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Fair and Efficient Student Placement with Couples

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  • Bettina Klaus
  • Flip Klijn

Abstract

We study situations of allocating positions to students based on priorities. An example is the assignment of medical students to hospital residencies on the basis of entrance exams. For markets without couples, e.g., for undergraduate student placement, acyclicity is a necessary and sufficient condition for the existence of a fair and efficient placement mechanism (Ergin, 2002). We show that in the presence of couples acyclicity is still necessary, but not sufficient. A second necessary condition is priority-togetherness of couples. A priority structure that satisfies both necessary conditions is called pt-acyclic. For student placement problems where all quotas are equal to one we characterize ptacyclicity and show that it is a sufficient condition for the existence of a fair and efficient placement mechanism. If in addition to pt-acyclicity we require reallocation- and vacancyfairness for couples, the so-called dictator-bidictator placement mechanism is the unique fair and efficient placement mechanism. Finally, for general student placement problems, we show that pt-acyclicity may not be sufficient for the existence of a fair and efficient placement mechanism. We identify a sufficient condition such that the so-called sequential placement mechanism produces a fair and efficient allocation.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 145.

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Date of creation: Jul 2004
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Handle: RePEc:bge:wpaper:145

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Keywords: Student placement; Fairness; efficiency; couples; acyclic priority structure;

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References

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  1. Lars Ehlers & Bettina Klaus, 2007. "Consistent House Allocation," Economic Theory, Springer, vol. 30(3), pages 561-574, March.
  2. Lars Ehlers & Bettina Klaus, 2003. "Efficient Priority Rules," Working Papers 103, Barcelona Graduate School of Economics.
  3. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  4. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
  5. Bettina Klaus & Flip Klijn, 2004. "Paths to Stability for Matching Markets with Couples," Working Papers 156, Barcelona Graduate School of Economics.
  6. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  7. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
  8. Bettina Klaus & Flip Klijn & Jordi Massó, 2007. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," Review of Economic Design, Springer, vol. 11(3), pages 175-184, November.
  9. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
  10. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  11. 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.
  12. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  13. Ehlers, Lars & Klaus, Bettina & Papai, Szilvia, 2002. "Strategy-proofness and population-monotonicity for house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 329-339, November.
  14. Lars Ehlers & Bettina Klaus, 2003. "Resource-Monotonicity for House Allocation," Working Papers 33, Barcelona Graduate School of Economics.
  15. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
  16. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
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Cited by:
  1. Boudreau, James W. & Knoblauch, Vicki, 2014. "What price stability? Social welfare in matching markets," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 27-33.
  2. James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.

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