Evaluation of Differential Privacy Budget Allocation for Artificial Intelligence Agriculture Yield-Prediction Models Under Cooperative Data-Sharing Consortia: A Governance Privacy-Utility Bound for Smallholder Participation

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Cooperative data-sharing consortia that pool smallholder yield records to train artificial intelligence (AI) prediction models face a governance problem that is not resolved by technical privacy guarantees alone: the allocation of a differential privacy budget across participating districts determines both the statistical utility of the resulting model and the distribution of privacy protection among members. The analysis is theoretical and methodological. It formalises the consortium as a federated learning arrangement in which a central curator allocates a total privacy budget across contributing units, and it derives the utility loss of the pooled yield predictor as a function of the per-unit budget, the number of contributing units, and the heterogeneity of yield distributions across units. The central result is a bound showing that equal per-unit budget allocation is utility-optimal only when units are homogeneous in sample size and yield variance; when they are not, equal allocation produces a privacy-utility frontier that is dominated by a size-weighted allocation rule. The paper further shows that the governance choice of allocation rule, not the choice of privacy mechanism, is the binding constraint on smallholder participation, because smallholders in heterogeneous districts face the largest utility penalty under equal allocation and therefore the strongest incentive to withdraw. The contribution is a governance privacy-utility bound that connects differential privacy budget allocation to participation incentives in cooperative agricultural data consortia, and a set of allocation principles that consortium designers can apply without access to the underlying data.

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