When Redundant Probes Help in Strategic Auditing

Audits often favor diverse probes to cover a broad range of failures. We study when this choice helps against a strategic agent that knows the audit policy and chooses an exploit to maximize expected payoff. In a geometric model, we compare two randomized audits: uniform sampling of probes, and volume-weighted sampling, which draws probe subsets with probability proportional to the volume they span, so near-duplicate probes are rarely selected together (a determinantal point process). When probes cluster around a dominant subspace, volume weighting improves protection against exploits in that subspace. Uniform sampling can perform better against exploits in weakly measured residual directions: differences between near-duplicate probes provide coverage that volume weighting tends to suppress. We derive the limiting average residual coverage and observe a crossover between policies in synthetic experiments. The uniform policy's payoff advantage is small despite a larger coverage ratio, and declines as regularization attenuates weak probe differences. These results identify a trade-off between diversity and residual coverage and motivate an audit-selection heuristic based on exploit geometry.