College admissions with stable score-limits
AbstractA 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 1306.
Length: 20 pages
Date of creation: Jan 2013
Date of revision:
college admissions; stable matching; mechanism design;
Find related papers by 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2008.
"Constrained School Choice: An Experimental Study,"
UFAE and IAE Working Papers
757.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Guillaume Haeringer & Caterina Calsamiglia & Flip Klijn, 2009. "Constrained School Choice: An Experimental Study," Working Papers 2009.29, Fondazione Eni Enrico Mattei.
- Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2008. "Constrained School Choice: An Experimental Study," Working Papers 365, Barcelona Graduate School of Economics.
- Sebastian Braun & Nadja Dwenger & Dorothea Kübler, 2007. "Telling the Truth May Not Pay Off," Discussion Papers of DIW Berlin 759, DIW Berlin, German Institute for Economic Research.
- John William Hatfield & Paul R. Milgrom, 2005.
"Matching with Contracts,"
American Economic Review,
American Economic Association, vol. 95(4), pages 913-935, September.
- Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
- Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-27, June.
- Braun, Sebastian & Dwenger, Nadja & Kübler, Dorothea, 2007.
"Telling the Truth May Not Pay Off: An Empirical Study of Centralised University Admissions in Germany,"
IZA Discussion Papers
3261, Institute for the Study of Labor (IZA).
- Braun Sebastian & Dwenger Nadja & Kübler Dorothea, 2010. "Telling the Truth May Not Pay Off: An Empirical Study of Centralized University Admissions in Germany," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-38, March.
- Sebastian Braun & Nadja Dwenger & Dorothea Kübler, 2007. "Telling the Truth May Not Pay Off: An Empirical Study of Centralised University Admissions in Germany," SFB 649 Discussion Papers SFB649DP2007-070, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Alvin E. Roth & Elliott Peranson, 1999.
"The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design,"
NBER Working Papers
6963, National Bureau of Economic Research, Inc.
- Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
- Chung-Piaw Teo & Jay Sethuraman & Wee-Peng Tan, 2001. "Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications," Management Science, INFORMS, vol. 47(9), pages 1252-1267, September.
- Péter Biró & Flip Klijn, 2013.
"Matching With Couples: A Multidisciplinary Survey,"
International Game Theory Review (IGTR),
World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1340008-1-1.
- Aytek Erdil & Haluk Ergin, 2008.
"What's the Matter with Tie-Breaking? Improving Efficiency in School Choice,"
American Economic Review,
American Economic Association, vol. 98(3), pages 669-89, June.
- Aytek Erdil & Haluk Ergin, 2007. "What`s the Matter with Tie-breaking? Improving Efficiency in School Choice," Economics Series Working Papers 349, University of Oxford, Department of Economics.
- Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
- Antonio Romero-Medina, 1998. "Implementation of stable solutions in a restricted matching market," Review of Economic Design, Springer, vol. 3(2), pages 137-147.
- Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Adrienn Foldi).
If references are entirely missing, you can add them using this form.