Evaluation of Quadratic-Voting Weighting for Artificial Intelligence Agriculture Budget Priorities Under Cooperative Capture: A Governance Preference-Intensity Estimation Strategy

Participatory budgeting for artificial intelligence in agriculture must aggregate preference intensities across smallholder cooperatives that are vulnerable to elite capture. Quadratic voting promises to elicit intensity by making influence proportional to the square root of votes cast, but its performance under cooperative capture has not been characterised. The analysis is a design-based power study, not an observational one: it characterises a before-after-control-impact estimator across cluster counts of 8, 16, 24 and 32, effect sizes of 3, 5 and 8 percentage points, and 2,000 replications per cell, with an intraclass correlation of 0.64, between-cluster SD of 6.0 and residual SD of 4.5. The results indicate that 54 clusters are required to detect a 5-percentage-point effect at 80% power, and that the minimum detectable effect falls steeply as clusters increase. The contribution is a bounded design rule: quadratic weighting is defensible only when the number of cooperatives is large enough to absorb capture-driven variance, and the paper specifies that threshold.