Counterfactual Explanation Stability Audits for Artificial Intelligence Agriculture Fertilizer Recommenders Under Soil-Test Sampling Density: An Interpretability Actionability Bound for Smallholder Nutrient Budgeting

Counterfactual explanations are increasingly proposed as the interface through which smallholder farmers and extension agents could act on artificial intelligence (AI) fertiliser recommendations, yet the stability of those explanations under realistic soil-test sampling densities has not been characterised. The audit is framed as a before-after-control-impact design in which the intervention is a change in sampling density and the outcome is the probability that a farmer acting on a counterfactual recommendation achieves the predicted nutrient-budget improvement. Operating characteristics were characterised under a declared variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 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.52 clusters are required to detect a 5 percentage point effect at 80 percent power, and that below this threshold the counterfactual explanation set is not stable enough to support field-level nutrient budgeting. The bound formalises the sampling density below which counterfactual explanations should be withheld from advisory use, and it reframes interpretability in AI agriculture as a property of the sampling design rather than of the model alone.