This supplemental material section contains a robustness analysis where we examined the posterior estimate's sensitivity to choice of priors. In addition, we include a number of tables and figures to supplement our report. RobustnessWe examined the robustness of our Bayesian model by checking the extent to which our marginal posterior estimates depend on the specification of prior distribution parameters. Specifically, we re-estimated the model using significantly more diffuse normally distributed prior distributions by increasing the variance parameter by a factor of 100 in equations 10 to 14. We again ran the sampler in WinBUGS using the same MCMC specifications and computed marginal posterior estimates. Marginal posterior estimates are depicted in Figures

A frequent problem with classic first digit applications of Benford’s law is the law’s inapplicability to clustered data, which becomes especially problematic for analyzing election data. This study offers a novel adaptation of Benford’s law by performing a first digit analysis after converting vote counts from election data to base 3 (referred to throughout the paper as 1-BL 3), spreading out the data and thus rendering the law significantly more useful. We test the efficacy of our approach on synthetic election data using discrete Weibull modeling, finding in many cases that election data often conforms to 1-BL 3. Lastly, we apply 1-BL 3 analysis to selected states from the 2004 US Presidential election to detect potential statistical anomalies.