Auditing for Demographic Bias in Opaque Rankings

Auditing algorithmic fairness is a critical challenge in high-stakes domains like hiring and credit scoring, especially given the intrinsic opacity of algorithmic decision-making systems. In this paper, we tackle the following problem: given a ranking of individuals, how can we assess whether the order is driven by protected attributes (e.g., gender or race) rather than task-relevant features, under a strict black-box assumption where the ranking mechanism cannot be queried? Building on kernel conditional independence and partial distance correlation, we introduce Condor, a model-agnostic audit framework. Condor first residualizes the ranking and protected attributes with respect to observables in a reproducing kernel Hilbert space. It then quantifies the remaining association via distance correlation on the residualized embeddings, returning a normalized effect-size score. This procedure captures general nonlinear dependencies without assuming access to latent scores, requires no hyperparameter fine-tuning, and naturally accommodates mixed continuous and categorical data. From Condor's effect-size score, we derive a hypothesis test for conditional independence. By combining this test with an unconditional independence test, auditors can achieve a comprehensive causal understanding of the protected attributes' influence. We validate our proposal on real and semi-synthetic datasets with controlled influence of the protected attributes on the ranking: our method reliably detects the influence of protected attributes, outperforming established statistical auditing baselines.