Individual Fairness under Varied Notions of Group Fairness in Bipartite Matching - One Framework to Approximate Them All

TL;DR

This paper introduces a polynomial-time framework for probabilistic matchings that balance individual and group fairness constraints, adaptable to various fairness notions, with empirical validation on real datasets.

Contribution

It presents a novel polynomial-time algorithm for approximately satisfying individual fairness while maintaining ex-ante group fairness in bipartite matchings.

Findings

Algorithm achieves near-optimal expected matching size.

Provides bi-criteria approximation algorithms for fairness trade-offs.

Extends to complex group fairness notions like maxmin and mindom.

Abstract

We study the probabilistic assignment of items to platforms that satisfies both group and individual fairness constraints. Each item belongs to specific groups and has a preference ordering over platforms. Each platform enforces group fairness by limiting the number of items per group that can be assigned to it. There could be multiple optimal solutions that satisfy the group fairness constraints, but this alone ignores item preferences. Our approach explores a `best of both worlds fairness' solution to get a randomized matching, which is ex-ante individually fair and ex-post group-fair. Thus, we seek a `probabilistic individually fair' distribution over `group-fair' matchings where each item has a `high' probability of matching to one of its top choices. This distribution is also ex-ante group-fair. Users can customize fairness constraints to suit their requirements. Our first result is a polynomial-time algorithm that computes a distribution over `group-fair' matchings such that the individual fairness constraints are approximately satisfied and the expected size of a matching is close to OPT. We empirically test this on real-world datasets. We present two additional polynomial-time bi-criteria approximation algorithms that users can choose from to balance group fairness and individual fairness trade-offs. For disjoint groups, we provide an exact polynomial-time algorithm adaptable to additional lower `group fairness' bounds. Extending our model, we encompass `maxmin group fairness,' amplifying underrepresented groups, and `mindom group fairness,' reducing the representation of dominant groups.'