  Although many fairness criteria have been proposed for decision making, their
long-term impact on the well-being of a population remains unclear. In this
work, we study the dynamics of population qualification and algorithmic
decisions under a partially observed Markov decision problem setting. By
characterizing the equilibrium of such dynamics, we analyze the long-term
impact of static fairness constraints on the equality and improvement of group
well-being. Our results show that static fairness constraints can either
promote equality or exacerbate disparity depending on the driving factor of
qualification transitions and the effect of sensitive attributes on feature
distributions. We also consider possible interventions that can effectively
improve group qualification or promote equality of group qualification. Our
theoretical results and experiments on static real-world datasets with
simulated dynamics show that our framework can be used to facilitate social
science studies.
