Counterfactual Fairness

A predictor Ŷ is counterfactually fair if, for any individual, the predicted outcome is the same in the actual world and in the closest possible world where their sensitive attribute A (e.g., race, gender) was changed. Formally: P(Ŷ_{A←a} = y | X=x, A=a) = P(Ŷ_{A←a'} = y | X=x, A=a). This definition, introduced by Kusner et al. (2017), explicitly relies on a Structural Causal Model (SCM) to compute the counterfactual query. It differs from observational fairness metrics by focusing on causal pathways rather than statistical parity.

Counterfactual fairness requires decomposing the causal graph into three distinct pathways from a sensitive attribute A to an outcome Y:

• Direct Discrimination: A causal path directly from A to Y.
• Red-Lining (Indirect Discrimination): A path from A to Y through a proxy variable (e.g., zip code) that is itself caused by A.
• Explained Variation: A path from A to Y through a resolving variable (e.g., qualification) that is not discriminatory. A fair predictor must eliminate the influence of the first two pathways while preserving the third.

Counterfactual fairness is a strict form of individual fairness, not a group-level metric. It guarantees that every single individual receives the same decision as their counterfactual self. This contrasts with group fairness criteria like Demographic Parity or Equalized Odds, which only enforce statistical constraints across populations. A model can satisfy group fairness while still being counterfactually unfair to specific individuals, making this causal definition a more granular and legally robust standard for high-stakes decisions.

Computing counterfactual fairness is impossible without a fully specified Structural Causal Model (SCM). The SCM consists of:

• Exogenous variables (U): Unobserved background factors representing an individual's unique characteristics.
• Endogenous variables (V): Observed features, including the sensitive attribute and outcome.
• Structural equations (F): Deterministic functions mapping causes to effects. The three-step process—Abduction (infer U), Action (intervene on A), and Prediction (compute Y)—is mandatory. This reliance on strong causal assumptions is both the method's greatest strength and its primary practical limitation.

Predictors can be categorized by their causal awareness:

• Level 1 (No Causality): Uses only non-descendants of A. Simple but may discard useful information.
• Level 2 (Partial Causality): Uses descendants of A that are not discriminatory proxies, requiring partial causal knowledge.
• Level 3 (Full Counterfactual): Uses all variables but applies the full SCM to compute the counterfactual distribution P(Ŷ_{A←a'}). Level 3 is the gold standard but demands a complete causal model. Level 1 is a safe, conservative fallback when causal knowledge is incomplete.

A nuanced variant that allows a sensitive attribute to influence the outcome through fair pathways while blocking unfair ones. For example, a university admission model might allow gender to influence admission through a 'chosen major' pathway (considered a legitimate choice) but block its influence through a 'biased recommendation letter' pathway. This is achieved by performing a path-specific intervention in the SCM, muting only the unfair causal edges while propagating the fair ones. This avoids the 'leveling down' problem of simpler fairness constraints.

The mathematical backbone required to compute counterfactual fairness. An SCM defines variables and their causal dependencies through structural equations, enabling the computation of interventional and counterfactual queries. Without a valid SCM, you cannot formally define the counterfactual world where a sensitive attribute like race or gender is altered while holding all other background variables constant. Key components:

• Exogenous variables (U): Unobserved background noise
• Endogenous variables (V): Observed nodes in the system
• Structural functions (F): Deterministic equations mapping causes to effects

A Directed Acyclic Graph (DAG) encoding the data scientist's assumptions about causal relationships. Nodes represent variables; directed edges represent direct causal influence. For counterfactual fairness, the graph must explicitly model how the sensitive attribute (A) causally affects both the decision (Ŷ) and other proxy features (X). If a feature like ZIP code is a descendant of race in the graph, it becomes a 'red-lining' proxy. The graph dictates which variables must be adjusted to compute the counterfactual.

A set of three inference rules developed by Judea Pearl for transforming expressions involving the do-operator into estimable statistical quantities from observational data. When a randomized controlled trial is impossible, do-calculus determines if a causal effect can be identified from the graph structure. For counterfactual fairness, it provides the mathematical machinery to estimate P(Ŷ_{A←a'} | X=x, A=a) — the probability of the decision in the counterfactual world.

The process of providing an end-user with actionable changes to flip a negative decision. Counterfactual fairness and recourse are deeply linked: a fair model should provide recourse that does not require changing an immutable, protected attribute. If the only way to get approved for a loan is to 'be older' or 'be a different gender,' the recourse is fundamentally unfair. Actionable recourse constrains recommendations to features the individual can realistically control.

A protected input attribute that cannot be changed and must be held constant when generating counterfactual explanations. In the fairness context, the sensitive attribute itself (race, gender, age) is the primary immutable feature. However, causal descendants of the sensitive attribute present a challenge: changing a mutable feature like 'education level' might be causally dependent on the immutable 'socioeconomic background,' requiring careful causal modeling to avoid penalizing the individual for their history.