal Policy 10(1):Article 22Google Scholar
  12. Calsamiglia C, Haeringer G, Klijn F (2010) Constrained school choice: an experimental study. Am Econ Rev 100(4):1860–1874CrossRefGoogle Scholar
  13. Central Applications Office Ireland website (2012) www.cao.ie
  14. Erdil A, Erkin H (2008) What’s the matter with tie-breaking? Improving efficiency in school choice. Am Econ Rev 98:669–689CrossRefGoogle Scholar
  15. Fleiner T, Jankó Zs (2012) Choice function based two-sided markets: stability, lattice property and path independence. Unpublished manuscriptGoogle Scholar
  16. Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Mathe Mon 69(1):9–15MATHMathSciNetCrossRefGoogle Scholar
  17. Hatfield JW, Milgrom PR (2005) Matching with contracts. Am Econ Rev 95(4):913–935CrossRefGoogle Scholar
  18. Immorlica N, Mahdian M (2005) Marriage, honesty, and stability. In: Proceedings of SODA 2005, pp 53–62Google Scholar
  19. Irving R (2012) Matching practices for entry-labor markets—Scotland. http://matching-in-practice.eu. Accessed 23 May 2012
  20. Irving RW, Manlove DF (2009) Finding large stable matchings. ACM J Exp Algorithmics, 14, section 1, article 2, 30 pGoogle Scholar
  21. Kelso AS, Crawford VP (1982) Job matching, coalition formation, and gross substitutes. Econometrica 50:1483–1504MATHCrossRefGoogle Scholar
  22. Knuth DE (1976) Mariages stables. Les Presses de L’Universite de MontrealGoogle Scholar
  23. Kojima F, Pathak PA (2009) Incentives and stability in large two-sided matching markets. Am Econ Rev 99:608–627Google Scholar
  24. Kübler D (2012) University admission practices—Germany. http://matching-in-practice.eu. Accessed 23 May 2012
  25. Matching in Practice website (2012) http://matching-in-practice.eu
  26. Romero-Medina A (1998) Implementation of stable solutions in a restricted matching market. Rev Econ Des 3(2):137–147Google Scholar
  27. Roth AE (1982) Roth the economics of matching: stability and incentives. Math Oper Res 7:617–628MATHMathSciNetCrossRefGoogle Scholar
  28. Roth AE (1984a) Roth stability and polarization of interests in job matching. Econometrica 52:47–58MATHCrossRefGoogle Scholar
  29. Roth AE (1984b) The evolution of the labor market for medical interns and residents: a case study in game theory. J Political Econ 6(4):991–1016CrossRefGoogle Scholar
  30. Roth AE, Peranson E (1999) The redesign of the matching market for American physicians: some engineering aspects of economic design. Am Econ Rev 89:748–780CrossRefGoogle Scholar
  31. UCAS website (2012) http://www.ucas.com
  32. Westkamp A (2012) An analysis of the German university admissions system. Bonn Econ Discussion Papers, no bgse02, 2012Google Scholar
  33. Zhang H (2009) An analysis of the Chinese college admission system. PhD Thesis, University of EdinburghGoogle Scholar
  34. Zhang Y (2011) The determinants of National College entrance exam performance in China—with an analysis of private tutoring. PhD Thesis, Columbia UniversityGoogle Scholar

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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