We present new developments sparked by the positive empirical model of election frauds introduced by Klimek, et al. (PNAS 2012). Taking a censored-Normal finite mixture likelihood implementation of Klimek et al.’s idea (Mebane, MPSA 2016) as a point of departure, we develop a variation of the model for which we estimate parameters using a Bayesian MCMC algorithm. The variation uses functional forms somewhat more familiar to political scientists than those used in the Klimek conception: e.g., logistic-binomial models for turnout and votes instead of censored Normal distributions. We consider the effect that introducing covariates to condition the means of turnout and of leading party vote share has on the performance and interpretability of the models. We assess the performance of the logistic model using simulated data in Monte Carlo sampling experiments. We apply both the Normal and logistic models to data from presidential elections in Brazil, the United States (California) and Kenya. The logistic model’s performance is promising, except for a problem with inferior multiple posterior modes. In the applications to real data the results from the logistic model are similar to results from the Normal likelihood model.