Fairness Auditing: Lower Bounds on Company Manipulation
Fairness audits are increasingly mandated in high-stakes applications such as hiring, lending, and automated decision-making. Recent work has established fundamental impossibility results for black-box fairness auditing, showing that sufficiently expressive models can evade any auditing strategy. We complement these results by quantifying the extent of unavoidable post-audit manipulation under finite audit resources. We formulate fairness auditing as a min-max optimization between a computationally unbounded company and a budget-constrained auditor. We study two auditing regimes: (i) a budgeted auditor that certifies fairness using a fixed-size audit set, and (ii) a budgeted {\alpha}-tolerant auditor that additionally requires the audit set to estimate the fairness of the certified model within an {\alpha} approximation. For both settings, we derive explicit lower bounds on the worst-case post-audit demographic parity deviation as functions of the audit budget, group imbalance, and fairness tolerance. Finally, we empirically illustrate these theoretical limits using simple audit-set construction heuristics with linear and neural network classifiers. Our results demonstrate that increasing audit resources reduces, but does not eliminate, the scope for post-audit manipulation, highlighting fundamental limitations of finite-budget fairness certification.