Evaluation of Shapley-Value Attribution Audits for Artificial Intelligence Agriculture Budget Allocation Under Ministerial Discretion: A Governance Accountability Bound for Audit Trail Verifiability

The problem is that discretionary allocation of AI agriculture funds lacks an audit trail that can withstand ministerial override, because the Shapley value of a coalition of budget claimants is not uniquely determined once the characteristic function is itself a ministerial choice. The central result is a verifiability bound: the maximum probability that an auditor can detect a discretionary deviation from the Shapley benchmark is bounded above by a function of the minister's discretion set and the audit signal's precision. The bound is derived analytically and its operating characteristics are characterised through a replication-based design evaluation using a before-after-control-impact estimator with a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64). Power was estimated across 2000 design cells. At 54 clusters the design attains 80 per cent power to detect a 5 percentage point effect, and that the minimum detectable effect at 80 per cent power declines with cluster count. Shapley attribution audits are best understood not as a mechanism for eliminating ministerial discretion but as a mechanism for making the exercise of that discretion legible, and that the verifiability bound provides a defensible standard for audit design in AI agriculture governance.