Median Stable Matching for College Admissions

  • Bettina KlausEmail author
  • Flip Klijn
Original Article


We give a simple and concise proof that so-called generalized median stable matchings are well-defined for college admissions problems. Furthermore, we discuss the fairness properties of median stable matchings and conclude with two illustrative examples of college admissions markets, the lattices of stable matchings, and the corresponding generalized median stable matchings.


Matching College admissions Stability Fairness 

JEL Classification

C78 D63 


  1. Aldershof B, Carducci OM, Lorenc DC (1999) Refined inequalities for stable marriage. Constraints 4:281–292CrossRefGoogle Scholar
  2. Barberà S, Gul F, Stacchetti E (1993) Generalized median voter schemes and committees. J Econ Theory 61:262–289CrossRefGoogle Scholar
  3. Blair C (1988) The lattice structure of the set of stable matchings with multiple partners. Math Oper Res 13:619–628Google Scholar
  4. Fleiner T (2002) Some results on stable matchings and fixed points. Technical Report, EGRES Report TR-2002-8, Egerváry Research Group, Budapest, Hungary [http://www.]Google Scholar
  5. Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15CrossRefGoogle Scholar
  6. Gusfield D, Irving RW (1989) The stable marriage problem: structure and algorithms. MIT Press, CambridgeGoogle Scholar
  7. Klaus B, Klijn F (2006) Procedurally fair and stable matching. Econ Theory 27:431–447CrossRefGoogle Scholar
  8. Ma J (1996) On randomized matching mechanisms. Econ Theory 8:377–381Google Scholar
  9. Martínez R, Massó J, Neme A, Oviedo J (2001) On the lattice structure of the set of stable matchings for a many-to-one model. Optimization 50:439–457CrossRefGoogle Scholar
  10. Masarani F, Gokturk SS (1989) On the existence of fair matching algorithms. Theory Decis 26:305–322CrossRefGoogle Scholar
  11. Moulin H (1980) On strategy-proofness and single peakedness. Public Choice 35:437–455CrossRefGoogle Scholar
  12. Rawls J (1971) A theory of justice. Harvard University Press, Cambridge, MAGoogle Scholar
  13. Roth AE (1985) The college admissions problem is not equivalent to the marriage problem. J Econ Theory 36:277–288CrossRefGoogle Scholar
  14. Roth AE, Sotomayor MAO (1989) The college admissions problem revisited. Econometrica 57:559–570CrossRefGoogle Scholar
  15. Roth AE, Sotomayor MAO (1990) Two-sided matching: a study in game-theoretic modeling and analysis. Econometric Society Monograph Series. Cambridge University Press, New YorkGoogle Scholar
  16. Sethuraman J, Teo C-P, Qian L (2004) Many-to-one stable matching: geometry and fairness. Working Paper TR-2004-02, Computational Optimization Research Center, Columbia University []Google Scholar
  17. Teo C-P, Sethuraman J (1998) The geometry of fractional stable matchings and its applications. Math Oper Res 23:874–891CrossRefGoogle Scholar

Copyright information

© Springer Verlag 2006

Authors and Affiliations

  1. 1.Department of EconomicsMaastricht UniversityMaastrichtThe Netherlands
  2. 2.Institut d’Anàlisi Econòmica (CSIC)Bellaterra (Barcelona)Spain

Personalised recommendations