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

arXiv: https://arxiv.org/abs/2202.11966 · HTML: https://mlsanity.com/paper/2202.11966/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual & Group Unfairness via Inequality Indices](https://mlsanity.com/paper/1807.00787/) (2018)
- [An Empirical Study of Rich Subgroup Fairness for Machine Learning](https://mlsanity.com/paper/1808.08166/) (2018)
- [Fairness Behind a Veil of Ignorance: A Welfare Analysis for Automated Decision Making](https://mlsanity.com/paper/1806.04959/) (2018)
- [Average Individual Fairness: Algorithms, Generalization and Experiments](https://mlsanity.com/paper/1905.10607/) (2019)
- [A Stochastic Optimization Framework for Fair Risk Minimization](https://mlsanity.com/paper/2102.12586/) (2021)
- [An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning](https://mlsanity.com/paper/2104.14504/) (2021)

## Abstract (arXiv)

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.