Seed fair lotteries are widely used by Rwandan village cooperatives to allocate invitations to improved-variety demonstrations, yet the sociological question of how fair invitation thresholds shape adoption divergence among smallholders remains unresolved. The framework treats the lottery as an encouragement instrument, distinguishes compliers from always-takers and never-takers, and formalises the before-after-control-impact estimator that identifies the local average treatment effect of fair invitation thresholds. Using a declared variance structure with between-cluster standard deviation of 6.0, residual standard deviation of 4.5 and intraclass correlation of 0.64, the design was evaluated across 2000 replications per cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. Power was estimated for the before-after-control-impact interaction, and the minimum detectable effect at 80% power was derived for each cluster count. The design requires 54 clusters to detect a 5 percentage point effect at 80% power. The framework contributes a sociological specification of lottery-based encouragement that separates fair assignment from adoption behaviour, and it identifies the cluster counts at which adoption divergence becomes statistically visible in village cooperative settings.
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Uwamahoro et al. (2026) studied this question.
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