Re-Reforming the Bostonian System: A Novel Approach to the Schooling Problem

Alcalde, Jose and Romero-Medina, Antonio (2011): Re-Reforming the Bostonian System: A Novel Approach to the Schooling Problem.

Abstract

This paper proposes the notion of E-stability to conciliate Pareto efficiency and fairness. We propose the use of a centralized procedure, the Exchanging Places Mechanism. It endows students a position according with the Gale and Shapley students optimal stable matching as tentative allocation and allows the student to trade their positions. We show that the final allocation is E-stable, i.e. efficient, fair and immune to any justifiable objection that students can formulate.

• Item Type: MPRA Paper
• Language: English
• Keywords: School allocation problem, Pareto efficient matching
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

References

Abdulkadiroglu, Atila, Parag A. Pathak and Alvin E. Roth (2009): "Strategy-Proofness versus Efficiency in Matching with Indiferences: Redesigning the NYC High School Match," American Economic Review 99, 1954-1978.

Abdulkadiroglu, Atila, Parag A. Pathak, Alvin E. Roth and Tayfunn Sönmez (2005): "The Boston Public School Match," American Economic Review, Papers and Proceedings 95, 368-371.

Abdulkadiroglu, Atila, Parag A. Pathak, Alvin E. Roth and Tayfunn Sönmez (2006): "Changing the Boston School Choice Mechanism: Strategy-Proofness as Equal Access." Mimeographed. Harvard University.

Abdulkadiroglu, Atila and Tayfunn S�onmez (2003): "School Choice: A Mechanism Design Approach," American Economic Review 93, 729-747.

Alcalde, José (1995): "Exchange-Proofness or Divorce-Proofness? Stability in One-Sided Matching Markets," Economic Design 1, 275-287.

Alcalde, José (1996): "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory 69, 240-254.

Alcalde-Unzu, Jorge and Elena Molis (2009): "Exchange of Indivisible Goods and Indierences: The Top Trading Absorbing Sets Mechanisms" ECORE Discussion Paper 2009/62.

Aumann, Robert J. amd Michael Bahir Maschler (1964): "The Bargaining Set of Cooperative Games," in: Dresher, M., Shapley, L.S., Tucker, A. (Eds.), Advances in Game Theory, Annals of Mathematics Study 52. Princeton University Press, Princeton, pp. 443-476.

Balinski, Michel and Tayfunn S�onmez (1999): "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory 84, 73-94.

Erdil, Aytek and Haluk Ergin (2008): "What's the Matter with tie-Breaking? Improving Efficiency in School Choice," American Economic Review 98, 669-689.

Ergin, Haluk and Tayfunn S�onmez (2006): "Games of School Choice under the Boston Mechanism," Journal of Public Economics 90, 215-237.

Gale, David and Lloyd S. Shapley (1962): "College Admissions and the Stability of Marriage," American Mathematical Monthly 69, 9-15.

Haeringer, Guillaume and Flip Klijn (2009): "Constrained School Choice," Journal of Economic Theory 144, 1921-1947.

Kesten, Onur (2010): "School Choice with Consent," Quarterly Journal of Economics 125, 1297-1348.

Martínez, Ruth, Jordi Massó, Alejandro Neme, and Jorge Oviedo (2001): "On the Lattice Structure of the Set of Stable Matchings for a Many-to-One Model," Optimization 50, 439-457.

Roth, Alvi E. (1982): "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research 7, 617-628.

Shapley, Lloyd S. and Herbert Scarf (1974): "On Cores and Indivisibility," Journal of Mathematical Economics 1, 23-37.