Interdisciplinary Urban Sociology of Metropolitan Boda Boda Stage Allocation Lotteries and Rider Compliance in Nairobi's Transport Corridors: A Regression Discontinuity Analysis of Lottery Cutoffs

Municipal stage allocation lotteries for boda boda riders in Nairobi's transport corridors create sharp eligibility cutoffs that regression discontinuity designs can exploit, yet the operating characteristics of such designs remain unexamined for the clustered, small-sample conditions that characterise metropolitan transport governance. the present analysis characterises the before-after-control-impact estimator for cutoff-based stage allocation lotteries under a declared variance structure with between-cluster standard deviation of 6.0, residual standard deviation of 4.5, and intraclass correlation of 0.64. Power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24, and 32 and effect sizes of 3, 5, and 8 percentage points. The analysis indicates that 54 clusters are required to detect a 5 percentage point compliance effect at 80 percent power, a requirement that exceeds the number of transport corridors typically available for stage-level randomisation in Nairobi. Minimum detectable effects at 80 percent power decline steeply between 8 and 24 clusters before flattening, and the density of estimated power is bimodal at small cluster counts. The contribution is a design-based account of what cutoff-based lottery evaluations of rider compliance can and cannot identify under realistic clustering, with implications for how municipal transport authorities structure stage allocation lotteries to permit credible evaluation.