Causal Fairness

The mathematical backbone of causal fairness. An SCM is a triple (U, V, F) defining exogenous variables (U), endogenous variables (V), and structural equations (F) that assign a causal mechanism to each variable.

• Nodes represent variables (e.g., education, hiring decision).
• Edges represent direct causal relationships.
• Exogenous variables capture unobserved background noise.

This graph allows auditors to explicitly encode assumptions about how the world works before testing for bias.

A prediction Ŷ is counterfactually fair if it would remain the same in the actual world and a counterfactual world where an individual's protected attribute (e.g., race) was different, but all other causally independent factors remain unchanged.

• Key Insight: It corrects for the 'red-lining' proxy problem.
• Requirement: A fully specified causal model to compute the intervention.
• Contrast: Unlike demographic parity, it allows legitimate statistical dependence through mediating variables like education if education is not itself a product of discrimination.

Not all causal paths from a protected attribute to an outcome are discriminatory. Path-specific fairness decomposes the total causal effect into fair and unfair pathways.

• Fair Path: A protected attribute influences a job-relevant skill, which legitimately influences hiring.
• Unfair Path: A protected attribute directly influences hiring via a biased interviewer (direct discrimination).
• Audit Logic: The goal is to nullify the effect along the unfair path while preserving the effect along the fair path, a technique known as path-specific counterfactual inference.

A core motivation for causal fairness is resolving statistical reversals. A model might appear fair in aggregate but be discriminatory in every sub-group, or vice versa.

• Example: A university admissions model might show no gender bias overall, but causal analysis reveals bias against women applying to competitive departments and against men applying to less competitive ones.
• Causal Solution: By conditioning on the correct confounders (applicant qualifications) and analyzing the direct effect of gender, the paradox is resolved, revealing the true discriminatory structure.

A formal causal fairness definition proposed by Kilbertus et al. It states that there should be no directed path from a protected attribute to the outcome, except via a resolving variable.

• Resolving Variable: A feature that society explicitly accepts as a legitimate basis for differential treatment (e.g., physical strength for a firefighter role).
• Audit Process: The auditor specifies the resolving variables. The model is fair if the protected attribute's influence is fully mediated by these variables, blocking all other back-door or direct paths.

A critical distinction in auditing. Observational criteria (like Demographic Parity) only look at data correlations. Causal criteria look at mechanisms.

• Observational: 'Are loan rates equal across groups?' (Can be fooled by proxy variables).
• Counterfactual: 'Would this specific applicant have received the loan if they were of a different race, holding all else equal?'
• Power: Causal reasoning allows for individual-level recourse and justification, whereas observational methods only guarantee group-level statistical properties.

A form of algorithmic bias where a non-protected feature, such as zip code or browser type, serves as a stand-in for a protected attribute like race. Causal graphs are essential for identifying and blocking these indirect discriminatory pathways.

• Redlining is a classic historical example
• Fairness through unawareness fails to prevent it
• Causal mediation analysis can quantify the proxy effect

A legal doctrine and quantitative metric identifying facially neutral practices that disproportionately harm a protected group. Often measured by the 80% rule: the selection rate for a disadvantaged group must be at least 80% of the rate for the advantaged group.

• Focuses on outcomes, not intent
• Does not distinguish between legitimate and illegitimate causal pathways
• Causal fairness decomposes disparate impact into explainable components

A separation-based fairness metric requiring a classifier to have equal True Positive Rates (TPR) and equal False Positive Rates (FPR) across sensitive groups. This ensures errors are distributed equally, but can clash with calibration when base rates differ.

• Mathematically: P(Ŷ=1|Y=y, A=a) = P(Ŷ=1|Y=y, A=b)
• Enforces equality of opportunity for both qualified and unqualified individuals
• Causal fairness often relaxes this to focus on specific causal pathways

A paradigm examining bias against subgroups defined by the combination of multiple protected attributes, such as Black women, rather than treating race and gender in isolation. Causal models can capture the complex interactions between multiple sensitive nodes.

• Aggregate group fairness can mask severe intersectional harms
• Requires sufficient data for statistically powered subgroup analysis
• Multicalibration is a leading technical framework to address this

The ability for an individual negatively affected by an algorithmic decision to understand the reasons and take actionable steps to reverse that decision. Causal fairness is foundational here, as it identifies which features an individual can actually change to flip a prediction.

• Contrastive explanations: 'You were denied because X. If you change Y, you will be approved.'
• Requires distinguishing mutable features from immutable ones
• Actionable recourse is the practical application of counterfactual generation