Impacts of Individual Fairness on Group Fairness from the Perspective of Generalized Entropy

TL;DR

This paper explores how controlling individual fairness via generalized entropy impacts group fairness, revealing that increasing individual fairness does not always improve group fairness, supported by theoretical analysis and experiments.

Contribution

It introduces a classification algorithm that enforces a specified degree of individual fairness using generalized entropy and proves its PAC learnability.

Findings

Strengthening individual fairness does not necessarily enhance group fairness.

The proposed fair ERM algorithm is PAC learnable under certain conditions.

Empirical results support the theoretical analysis of fairness trade-offs.

Abstract

This paper investigates how the degree of group fairness changes when the degree of individual fairness is actively controlled. As a metric quantifying individual fairness, we consider generalized entropy (GE) recently introduced into machine learning community. To control the degree of individual fairness, we design a classification algorithm satisfying a given degree of individual fairness through an empirical risk minimization (ERM) with a fairness constraint specified in terms of GE. We show the PAC learnability of the fair ERM problem by proving that the true fairness degree does not deviate much from an empirical one with high probability for finite VC dimension if the sample size is big enough. Our experiments show that strengthening individual fairness degree does not always lead to enhancement of group fairness.