Weak Stability and Pareto Efficiency in School Choice

28 Pages Posted: 31 May 2017 Last revised: 20 Feb 2020

See all articles by Qianfeng Tang

Qianfeng Tang

Shanghai University of Finance and Economics - School of Economics

Yongchao Zhang

Shanghai University of Finance and Economics - School of Economics

Date Written: February 19, 2020

Abstract

We study the trade-off between stability and students’ welfare in school choice problems. We call a matching weakly stable if none of its blocking pairs can be matched in a more stable matching–one with a weakly smaller set of blocking pairs. A matching is said to be self-constrained efficient if for students it is not Pareto dominated by any more stable matching, and it is self-constrained optimal if it weakly Pareto dominates all such matchings. We show that the following are equivalent for any matching: (i) it is weakly stable and self-constrained efficient; (ii) it is self-constrained optimal; (iii) it is an efficiency-adjusted deferred acceptance mechanism (EADAM) outcome under some consenting constraint; and (iv) it is exactly the EADAM outcome when its own set of blocking pairs is used as consenting constraint.

Keywords: Deferred acceptance algorithm, Pareto efficiency, school choice, stability

JEL Classification: C78, D61, D78, I20

Suggested Citation

Tang, Qianfeng and Zhang, Yongchao, Weak Stability and Pareto Efficiency in School Choice (February 19, 2020). Available at SSRN: https://ssrn.com/abstract=2972611 or http://dx.doi.org/10.2139/ssrn.2972611

Qianfeng Tang (Contact Author)

Shanghai University of Finance and Economics - School of Economics ( email )

777 Guoding Road
Shanghai, 200433
China

Yongchao Zhang

Shanghai University of Finance and Economics - School of Economics ( email )

777 Guoding Road Yangpu D.
Shanghai, Shanghai 200433
China

HOME PAGE: http://zhangyongchao.weebly.com

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