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：追求长期公平性涉及决策过程与底层数据生成机制之间的相互作用。本文通过在有向无环图（DAG）上对决策-分布相互作用进行因果建模，从动态视角探讨实现长期公平性的可能性。我们提出"层级均衡"（Tier Balancing）这一概念——在长期动态公平性分析语境下，该概念在技术上更具挑战性但更为自然。与以往仅基于观测变量定义的公平性概念不同，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）的幕后情境变化。在特定动力学条件下，我们证明仅通过单步干预通常无法实现长期公平目标。此外，在探索长期公平性的过程中，我们考虑了"趋近"长期公平目标的使命，并据此给出了可能性和不可能性结论。