Evaluation of Counterfactual Explanation Reachability for Artificial Intelligence Agriculture Herbicide-Advisory Systems Under Cost-Constrained Smallholder Budgets: An Interpretability Actionability Bound for Misapplication Harm

Counterfactual explanations are widely proposed as the interpretability mechanism that makes artificial intelligence herbicide-advisory systems actionable for smallholder farmers, yet their actionability depends on whether the recommended input change is affordable within the farmer's budget. the present analysis formalises counterfactual explanation reachability as a budget-constrained optimisation problem and derives an interpretability actionability bound that relates the probability of a reachable counterfactual to the cost distribution of recommended changes, the farmer's budget, and the number of counterfactuals generated. The analysis is theoretical and methodological: no observational data are used or claimed. The bound is derived analytically and its operating characteristics are characterised under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64) across a design grid of 8, 16, 24 and 32 clusters, effect sizes of 3, 5 and 8 percentage points, and 2000 replications per cell. The derived bound shows that reachability probability declines sharply as the cost of the recommended change approaches the budget, and that generating multiple counterfactuals raises reachability only logarithmically in the number of candidates. Interpretability evaluations for herbicide-advisory systems should report reachability alongside fidelity, and it specifies the design conditions under which an advisory system can be certified as actionability-safe for cost-constrained smallholders.