# An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning

arXiv: https://arxiv.org/abs/2104.14504 · HTML: https://mlsanity.com/paper/2104.14504/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 29 Apr 2021.

## Builds on (most cited first, 12 of 12)

- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Identifying and Correcting Label Bias in Machine Learning](https://mlsanity.com/paper/1901.04966/) (2019)
- [A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual & Group Unfairness via Inequality Indices](https://mlsanity.com/paper/1807.00787/) (2018)
- [Learning Fair Policies in Multiobjective (Deep) Reinforcement Learning with Average and Discounted Rewards](https://mlsanity.com/paper/2008.07773/) (2020)
- [Accuracy comparison across face recognition algorithms: Where are we on measuring race bias?](https://mlsanity.com/paper/1912.07398/) (2019)
- [Fairness Behind a Veil of Ignorance: A Welfare Analysis for Automated Decision Making](https://mlsanity.com/paper/1806.04959/) (2018)
- [Fair Classification and Social Welfare](https://mlsanity.com/paper/1905.00147/) (2019)
- [Advancing subgroup fairness via sleeping experts](https://mlsanity.com/paper/1909.08375/) (2019)
- [Probably Approximately Metric-Fair Learning](https://mlsanity.com/paper/1803.03242/) (2018)
- [Balancing Competing Objectives with Noisy Data: Score-Based Classifiers for Welfare-Aware Machine Learning](https://mlsanity.com/paper/2003.06740/) (2020)
- [Decision trees as partitioning machines to characterize their generalization properties](https://mlsanity.com/paper/2010.07374/) (2020)
- [Learning to Unlearn: Building Immunity to Dataset Bias in Medical Imaging Studies](https://mlsanity.com/paper/1812.01716/) (2018)

## Built on by (most cited first, 18 of 18)

- [Optimizing generalized Gini indices for fairness in rankings](https://mlsanity.com/paper/2204.06521/) (2022)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [Learning Social Welfare Functions](https://mlsanity.com/paper/2405.17700/) (2024)
- [Welfare as a Guiding Principle for Machine Learning -- From Compass, to Lens, to Roadmap](https://mlsanity.com/paper/2502.11981/) (2025)
- [Learning Fair Pareto-Optimal Policies in Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2606.18111/) (2026)
- [Correcting Underrepresentation and Intersectional Bias for Classification](https://mlsanity.com/paper/2306.11112/) (2023)
- [Intuitions of Compromise: Utilitarianism vs. Contractualism](https://mlsanity.com/paper/2410.05496/) (2024)
- [Fair and Welfare-Efficient Constrained Multi-matchings under Uncertainty](https://mlsanity.com/paper/2411.02654/) (2024)
- [Can an AI Agent Safely Run a Government? Existence of Probably Approximately Aligned Policies](https://mlsanity.com/paper/2412.00033/) (2024)
- [Impacts of Individual Fairness on Group Fairness from the Perspective of Generalized Entropy](https://mlsanity.com/paper/2202.11966/) (2022)
- [Dividing Good and Better Items Among Agents with Bivalued Submodular Valuations](https://mlsanity.com/paper/2302.03087/) (2023)
- [Weighted Notions of Fairness with Binary Supermodular Chores](https://mlsanity.com/paper/2303.06212/) (2023)
- [To Pool or Not To Pool: Analyzing the Regularizing Effects of Group-Fair Training on Shared Models](https://mlsanity.com/paper/2402.18803/) (2024)
- [Welfare-Centric Clustering](https://mlsanity.com/paper/2508.10345/) (2025)
- [Online Social Welfare Function-based Resource Allocation](https://mlsanity.com/paper/2602.01400/) (2026)
- [GF-Score: Certified Class-Conditional Robustness Evaluation with Fairness Guarantees](https://mlsanity.com/paper/2604.12757/) (2026)
- [Inference-Time Policy Alignment for Fair Reinforcement Learning](https://mlsanity.com/paper/2608.00175/) (2026)
- [Fair Policy Optimization in Major-Minor Weakly Coupled Markov Decision Processes](https://mlsanity.com/paper/2609.36174/) (2026)

## Abstract (arXiv)

We address an inherent difficulty in welfare-theoretic fair machine learning by proposing an equivalently axiomatically-justified alternative and studying the resulting computational and statistical learning questions. Welfare metrics quantify overall wellbeing across a population of one or more groups, and welfare-based objectives and constraints have recently been proposed to incentivize fair machine learning methods to produce satisfactory solutions that consider the diverse needs of multiple groups. Unfortunately, many machine-learning problems are more naturally cast as loss minimization tasks, rather than utility maximization, which complicates direct application of welfare-centric methods to fair machine learning. In this work, we define a complementary measure, termed malfare, measuring overall societal harm (rather than wellbeing), with axiomatic justification via the standard axioms of cardinal welfare. We then cast fair machine learning as malfare minimization over the risk values (expected losses) of each group. Surprisingly, the axioms of cardinal welfare (malfare) dictate that this is not equivalent to simply defining utility as negative loss. Building upon these concepts, we define fair-PAC (FPAC) learning, where an FPAC learner is an algorithm that learns an varepsilon-δ malfare-optimal model with bounded sample complexity, for any data distribution, and for any (axiomatically justified) malfare concept. Finally, we show broad conditions under which, with appropriate modifications, standard PAC-learners may be converted to FPAC learners. This places FPAC learning on firm theoretical ground, as it yields statistical and computational efficiency guarantees for many well-studied machine-learning models, and is also practically relevant, as it democratizes fair ML by providing concrete training algorithms and rigorous generalization guarantees for these models