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Social Choice and Welfare
Published in: Social Choice and Welfare 2/2022

19-08-2021 | Original Paper

When is the deferred acceptance mechanism responsive to priority-based affirmative action?

Authors: Zhenhua Jiao, Ziyang Shen, Guoqiang Tian

Published in: Social Choice and Welfare | Issue 2/2022

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Abstract

For school choice with affirmative action, responsiveness is used as a measure of how a matching mechanism performs in terms of a certain type of affirmative action policy. We know that the Deferred Acceptance (DA) mechanism is not responsive to the priority-based affirmative action on the universal domain of school choice problems. As a further study, we show in this paper that, the DA mechanism is responsive to the priority-based affirmative action if and only if the exogenous school choice structure (ESCS), which is given by the set of students, the set of schools, the schools’ capacity profile, and schools’ original priority structure, satisfies an acyclicity condition characterized in this paper. This acyclicity condition is stronger than Doğan’s acyclicity, which is the necessary and sufficient condition for the DA mechanism to be responsive to the reserved-based affirmative action.
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Appendix
Available only for authorised users
Footnotes
1
See, for instance, Hafalir et al. (2013), Ehlers et al. (2014), and Doğan (2016) for detailed discussions, including disadvantages of the policy such as the avoidable inefficiency.
 
2
As Chen and Kesten (2017) pointed out, in recent years, there are about 10 million high school seniors who compete for 6 million seats at universities in China each year. In the college admissions, students’ priority orders at colleges are determined by students’ scores in the National College Entrance Examination.
 
3
Kojima (2012) first introduces the spirit of this concept. He calls it respecting the spirit of affirmative action. Recently, Doğan (2016) starts to use the notion of responsiveness.
 
4
In the literature, there are many types of acyclicity conditions having a similar spirit. See Ergin (2002), Kesten (2006), Haeringer and Klijn (2009), Kojima (2013), Klaus and Klijn (2013), and Hatfield et al. (2016) for details.
 
5
One should note that when we simply mention a “cycle” in this paper, we are actually talking about the cycle characterized by Definition 3. That is, an Ergin’s cycle is not a cycle in this paper.
 
6
Specifically, with an improvement for minority students over \(\succ\) in Definition 3, we can achieve a new priority structure \(\succ ^{\prime }\) which satisfies \(s_{k-1}\succ ^{\prime }_{c_1}m\succ ^{\prime }_{c_1}M\succ ^{\prime }_{c_2}s_1\succ ^{\prime }_{c_3}s_2\succ ^{\prime }_{c_4}\cdots \succ ^{\prime }_{c_k}s_{k-1}\). This leads to a generalized cycle.
 
7
Alternatively, since there is only one minority student, the responsiveness is actually equivalent to the property of respecting improvement introduced by Balinski and Sönmez (1999). Then, we can infer that the DA mechanism is responsive to the priority-based affirmative action, as Balinski and Sönmez (1999) show that the DA mechanism respects improvement.
 
8
The spirit of this notion is the same as the ones defined by Kesten (2010) and Doğan (2016).
 
9
Student s can either be \(s^{\prime }\) or some other majority student.
 
Literature
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Abdulkadiroğlu A, Sönmez T (2003) School choice: A mechanism design approach. Am Econ Rev 93(3):729–747CrossRef
Balinski M, Sönmez T (1999) A tale of two mechanisms: Student placement. J Econ Theory 84(1):73–94CrossRef
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Hafalir IE, Yenmez MB, Yildirim MA (2013) Effective affirmative action in school choice. Theor Econ 8(2):325–363CrossRef
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Metadata
Title
When is the deferred acceptance mechanism responsive to priority-based affirmative action?
Authors
Zhenhua Jiao
Ziyang Shen
Guoqiang Tian
Publication date
19-08-2021
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 2/2022
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-021-01357-4

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