  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.
