Fairly Stable Two-Sided Matching with Indifferences

Benjamin Cookson, Nisarg Shah

Keywords: Stable Matching, Algorithmic Fairness

TL;DR: We extend known fractional matching models to work when both sides of the matching have indifferences in their preferences.

Abstract:

Stability has been a foundational criterion for two-sided matching. When agents on one side have weak preferences involving indifferences, the seminal work of Kesten and Ünver [2015] proposes the Fractional Deferred Acceptance (FDA) algorithm for computing a fractional matching that satisfies (ex ante) stability along with a fairness criterion that ensures no discrimination among (equally-preferred) agents on one side.

We show that their algorithm can actually fail to terminate, refuting their claim of (polynomial-time) termination. Using substantially new algorithmic ideas, we develop an algorithm, Doubly-Fractional Deferred Acceptance Via Strongly Connected Components (DFDA-SCC), which can handle agents on both sides exhibiting indifferences and, in polynomial time, compute a fractional matching satisfying ex ante stability and no ex ante discrimination among agents on both sides.

Submission Number: 11