Local non-bossiness

TL;DR

This paper investigates how the widely used student-proposing Deferred Acceptance mechanism ($DA$) behaves when students care about others’ school assignments. It introduces the property of local non-bossiness, showing that $DA$ cannot change a student’s schoolmates without altering her own assignment, a feature that is independent of stability or strategy-proofness. It then provides a new axiomatic characterization of $DA$ valid for many-to-one school choice, using six axioms (individual rationality, weak non-wastefulness, population-monotonicity, strategy-proofness, S-WrARP, and weak local non-bossiness) to identify $DA^{\succ}$ for some priority profile $\succ$. The paper also extends the analysis to settings with externalities, showing that if preferences are school-lexicographic over colleagues, $DA$ induces a stable and strategy-proof mechanism on the domain where each student cares first about her assigned school and then about her schoolmates, denoted $\overline{DA}$. Overall, the results clarify that $DA$ remains robust to a class of incentives involving others’ allocations, while highlighting the fragility of stability under broader preference domains and the limited scope for relaxing the domain without sacrificing desirable properties.

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.

Figures (1)

• Figure 1: On local non-bossiness and other incentive properties.

Theorems & Definitions (43)

• Definition 1
• Definition 2
• Theorem 1
• proof : Proof of \ref{['loc_nonb']}
• Remark 1
• Remark 2
• Corollary 1
• Definition 3
• Definition 4
• Theorem 2