What Pareto-Efficiency Adjustments Cannot Fix

TL;DR

This paper demonstrates that common Pareto-efficiency adjustments cannot fix the inherent inefficiencies and inequalities of the Deferred Acceptance algorithm, especially regarding student segregation and demographic composition.

Contribution

It proves that Pareto-efficient mechanisms cannot correct DA's rank-inefficiency and inequality, and that school segregation remains unchanged under such mechanisms.

Findings

Pareto-efficiency adjustments do not fix DA's inefficiencies.

School demographic composition remains unchanged under Pareto-efficient mechanisms.

Segregation patterns are preserved even with alternative mechanisms.

Abstract

The Deferred Acceptance (DA) algorithm is stable and strategy-proof, but can produce outcomes that are Pareto-inefficient for students, and thus several alternative mechanisms have been proposed to correct this inefficiency. However, we show that these mechanisms cannot correct DA's rank-inefficiency and inequality, because these shortcomings can arise even in cases where DA is Pareto-efficient. We also examine students' segregation in settings with advantaged and marginalized students. We prove that the demographic composition of every school is perfectly preserved under any Pareto-efficient mechanism that dominates DA, and consequently fully segregated schools under DA maintain their extreme homogeneity.