# Optimizing generalized Gini indices for fairness in rankings arXiv: https://arxiv.org/abs/2204.06521 ยท HTML: https://mlsanity.com/paper/2204.06521/ ## Key facts - Cited by 13 papers in the map (data through 14 Oct 2026). - Builds on 37 of its 86 references that are in the map. - First posted on arXiv 2 Apr 2022. ## Builds on (most cited first, 30 of 37) - [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020) - [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018) - [Equity of Attention: Amortizing Individual Fairness in Rankings](https://mlsanity.com/paper/1805.01788/) (2018) - [Differentiable Ranks and Sorting using Optimal Transport](https://mlsanity.com/paper/1905.11885/) (2019) - [Stochastic Optimization of Sorting Networks via Continuous Relaxations](https://mlsanity.com/paper/1903.08850/) (2019) - [A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual & Group Unfairness via Inequality Indices](https://mlsanity.com/paper/1807.00787/) (2018) - [Discrimination in Online Ad Delivery](https://mlsanity.com/paper/1301.6822/) (2013) - [Fairness risk measures](https://mlsanity.com/paper/1901.08665/) (2019) - [Automated Experiments on Ad Privacy Settings: A Tale of Opacity, Choice, and Discrimination](https://mlsanity.com/paper/1408.6491/) (2014) - [FairRec: Two-Sided Fairness for Personalized Recommendations in Two-Sided Platforms](https://mlsanity.com/paper/2002.10764/) (2020) - [Multisided Fairness for Recommendation](https://mlsanity.com/paper/1707.00093/) (2017) - [The Unfairness of Popularity Bias in Recommendation](https://mlsanity.com/paper/1907.13286/) (2019) - [Controlling Fairness and Bias in Dynamic Learning-to-Rank](https://mlsanity.com/paper/2005.14713/) (2020) - [Learning Fair Policies in Multiobjective (Deep) Reinforcement Learning with Average and Discounted Rewards](https://mlsanity.com/paper/2008.07773/) (2020) - [Evaluating Stochastic Rankings with Expected Exposure](https://mlsanity.com/paper/2004.13157/) (2020) - [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) - [Learning Fair Policies in Decentralized Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2012.09421/) (2020) - [Reducing Disparate Exposure in Ranking: A Learning To Rank Approach](https://mlsanity.com/paper/1805.08716/) (2018) - [TFROM: A Two-sided Fairness-Aware Recommendation Model for Both Customers and Providers](https://mlsanity.com/paper/2104.09024/) (2021) - [Bridging Machine Learning and Mechanism Design towards Algorithmic Fairness](https://mlsanity.com/paper/2010.05434/) (2020) - [The Complexity of Large-scale Convex Programming under a Linear Optimization Oracle](https://mlsanity.com/paper/1309.5550/) (2013) - [Multi-objective Bandits: Optimizing the Generalized Gini Index](https://mlsanity.com/paper/1706.04933/) (2017) - [Two-sided fairness in rankings via Lorenz dominance](https://mlsanity.com/paper/2110.15781/) (2021) - [User Fairness, Item Fairness, and Diversity for Rankings in Two-Sided Markets](https://mlsanity.com/paper/2010.01470/) (2020) - [The Anatomy of a Scientific Rumor](https://mlsanity.com/paper/1301.2952/) (2013) - [Online certification of preference-based fairness for personalized recommender systems](https://mlsanity.com/paper/2104.14527/) (2021) - [An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning](https://mlsanity.com/paper/2104.14504/) (2021) - [Projection Efficient Subgradient Method and Optimal Nonsmooth Frank-Wolfe Method](https://mlsanity.com/paper/2010.01848/) (2020) - [A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming](https://mlsanity.com/paper/1804.08544/) (2018) ## Built on by (most cited first, 13 of 13) - [Fairness in Matching under Uncertainty](https://mlsanity.com/paper/2302.03810/) (2023) - [Performative Debias with Fair-exposure Optimization Driven by Strategic Agents in Recommender Systems](https://mlsanity.com/paper/2406.17475/) (2024) - [Contextual bandits with concave rewards, and an application to fair ranking](https://mlsanity.com/paper/2210.09957/) (2022) - [End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty](https://mlsanity.com/paper/2402.07772/) (2024) - [Learning Fair Pareto-Optimal Policies in Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2606.18111/) (2026) - [Learning Fair Ranking Policies via Differentiable Optimization of Ordered Weighted Averages](https://mlsanity.com/paper/2402.05252/) (2024) - [AI-EDI-SPACE: A Co-designed Dataset for Evaluating the Quality of Public Spaces](https://mlsanity.com/paper/2411.00956/) (2024) - [Learning to Re-rank with Constrained Meta-Optimal Transport](https://mlsanity.com/paper/2305.00319/) (2023) - [FEIR: Quantifying and Reducing Envy and Inferiority for Fair Recommendation of Limited Resources](https://mlsanity.com/paper/2311.04542/) (2023) - [End-to-End Optimization and Learning of Fair Court Schedules](https://mlsanity.com/paper/2410.17415/) (2024) - [Toward Unifying Group Fairness Evaluation from a Sparsity Perspective](https://mlsanity.com/paper/2511.00359/) (2025) - [Contrastive Learning for Diversity-Aware Product Recommendations in Retail](https://mlsanity.com/paper/2602.08886/) (2026) - [Inference-Time Policy Alignment for Fair Reinforcement Learning](https://mlsanity.com/paper/2608.00175/) (2026) ## Abstract (arXiv) There is growing interest in designing recommender systems that aim at being fair towards item producers or their least satisfied users. Inspired by the domain of inequality measurement in economics, this paper explores the use of generalized Gini welfare functions (GGFs) as a means to specify the normative criterion that recommender systems should optimize for. GGFs weight individuals depending on their ranks in the population, giving more weight to worse-off individuals to promote equality. Depending on these weights, GGFs minimize the Gini index of item exposure to promote equality between items, or focus on the performance on specific quantiles of least satisfied users. GGFs for ranking are challenging to optimize because they are non-differentiable. We resolve this challenge by leveraging tools from non-smooth optimization and projection operators used in differentiable sorting. We present experiments using real datasets with up to 15k users and items, which show that our approach obtains better trade-offs than the baselines on a variety of recommendation tasks and fairness criteria.