Detecting election Fraud from irregularities in vote-share distributions

I develop a novel method to detect election fraud from irregular patterns in the distribution of vote-shares. I build on a widely discussed observation that in some elections where fraud allegations abound, suspiciously many polling stations return coarse vote-shares (e.g., 0.50, 0.60, 0.75) for the ruling party, which seems highly implausible in large electorates. Using analytical results and simulations, I showthat sheer frequency of such coarse vote-shares is entirely plausible due to simple numeric laws and does not by itself constitute evidence of fraud. To avoid false positive errors in fraud detection, I propose a resampled kernel density method (RKD) to measure whether the coarse vote-shares occur too frequently to raise a statistically qualified suspicion of fraud. I illustrate the method on election data from Russia and Canada as well as simulated data. A software package is provided for an easy implementation of the method.