Designing Long-term Group Fair Policies in Dynamical Systems

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 into account in the policy design process. In this paper, we propose a novel framework for studying 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. Our framework enables the utilization of historical temporal data to tackle challenges associated with delayed feedback when learning long-term fair policies in practice. Importantly, our framework shows that interventions on the data distribution (e.g., subsidies) can be used to achieve policy learning that is both short- and long-term fair. We provide examples of different targeted fair states of the system, encompassing a range of long-term goals for society and policymakers. In semi-synthetic simulations based on real-world datasets, we show how our approach facilitates identifying effective interventions for long-term fairness.