Differential-Privacy Evaluation for Computer Agriculture Cooperative Yield Aggregation Under Smallholder Re-Identification Risk: An Artificial Intelligence Membership-Inference Audit

Cooperative yield aggregation is the standard route by which smallholder harvests become the training data of agricultural artificial intelligence, yet the privacy guarantees attached to those aggregates are rarely audited against the re-identification risk that smallholder membership actually carries. the present analysis treats the differential-privacy budget as a design parameter of a membership-inference audit and characterises, analytically and by replication, how the before-after-control-impact estimator behaves when the privacy mechanism is layered onto cooperative-level aggregation. The analysis is a design study: no observational data are used or claimed. Under a declared variance structure with between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.640, power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effects of 3, 5 and 8 percentage points. The design requires 54 clusters to detect a 5-percentage-point effect at 80% power, a requirement that exceeds every cluster count examined and that the differential-privacy mechanism can only worsen by inflating residual variance. The contribution is a membership-inference audit protocol that reports the privacy budget, the intraclass correlation and the detectable effect jointly, so that a cooperative's disclosure claim is bounded by the same arithmetic that bounds its inferential claim.