TIER BALANCING: TOWARDS DYNAMIC FAIRNESS OVER UNDERLYING CAUSAL FACTORS

Abstract

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.

1. INTRODUCTION

The long-term fairness endeavor inevitably involves the interplay between decision policies and the underlying data generating process: when deriving a decision-making system, one usually makes use of data at hand; when we deploy such a system, the decision would impact how data will look in the future (Perdomo et al., 2020; Liu et al., 2021) . To understand why and how a data distribution responds to decision-making strategies, the investigation has to resort to causal modeling. The pursuit of long-term fairness, in turn, should also consider the changes in the underlying causal factors. In the effort of enforcing fairness in the dynamic setting, researchers have approached the problem from different angles: they provide causal modeling for fairness notions (Creager et al., 2020) , analyze the delayed impact or downstream effect on utilities (Liu et al., 2018; Heidari et al., 2019; Kannan et al., 2019; Nilforoshan et al., 2022) , enforce fairness in sequential or online decision-making (Joseph et al., 2016; Liu et al., 2017; Hashimoto et al., 2018; Heidari & Krause, 2018; Bechavod et al., 2019) , investigate the relation between the long-term population qualification and fair decisions (Zhang et al., 2020) , take into consideration the user behavior/action when deriving a decision policy (Zhang et al., 2019; Ustun et al., 2019; Miller et al., 2020; von Kügelgen et al., 2022) , provide fairness transferability guarantee across domains (Schumann et al., 2019; Singh et al., 2021) , or derive robust fair predictors (Coston et al., 2019; Rezaei et al., 2021) . The proposed dynamic fairness enforcing



Various fairness notions with different flavors have been proposed in the literature: associative fairness notions that capture the correlation or dependence between variables, e.g., Demographic Parity(Calders et al., 2009), Equalized Odds (Hardt et al., 2016); causal fairness notions that involve modeling causal relations between variables, e.g., Counterfactual Fairness(Kusner et al., 2017;  Russell et al., 2017), Path-Specific Counterfactual Fairness(Chiappa, 2019; Wu et al., 2019), Causal Multi-Level Fairness (Mhasawade & Chunara, 2021). The previously proposed fairness notions are with respect to a snapshot of the static reality, and do not have a built-in capacity to model the distribution-decision interplay in the long-term fairness pursuit.

