Optimal Tax Enforcement with Fallible AI Auditors: False Positives, Deterrence, and Endogenous Precision

Tax administrations use predictive scores to select audits, but the number of audits is an equilibrium outcome rather than a direct measure of enforcement. We study a committed score-based policy with heterogeneous firms, binary tax evasion, bounded statutory penalties, and an extra resource cost when compliant firms are investigated. A power receiver-operating-characteristic technology separates the conditional audit risk faced by evaders from false-positive rates and aggregate audit volume. We prove threshold dominance within the score-only policy class and characterize a unique enforcement choice under a sufficient convexity condition. Higher false-positive costs reduce conditional deterrence, whereas higher administrative audit costs can strengthen it. Better information raises optimized cost-adjusted fiscal value, but audit volume, net treasury receipts, and resource surplus need not rise. A certified receipts decline reflects the authority accepting weaker deterrence to save external costs. A constructive open parameter region exhibits stronger deterrence, fewer audits, and higher resource surplus. Endogenous precision equates its marginal fiscal value with investment cost; comparative statics depend on the compliance regime. Seeded numerical exercises and counterexample searches document the limits of stronger claims. The analysis concerns screening errors, assumes accurate subsequent investigation, and distinguishes its fiscal objective from social welfare. This record is a non-peer-reviewed theoretical working paper. Generative AI and coding agents assisted literature discovery, coding, symbolic checks, numerical implementation, language editing, LaTeX preparation and internal review. Kun Huang retains full responsibility. All references were verified, and numerical results use executable illustrative models without private data. AI internal reviews are not human peer review.