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.

翻译：长期公平的追求涉及决策与底层数据生成过程之间的相互作用。本文通过基于有向无环图（DAG）对决策-分布相互作用的因果建模，从动态视角探讨实现长期公平的可能性。我们提出“层级平衡”（Tier Balancing）这一概念——在长期动态公平分析语境下，该概念在技术上更具挑战性但更符合自然直觉。与以往仅基于观测变量定义的公平概念不同，我们的概念更进一步，捕捉了未观测潜在因果因素（这些因素直接承载当前决策对未来数据分布的影响）背后的情境变化。在既定动态框架下，我们证明：普遍情况下无法仅通过单步干预实现长期公平目标。此外，在逼近长期公平的努力中，我们考虑“趋近”长期公平目标的任务，并据此给出其可能性与不可能性结论。