# Designing Long-term Group Fair Policies in Dynamical Systems

arXiv: https://arxiv.org/abs/2311.12447 · HTML: https://mlsanity.com/paper/2311.12447/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 97 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 30 of 53)

- [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)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Learning to reinforcement learn](https://mlsanity.com/paper/1611.05763/) (2016)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [Minimax Pareto Fairness: A Multi Objective Perspective](https://mlsanity.com/paper/2011.01821/) (2020)
- [Algorithmic Fairness](https://mlsanity.com/paper/2001.09784/) (2020)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [How Algorithmic Confounding in Recommendation Systems Increases Homogeneity and Decreases Utility](https://mlsanity.com/paper/1710.11214/) (2017)
- [Deployment-Efficient Reinforcement Learning via Model-Based Offline Optimization](https://mlsanity.com/paper/2006.03647/) (2020)
- [Fairness in Reinforcement Learning](https://mlsanity.com/paper/1611.03071/) (2016)
- [On the Fairness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2010.06529/) (2020)
- [How Do Fair Decisions Fare in Long-term Qualification?](https://mlsanity.com/paper/2010.11300/) (2020)
- [Algorithms for Fairness in Sequential Decision Making](https://mlsanity.com/paper/1901.08568/) (2019)
- [Simulation-based reinforcement learning for real-world autonomous driving](https://mlsanity.com/paper/1911.12905/) (2019)
- [α-Rank: Multi-Agent Evaluation by Evolution](https://mlsanity.com/paper/1903.01373/) (2019)
- [On the Long-term Impact of Algorithmic Decision Policies: Effort Unfairness and Feature Segregation through Social Learning](https://mlsanity.com/paper/1903.01209/) (2019)

## Built on by (most cited first, 9 of 9)

- [Time Can Invalidate Algorithmic Recourse](https://mlsanity.com/paper/2410.08007/) (2024)
- [Algorithmic Fairness in Performative Policy Learning: Escaping the Impossibility of Group Fairness](https://mlsanity.com/paper/2405.20447/) (2024)
- [Long-term Fairness For Real-time Decision Making: A Constrained Online Optimization Approach](https://mlsanity.com/paper/2401.02552/) (2024)
- [Fairness under uncertainty in sequential decisions](https://mlsanity.com/paper/2604.21711/) (2026)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [How Predicted Links Influence Network Evolution: Disentangling Choice and Algorithmic Feedback in Dynamic Graphs](https://mlsanity.com/paper/2603.03945/) (2026)
- [Price of Fairness in Short-Term and Long-Term Algorithmic Selections](https://mlsanity.com/paper/2605.06227/) (2026)
- [Long-term Fairness with Selective Labels](https://mlsanity.com/paper/2605.22291/) (2026)
- [Algorithmic Fairness Over Time: Advances & Prospects](https://mlsanity.com/paper/2610.15015/) (2026)

## Abstract (arXiv)

Neglecting the effect that decisions have on individuals (and thus, on the underlying data distribution) when designing algorithmic decision-making policies may increase inequalities and unfairness in the long term - even if fairness considerations were taken in the policy design process. In this paper, we propose a novel framework for achieving long-term group fairness in dynamical systems, in which current decisions may affect an individual's features in the next step, and thus, future decisions. Specifically, our framework allows us to identify a time-independent policy that converges, if deployed, to the targeted fair stationary state of the system in the long term, independently of the initial data distribution. We model the system dynamics with a time-homogeneous Markov chain and optimize the policy leveraging the Markov chain convergence theorem to ensure unique convergence. We provide examples of different targeted fair states of the system, encompassing a range of long-term goals for society and policymakers. Furthermore, we show how our approach facilitates the evaluation of different long-term targets by examining their impact on the group-conditional population distribution in the long term and how it evolves until convergence.