Local non-bossiness

TL;DR

This paper introduces the concept of local non-bossiness in school choice mechanisms, providing a new characterization of the student-optimal stable mechanism (DA) and analyzing its incentive properties regarding students' preferences over colleagues.

Contribution

It defines local non-bossiness as a new property, offering a stability-independent characterization of DA and exploring its implications for incentive compatibility.

Findings

DA is uniquely characterized by local non-bossiness and stability.

Local non-bossiness limits students' ability to influence peers without changing their own assignment.

DA remains the only stable, strategy-proof mechanism under certain preference structures.

Abstract

The student-optimal stable mechanism (DA), the most popular mechanism in school choice, is the only one that is stable and strategy-proof. However, when DA is implemented, a student can change the schools of others without changing her own. We show that this drawback is limited: a student cannot change her schoolmates while remaining at the same school. We refer to this new property as local non-bossiness and use it to provide a new characterization of DA that does not rely on stability. Furthermore, we show that local non-bossiness plays a crucial role in providing incentives to be truthful when students have preferences over their colleagues. As long as students first consider the school to which they are assigned and then their schoolmates, DA induces the only stable and strategy-proof mechanism. There is limited room to expand this preference domain without compromising the existence of a stable and strategy-proof mechanism.