Differentially Private Soil Fertility Maps for Artificial Intelligence Agriculture Subsidy Targeting Under Village-Level Aggregation: A Reconstruction-Attack Risk Evaluation

Village-level soil fertility maps are increasingly proposed as the spatial substrate for artificial intelligence (AI) systems that target agricultural input subsidies, yet the aggregation unit that makes such maps administratively useful is also the unit at which differencing and reconstruction attacks become feasible. the present analysis formalises the reconstruction risk that arises when a differentially private fertility map is published at village resolution and an adversary holds auxiliary information from neighbouring villages or from successive publication rounds. It derives a bound on the number of villages whose fertility stratum can be recovered under (ε, δ)-differential privacy as a function of the privacy budget, the number of published marginals, and the auxiliary knowledge available to the adversary. The analysis is methodological and theoretical: no observational soil data are used or claimed. A replication-based evaluation of the before-after-control-impact estimator characterises the operating characteristics of the design 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 over 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 80% power at a 5 percentage point effect. Village-level publication of fertility maps requires a privacy budget that scales with the number of published marginals rather than with the number of villages alone, and it specifies the conditions under which a reconstruction-attack risk evaluation should precede deployment of AI subsidy-targeting systems.