Reforms meet fairness concerns in school and college admissions

TL;DR

This paper analyzes recent reforms in school and college admissions matching mechanisms, showing they are more fair in terms of stability and blocking students, and exploring the relationship between fairness and manipulability.

Contribution

It provides a novel analysis demonstrating that reforms improve fairness by stability and counting, and links fairness with manipulability in matching mechanisms.

Findings

Reforms lead to more stable mechanisms with fewer blocking students.

Reforms reduce the number of blocking students compared to previous mechanisms.

Fairness and manipulability are strongly logically related in matching mechanisms.

Abstract

Recently, many matching systems around the world have been reformed. These reforms responded to objections that the matching mechanisms in use were unfair and manipulable. Surprisingly, the mechanisms remained unfair even after the reforms: the new mechanisms may induce an outcome with a blocking student who desires and deserves a school which she did not receive. However, as we show in this paper, the reforms introduced matching mechanisms which are more fair compared to the counterfactuals. First, most of the reforms introduced mechanisms that are more fair by stability: whenever the old mechanism does not have a blocking student, the new mechanism does not have a blocking student either. Second, some reforms introduced mechanisms that are more fair by counting: the old mechanism always has at least as many blocking students as the new mechanism. These findings give a novel rationale to the reforms and complement the recent literature showing that the same reforms have introduced less manipulable matching mechanisms. We further show that the fairness and manipulability of the mechanisms are strongly logically related.