Causal Fairness

The mathematical foundation of causal fairness. An SCM is a triple (U, V, F) representing exogenous background variables, endogenous observed variables, and structural equations that define causal mechanisms. Unlike purely statistical approaches, SCMs encode cause-effect relationships as directed acyclic graphs, enabling the formal distinction between correlation and causation. This allows auditors to isolate the specific pathways through which a protected attribute influences a decision.

The core mechanism for causal fairness evaluation. This technique computes what a decision would have been had a protected attribute been different along only unfair causal pathways, while holding legitimate pathways constant. For example, in university admissions, an applicant's race might influence their access to test preparation resources (potentially unfair) but also their lived experience (potentially fair context). Path-specific counterfactuals isolate the discriminatory effect from the legitimate signal.

Causal fairness directly addresses statistical paradoxes that confound observational metrics. Simpson's Paradox occurs when a trend appears in several groups of data but disappears or reverses when the groups are combined. For instance, a university may show no gender bias overall, but exhibit significant bias within each department. Causal graphs explicitly model the confounding variable (department choice) and its relationship to both gender and admission, preventing misleading fairness conclusions drawn from aggregated data.

A specific causal fairness test proposed by Kilbertus et al. (2017). A predictor satisfies this criterion if it does not use any descendant of the protected attribute in the causal graph that is also a proxy for that attribute. For example, if 'zip code' is a descendant of 'race' in the causal graph and serves as a proxy for it, a fair model must not use zip code in its decision function. This formalizes the legal concept of disparate impact through causal reasoning.

A rigorous definition stating that a decision is fair if it would remain the same in the closest possible world where an individual belonged to a different demographic group, given all other causally relevant factors. Formally: P(Ŷ_{A←a} = y | X=x, A=a) = P(Ŷ_{A←a'} = y | X=x, A=a). This requires computing three-step abduction-action-prediction counterfactuals, making it computationally intensive but philosophically robust for high-stakes decisions.

A diagnostic tool for causal fairness analysis. A fairness map plots the direct, indirect, and spurious effects of a protected attribute on a decision outcome. - Direct effect: The attribute's influence not mediated by any other variable - Indirect effect: Influence through mediating variables - Spurious effect: Non-causal association due to confounding This decomposition allows governance teams to visually identify which causal channels require mitigation.

A causal fairness technique that decomposes the total effect of a protected attribute on a decision into distinct causal pathways, allowing modelers to eliminate discriminatory effects while preserving legitimate ones.

• Direct discrimination: The causal path directly from protected attribute to outcome
• Indirect discrimination: Paths mediated through redlining variables like zip code
• Explained influence: Legitimate paths through job-relevant qualifications
• Enables fine-grained fairness interventions without sacrificing all predictive power

A subfield integrating fairness definitions directly into the model training, evaluation, and selection processes to produce non-discriminatory outcomes.

• Pre-processing: Transform training data to remove causal dependencies on protected attributes
• In-processing: Add fairness constraints or regularization terms to the loss function
• Post-processing: Adjust decision thresholds per group to satisfy causal fairness criteria
• Causal approaches in this domain use SCMs to identify which variables require adjustment

A fairness criterion requiring a classifier to achieve equal true positive rates and equal false positive rates across different protected groups.

• Mathematically: P(Ŷ=1|Y=y, A=a) = P(Ŷ=1|Y=y, A=b) for all y, a, b
• Unlike causal fairness, this is an observational metric that does not distinguish between direct and indirect discrimination
• May encode proxy discrimination if legitimate features are correlated with protected attributes
• Often compared against causal approaches to highlight limitations of associational fairness

The ability to provide a negatively impacted individual with actionable, feasible steps they can take to reverse an unfavorable automated decision.

• Causal models identify which features an individual can actually change to flip a decision
• Contrasts with purely correlational explanations that may suggest immutable or causally irrelevant changes
• Example: A causal recourse model tells a denied applicant to increase their credit score, not to change their zip code
• Connects causal fairness to individual-level justice and agency