Learning-to-Defer Inference for Computer Agriculture Irrigation Advisories Under Conflicting Human-Agent Competence: An Artificial Intelligence Deferral-Regret Evaluation

Irrigation advisories generated by artificial intelligence agents are increasingly paired with farmer judgement, yet the two sources of competence are rarely aligned: the agent may be better informed about soil-moisture dynamics while the farmer is better informed about local water availability, crop condition and institutional constraints. the present analysis formalises the resulting decision problem as a learning-to-defer inference task in which a deferral policy routes each advisory instance either to the agent or to the human expert, and it evaluates the policy through a deferral-regret criterion rather than through predictive accuracy alone. The analysis is theoretical and methodological: no observational data are used or claimed. A before-after-control-impact design is characterised under a declared variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, and power is estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design requires 54 clusters to detect a 5-percentage-point effect at 80 per cent power. The paper derives a deferral-regret decomposition that separates the regret attributable to agent error from the regret attributable to human error and from the regret attributable to misrouted deferral, and it shows that the three components have different sample-size requirements. The contribution is a formal criterion and an evaluation design for deferral policies in irrigation advisory systems, together with the boundary conditions under which deferral improves on either agent-only or human-only advice.