  The pursuit of long-term fairness involves the interplay between
decision-making and the underlying data generating process. In this paper,
through causal modeling with a directed acyclic graph (DAG) on the
decision-distribution interplay, we investigate the possibility of achieving
long-term fairness from a dynamic perspective. We propose Tier Balancing, a
technically more challenging but more natural notion to achieve in the context
of long-term, dynamic fairness analysis. Different from previous fairness
notions that are defined purely on observed variables, our notion goes one step
further, capturing behind-the-scenes situation changes on the unobserved latent
causal factors that directly carry out the influence from the current decision
to the future data distribution. Under the specified dynamics, we prove that in
general one cannot achieve the long-term fairness goal only through one-step
interventions. Furthermore, in the effort of approaching long-term fairness, we
consider the mission of "getting closer to" the long-term fairness goal and
present possibility and impossibility results accordingly.
