Identifying and Quantifying (Un)Improvable Students

TL;DR

This paper analyzes the inefficiency of the Deferred Acceptance mechanism in student placements, showing most students are improvable and Pareto-dominant mechanisms can significantly improve outcomes.

Contribution

It characterizes the set of unimprovable students and demonstrates the widespread potential for improvement through trading cycles in DA.

Findings

Most students are improvable under DA.

Trading cycles can enable simultaneous improvements for many students.

Pareto-dominant mechanisms effectively address DA's inefficiency.

Abstract

The Deferred Acceptance (DA) mechanism can generate inefficient placements. Although Pareto-dominant mechanisms exist, it remains unclear which and how many students could improve. We characterize the set of unimprovable students and show that it includes those unassigned or matched with their least preferred schools. Nevertheless, by proving that DA's envy digraph contains a unique giant strongly connected component, we establish that almost all students are improvable, and furthermore, they can benefit simultaneously via disjoint trading cycles. Our findings reveal the pervasiveness of DA's inefficiency and the remarkable effectiveness of Pareto-dominant mechanisms in addressing it, regardless of the specific mechanism chosen.