We present new developments regarding positive empirical models of election frauds. We further develop the general framework for Bayesian estimation of finite mixture models of election frauds (models that include covariates) to support estimating the number of types of frauds. There can be no frauds, one type of fraud or two types. By allowing the dimensionality of the model to vary, fraud components that do not occur completely disappear from the model. We consider how to make statistical decisions about the presence of frauds based on loss functions and posterior predictive distributions of fraud magnitudes. We use the decision framework to compare the varying dimension approach to a fixed-dimensional approach in which the probablities of frauds can become small but always remain positive. Among transdimensional MCMC methods we use reversible jump MCMC but also consider nonparametric Bayes and path sampling methods. We use the model to investigate fraud in several settings, including Kenya and Brazil. Covariates to describe characteristics of voters and polling places are available in the case of Brazil.