Evaluation of Label-Differential-Privacy Calibration for Artificial Intelligence Agriculture Cooperative Yield Registers Under District Vote-Mobilization Targeting: A Governance Re-Identification-Risk Bound for Smallholder Privacy

Agricultural cooperatives increasingly pool smallholder yield records into registers that artificial intelligence systems use for input targeting and advisory allocation, and district-level political actors have strong incentives to re-identify individual plots for vote-mobilization purposes. Label differential privacy (label-DP) has been proposed as a calibration mechanism for such registers, but its governance properties under adversarial targeting remain uncharacterised. The analysis characterises the estimator under a declared variance structure with between-cluster standard deviation of 6.0, residual standard deviation of 4.5, and intraclass correlation of 0.64, across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design analysis indicates that 54 clusters are required to detect a 5-percentage-point effect at 80 per cent power under this variance structure. Label-DP calibration alone cannot bound re-identification risk when the adversary holds district-level auxiliary information, and that a governance bound must incorporate the auxiliary-information advantage of the targeting actor. The contribution is a formal bound that makes the privacy-governance trade-off explicit and a design-analysis protocol that specifies the cluster counts at which the bound can be credibly evaluated.