Counterfactual Fairness

Unlike statistical fairness metrics, counterfactual fairness is grounded in structural causal models (SCMs). It requires explicitly modeling the causal relationships between variables, distinguishing between legitimate explanatory factors (e.g., work experience) and discriminatory pathways (e.g., race). A decision is fair if it is not a function of any descendant of the protected attribute in the causal graph.

This metric provides a strong, individual-level fairness guarantee rather than an average group-level one. It asks: "Would this specific person have received the same outcome if their race or gender were different, all else being equal?" This contrasts with demographic parity, which only equalizes outcomes across groups and can still be unfair to individuals within those groups.

Counterfactual fairness explicitly addresses proxy discrimination. A naive model denied access to race might use zip code as a proxy, leading to red-lining. A counterfactually fair model, however, must adjust for the causal effect of race on zip code. It isolates the non-discriminatory signal (e.g., local property taxes affecting credit) from the discriminatory one, preventing indirect bias.

A common implementation uses latent variable models. The core assumption is that an individual's sensitive attributes and other features are generated by a set of unobserved, non-discriminatory latent variables (e.g., 'aptitude', 'socioeconomic background'). The model is trained to predict outcomes solely from these inferred latent variables, guaranteeing that the sensitive attribute has no direct causal path to the prediction.

This framework is tightly coupled with algorithmic recourse. For a decision to be fair, an individual must be able to identify actionable changes to their non-sensitive features that would alter the outcome. A counterfactual explanation provides this path: "Your loan would have been approved if your income were $5,000 higher." This makes fairness auditable and actionable for the end-user.

The primary vulnerability of counterfactual fairness is its reliance on the correct specification of the causal model. If the structural causal model is wrong—for instance, by omitting a confounder or misdirecting a causal arrow—the fairness guarantee is void. This shifts the auditing burden from the predictive model to the domain experts and causal assumptions used to build the SCM.

The overarching framework for defining fairness using causal inference and structural causal models (SCMs). It moves beyond statistical correlations to distinguish between discriminatory and legitimate causal pathways in a prediction. Counterfactual fairness is a specific, rigorous instantiation of this framework, requiring the formal specification of a causal graph to test whether a protected attribute has a direct causal effect on the outcome.

A fairness principle requiring that similar individuals receive similar predictions. It is formalized by defining a task-specific distance metric on the input space and a constraint on the output space. Counterfactual fairness is a causal refinement of this idea: it defines similarity not by observable features, but by an individual's identity in a counterfactual world where only their protected attribute has changed, isolating the causal effect of group membership.

A class of definitions that partition a population into groups defined by a protected attribute and require a statistical measure to be equal across them. Key metrics include:

• Demographic Parity: Equal positive prediction rates.
• Equalized Odds: Equal TPR and FPR.
• Equal Opportunity: Equal TPR only. Counterfactual fairness is fundamentally an individual-level criterion, but it can imply certain group-level statistical patterns depending on the causal model's structure.

A form of algorithmic bias where a non-protected feature, such as zip code or browsing history, serves as a stand-in for a protected attribute like race or gender. This allows disparate impact to occur indirectly, defeating naive interventions like 'fairness through unawareness.' Counterfactual fairness directly addresses this by modeling the causal structure, explicitly identifying and blocking the use of variables that are descendants of the protected attribute in the causal graph.

The ability for an individual negatively affected by an algorithmic decision to understand the reasons and take actionable steps to reverse that decision in the future. Counterfactual explanations are the primary technical tool for providing recourse, generating the minimal set of changes to an individual's features that would flip a model's prediction. Counterfactual fairness ensures the recourse itself is not discriminatory.

The mathematical engine behind counterfactual fairness. An SCM defines a system of structural equations that describe how each variable in a domain is causally generated by its direct causes and an independent noise term. This allows for the computation of three layers of causal reasoning:

• Association (seeing)
• Intervention (doing)
• Counterfactuals (imagining) The SCM's noise terms represent an individual's unique, unobserved characteristics, which are held constant when computing a counterfactual.