# A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual & Group Unfairness via Inequality Indices

arXiv: https://arxiv.org/abs/1807.00787 · HTML: https://mlsanity.com/paper/1807.00787/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2018.

## Built on by (most cited first, 30 of 97)

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- [Fairify: Fairness Verification of Neural Networks](https://mlsanity.com/paper/2212.06140/) (2022)
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- [An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning](https://mlsanity.com/paper/2104.14504/) (2021)
- [Loss-Aversively Fair Classification](https://mlsanity.com/paper/2105.04273/) (2021)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Towards Understanding Fairness and its Composition in Ensemble Machine Learning](https://mlsanity.com/paper/2212.04593/) (2022)
- [Fairness through Aleatoric Uncertainty](https://mlsanity.com/paper/2304.03646/) (2023)
- [Bias in Machine Learning Models Can Be Significantly Mitigated by Careful Training: Evidence from Neuroimaging Studies](https://mlsanity.com/paper/2205.13421/) (2022)
- [Optimizing generalized Gini indices for fairness in rankings](https://mlsanity.com/paper/2204.06521/) (2022)
- [MMD-B-Fair: Learning Fair Representations with Statistical Testing](https://mlsanity.com/paper/2211.07907/) (2022)
- [Equality before the Law: Legal Judgment Consistency Analysis for Fairness](https://mlsanity.com/paper/2103.13868/) (2021)
- [Towards A Holistic View of Bias in Machine Learning: Bridging Algorithmic Fairness and Imbalanced Learning](https://mlsanity.com/paper/2207.06084/) (2022)
- [Auditing of AI: Legal, Ethical and Technical Approaches](https://mlsanity.com/paper/2407.06235/) (2024)
- [Bias-inducing geometries: an exactly solvable data model with fairness implications](https://mlsanity.com/paper/2205.15935/) (2022)
- [On the Richness of Calibration](https://mlsanity.com/paper/2302.04118/) (2023)
- [Fairness in Preference-based Reinforcement Learning](https://mlsanity.com/paper/2306.09995/) (2023)
- [AIM: Attributing, Interpreting, Mitigating Data Unfairness](https://mlsanity.com/paper/2406.08819/) (2024)
- [Measuring Disparate Outcomes of Content Recommendation Algorithms with Distributional Inequality Metrics](https://mlsanity.com/paper/2202.01615/) (2022)
- [Mitigating Unfairness via Evolutionary Multi-objective Ensemble Learning](https://mlsanity.com/paper/2210.16754/) (2022)
- [Understanding Unfairness in Fraud Detection through Model and Data Bias Interactions](https://mlsanity.com/paper/2207.06273/) (2022)

## Abstract (arXiv)

Discrimination via algorithmic decision making has received considerable attention. Prior work largely focuses on defining conditions for fairness, but does not define satisfactory measures of algorithmic unfairness. In this paper, we focus on the following question: Given two unfair algorithms, how should we determine which of the two is more unfair? Our core idea is to use existing inequality indices from economics to measure how unequally the outcomes of an algorithm benefit different individuals or groups in a population. Our work offers a justified and general framework to compare and contrast the (un)fairness of algorithmic predictors. This unifying approach enables us to quantify unfairness both at the individual and the group level. Further, our work reveals overlooked tradeoffs between different fairness notions: using our proposed measures, the overall individual-level unfairness of an algorithm can be decomposed into a between-group and a within-group component. Earlier methods are typically designed to tackle only between-group unfairness, which may be justified for legal or other reasons. However, we demonstrate that minimizing exclusively the between-group component may, in fact, increase the within-group, and hence the overall unfairness. We characterize and illustrate the tradeoffs between our measures of (un)fairness and the prediction accuracy.