# Enforcing Group Fairness in Algorithmic Decision Making: Utility Maximization Under Sufficiency

arXiv: https://arxiv.org/abs/2206.02237 · HTML: https://mlsanity.com/paper/2206.02237/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 5 Jun 2022.

## Builds on (most cited first, 18 of 18)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [A comparative study of fairness-enhancing interventions in machine learning](https://mlsanity.com/paper/1802.04422/) (2018)
- [Algorithmic Fairness](https://mlsanity.com/paper/2001.09784/) (2020)
- [A Confidence-Based Approach for Balancing Fairness and Accuracy](https://mlsanity.com/paper/1601.05764/) (2016)
- [Fairness in Credit Scoring: Assessment, Implementation and Profit Implications](https://mlsanity.com/paper/2103.01907/) (2021)
- [Fairness Metrics: A Comparative Analysis](https://mlsanity.com/paper/2001.07864/) (2020)
- [From Soft Classifiers to Hard Decisions: How fair can we be?](https://mlsanity.com/paper/1810.02003/) (2018)
- [Enhancing the Accuracy and Fairness of Human Decision Making](https://mlsanity.com/paper/1805.10318/) (2018)
- [Distributive Justice and Fairness Metrics in Automated Decision-making: How Much Overlap Is There?](https://mlsanity.com/paper/2105.01441/) (2021)

## Built on by (most cited first, 19 of 19)

- [FFB: A Fair Fairness Benchmark for In-Processing Group Fairness Methods](https://mlsanity.com/paper/2306.09468/) (2023)
- [Consensus and Subjectivity of Skin Tone Annotation for ML Fairness](https://mlsanity.com/paper/2305.09073/) (2023)
- [To Be Forgotten or To Be Fair: Unveiling Fairness Implications of Machine Unlearning Methods](https://mlsanity.com/paper/2302.03350/) (2023)
- [A Classification of Feedback Loops and Their Relation to Biases in Automated Decision-Making Systems](https://mlsanity.com/paper/2305.06055/) (2023)
- [On Prediction-Modelers and Decision-Makers: Why Fairness Requires More Than a Fair Prediction Model](https://mlsanity.com/paper/2310.05598/) (2023)
- [Deceptive Fairness Attacks on Graphs via Meta Learning](https://mlsanity.com/paper/2310.15653/) (2023)
- [Fairness and Sequential Decision Making: Limits, Lessons, and Opportunities](https://mlsanity.com/paper/2301.05753/) (2023)
- [Equalised Odds is not Equal Individual Odds: Post-processing for Group and Individual Fairness](https://mlsanity.com/paper/2304.09779/) (2023)
- [A Justice-Based Framework for the Analysis of Algorithmic Fairness-Utility Trade-Offs](https://mlsanity.com/paper/2206.02891/) (2022)
- [Distributive Justice as the Foundational Premise of Fair ML: Unification, Extension, and Interpretation of Group Fairness Metrics](https://mlsanity.com/paper/2206.02897/) (2022)
- [Cherry on the Cake: Fairness is NOT an Optimization Problem](https://mlsanity.com/paper/2406.16606/) (2024)
- [Group Fairness in Prediction-Based Decision Making: From Moral Assessment to Implementation](https://mlsanity.com/paper/2210.10456/) (2022)
- [Size-adaptive Hypothesis Testing for Fairness](https://mlsanity.com/paper/2506.10586/) (2025)
- [Fairness vs Performance: Characterizing the Pareto Frontier of Algorithmic Decision Systems](https://mlsanity.com/paper/2605.10604/) (2026)
- [Assessing Group Fairness with Social Welfare Optimization](https://mlsanity.com/paper/2405.11421/) (2024)
- [A Semidefinite Relaxation Approach for Fair Graph Clustering](https://mlsanity.com/paper/2410.15233/) (2024)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [Fair Classification by Direct Intervention on Operating Characteristics](https://mlsanity.com/paper/2509.25481/) (2025)
- [Fair Decisions from Calibrated Scores: Achieving Optimal Classification While Satisfying Sufficiency](https://mlsanity.com/paper/2602.07285/) (2026)

## Abstract (arXiv)

Binary decision making classifiers are not fair by default. Fairness requirements are an additional element to the decision making rationale, which is typically driven by maximizing some utility function. In that sense, algorithmic fairness can be formulated as a constrained optimization problem. This paper contributes to the discussion on how to implement fairness, focusing on the fairness concepts of positive predictive value (PPV) parity, false omission rate (FOR) parity, and sufficiency (which combines the former two). We show that group-specific threshold rules are optimal for PPV parity and FOR parity, similar to well-known results for other group fairness criteria. However, depending on the underlying population distributions and the utility function, we find that sometimes an upper-bound threshold rule for one group is optimal: utility maximization under PPV parity (or FOR parity) might thus lead to selecting the individuals with the smallest utility for one group, instead of selecting the most promising individuals. This result is counter-intuitive and in contrast to the analogous solutions for statistical parity and equality of opportunity. We also provide a solution for the optimal decision rules satisfying the fairness constraint sufficiency. We show that more complex decision rules are required and that this leads to within-group unfairness for all but one of the groups. We illustrate our findings based on simulated and real data.