Evaluation of Differentially Private Query Mechanisms for Artificial Intelligence Agriculture Subsidy Registries Under Village-Level Income Verification Gaps: A Governance Disclosure-Risk Bound for Beneficiary Privacy

Artificial intelligence agriculture subsidy registries increasingly rely on village-level income verification, yet verification gaps create a disclosure-risk problem that differential privacy mechanisms are meant to address. the present analysis evaluates the governance implications of differentially private query mechanisms for such registries by characterising the disclosure-risk bound that emerges when verification coverage is incomplete. The analysis is a replication-based evaluation of the before-after-control-impact estimator under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with power estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The results indicate that 54 clusters are required for 5 percentage points at 80% power, and that the intraclass correlation of 0.64 substantially inflates the minimum detectable effect at small cluster counts. Differential privacy in subsidy registries is not a technical add-on but a governance instrument whose disclosure-risk bound is conditional on verification coverage, and that the bound tightens only when cluster-level design and privacy budget allocation are jointly specified. The contribution is a governance disclosure-risk bound that links privacy parameter choice to the institutional reality of village-level verification gaps.