# Priority-driven behaviors under the Boston mechanism

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## Abstract

We study school choice markets where the non-strategy-proof Boston mechanism is used to assign students to schools. Inspired by previous field and experimental evidence, we analyze a type of behavior called priority-driven: students have a common ranking over the schools and then give a bonus in their submitted preferences to those schools for which they have high priority. We first prove that under this behavior, there is a unique stable and efficient matching, which is the outcome of the Boston mechanism. Second, we show that the three most prominent mechanisms on school choice (Boston, deferred acceptance, and top trading cycles) coincide when students’ submitted preferences are priority-driven. Finally, we run some computational simulations to show that the assumption of priority-driven preferences can be relaxed by introducing an idiosyncratic preference component, and our qualitative results carry over to a more general model of preferences.

## Keywords

Two-sided many-to-one matching School choice Boston algorithm Manipulation strategies Deferred acceptance algorithm## JEL Classification

C72 D47 D78 D82## References

- Abdulkadiroglu A, Pathak P, Roth AE, Sonmez T (2006) Changing the Boston school choice mechanism: strategy-proofness as equal access. Discussion paper, National Bureau of Economic ResearchGoogle Scholar
- Abdulkadiroğlu A, Sönmez T (2003) School choice: a mechanism design approach. Am Econ Rev 93(3):729–747CrossRefGoogle Scholar
- Alcalde J (1996) Implementation of stable solutions to marriage problems. J Econ Theory 69(1):240–254CrossRefGoogle Scholar
- Calsamiglia C, Güell M (2014) The illusion of school choice: empirical evidence from Barcelona, unpublished manuscriptGoogle Scholar
- Calsamiglia C, Haeringer G, Klijn F (2010) Constrained school choice: an experimental study. Am Econ Rev 100(4):1860–1874Google Scholar
- Calsamiglia C, Miralles A (2016) Catchment areas and access to better schools, unpublished manuscriptGoogle Scholar
- Chen Y, Jiang M, Kesten O, Robin S, Zhu M (2013) A large scale school choice experiment. In AFSE Meeting 2013Google Scholar
- Chen Y, Kesten O (2013) From Boston to Chinese parallel to deferred acceptance: theory and experiments on a family of school choice mechanisms, unpublished manuscriptGoogle Scholar
- Chen Y, Kesten O (2017) Chinese college admissions and school choice reforms: a theoretical analysis. J Polit Econ 125(1):99–139Google Scholar
- Chen Y, Sönmez T (2006) School choice: an experimental study. J Econ Theory 127(1):202–231CrossRefGoogle Scholar
- Ding T, Schotter A (2014) Intergenerational advice and matching: an experimental study, unpublished manuscriptGoogle Scholar
- Dur U (2015) The modified Boston mechanism, unpublished manuscriptGoogle Scholar
- Echenique F, Wilson AJ, Yariv L (2016) Clearinghouses for two-sided matching: an experimental study. Quant Econ 7(2):449–482CrossRefGoogle Scholar
- Erev I, Roth A E (2014) Maximization, learning and economic behavior, unpublished manuscriptGoogle Scholar
- Ergin H, Sönmez T (2006) Games of school choice under the Boston mechanism. J Publ Econ 90(1):215–237CrossRefGoogle Scholar
- Haeringer G, Halaburda H (2011) Better-reply dynamics in deferred acceptance games, unpublished manuscriptGoogle Scholar
- Harless P (2015) Immediate acceptance in school choice: comparing implementations, unpublished manuscriptGoogle Scholar
- Mennle T, Seuken S (2015) Trade-offs in school choice: comparing deferred acceptance, the Naıve and the adaptive Boston mechanism, unpublished manuscriptGoogle Scholar
- Pais J, Pintér Á (2008) School choice and information: an experimental study on matching mechanisms. Games Econ Behav 64(1):303–328CrossRefGoogle Scholar
- Shapley L, Scarf H (1974) On cores and indivisibility. J Math Econ 1(1):23–37CrossRefGoogle Scholar
- Sönmez T (1997) Games of manipulation in marriage problems. Games Econ Behav 20(2):169–176CrossRefGoogle Scholar