Causal and Counterfactual Fairness

Graph, intervention, counterfactual, path judgment, identification. The first four are assumptions. The fifth asks whether the data can support any of them.

A sensitive attribute often reaches a decision along two kinds of route at once. Some of those routes the team considers fair, some it does not. Chiappa formalised that case in 2019 and called it path-specific counterfactual fairness. The paper opens on exactly the situation the path judgment node names: “We consider the problem of learning fair decision systems from data in which a sensitive attribute might affect the decision along both fair and unfair pathways.” Her method then corrects only the observations affected along the unfair pathways.

Somebody had to declare which pathways those were, before any estimation began. The split is the input to the method, not its output.

Build the graph with domain experts and affected people in the room, then test whether the data can identify the effect that graph implies.

For a salary team in the European Union, step 1 and step 5 have stopped being discretionary. Three conditions, holding together, oblige an employer to run a joint pay assessment with its workers' representatives. The pay reporting shows a difference in average pay level between female and male workers of at least 5 % in some category of workers. The employer “has not justified such a difference in the average pay level on the basis of objective, gender-neutral criteria”. And six months have passed since the pay reporting was submitted, unremedied. That duty is Article 10(1) of Directive (EU) 2023/970.

That is step 1 written into statute: the decision question is whether an objective, gender-neutral explanation for the difference exists. It is also step 5 with a clock attached. Nobody decides to open the assessment. The rule opens it.

The reach of that kind of duty is widening. Private-sector gender pay gap reporting is mandatory in 21 of 38 OECD countries — 55 %, unchanged since the 2023 stocktaking. By the end of 2026 it is expected to cover 32 of 38, or 84 %. The OECD's 2026 report Pay Transparency in Progress gives those figures, and names the EU directive as what is driving the expansion. A review that cannot say what its graph implies, and what it would take to move the conclusion, will meet that deadline with nothing to submit.

A credit model was trained with gender deliberately left out of the data, so that men and women with identical features receive identical predictions. On a toggle test that model scores perfectly. There is no gender field left in it to flip.

That experiment has been run. An L2-penalised logistic regression, a processed german credit dataset of 1,000 individuals and 26 features, gender withheld. Ustun and colleagues built it in 2019, then measured what it would cost a person to change the decision. Their finding was that “the cost of recourse can differ between males and females even when models ignore gender”.

Identical predictions for identical feature vectors, and a different price for the same outcome at comparable predicted risk. The invariance a toggle demonstrates and the fairness a team wants to claim are two different properties. The first is compatible with the failure of the second.

Causal fairness asks how protected attributes, social processes, mediators, decisions and outcomes relate under explicit assumptions. A counterfactual claim needs a structural model behind it. Changing a field in a row is not the same as intervening on the world that produced the row. The methods — causal graphs, counterfactual fairness, path-specific analysis, mediation, causal recourse — earn their place by making assumptions and mechanisms visible. They turn fragile as soon as the graph, the latent variables or the intervention semantics are disputed.

In aggregate, Berkeley's 1973 graduate admissions data showed a clear pattern of bias against women. Pooling that respected departmental autonomy reversed the sign. Bickel and colleagues reported it in Science in 1975, and put the mechanism upstream of the committees being audited: “The bias in the aggregated data stems not from any pattern of discrimination on the part of admissions committees, which seem quite fair on the whole, but apparently from prior screening at earlier levels of the educational system.” Department was the variable the disparity ran through. Job level is its analogue in a pay model.

That is what makes the row edit a different operation from the intervention. Flipping the applicant's sex while leaving the department of application standing edits the one field and preserves the mediator that the field's real history produced. The person so constructed did not go through prior screening at earlier levels of the educational system. The person in the row did.

An associational audit measures what co-occurs. It needs fewer causal assumptions, it is useful for disparity detection such as error rates by group, and it cannot establish the mechanism alone. A causal analysis models what an intervention would do. Counterfactual recourse asks what this particular person could change. Each of the last two has a published result marking a limit the column headings only gesture at.

Causal analysis first. Both families of causal fairness definitions almost always yield strongly Pareto-dominated policies — Nilforoshan and colleagues proved that in 2022. One result is sharper still: “under a prominent definition of causal fairness, we prove the resulting policies require admitting all students with the same probability, regardless of academic qualifications or group membership”. A definition that forces a lottery is not fragile in some vague sense. It has a proved consequence. A team that adopts the definition adopts the consequence with it.

Then recourse. A nearest counterfactual explanation is not a recommendable set of actions, Karimi and colleagues argued in 2021, on causal grounds: “counterfactual explanations inform an individual where they need to get to, but not how to get there”. Their proposal is to replace recourse-by-counterfactual-explanation with recourse through minimal interventions — the route, not just the destination. That is the difference between telling someone which feature vector would have been approved and telling them something they can do.

Causal conclusions rest on a graph somebody drew. So publish the graph, the structures that were considered instead, and how far the conclusion moves when the assumptions change. The 2017 paper calls the counterfactual assumptions behind such a graph “in general unfalsifiable”. When the data cannot settle an assumption, writing it down where somebody else can argue with it is the only accountability left.

Then define when the analysis requires the team to redesign, restrict, remedy or retire the system. Where Directive (EU) 2023/970 applies, one such trigger is already fixed for you. A difference in average pay level of at least 5 % in a category of workers, unjustified on objective, gender-neutral criteria and unremedied after six months, obliges the joint pay assessment under Article 10(1). It fires whether the team's own thresholds would have fired or not.