The forensics of fraud: Evidence from the 2018 Brazilian presidential election

OBJECTIVE: This paper studies the integrity of the vote counting system in Brazil. METHOD: We analyze data from the Superior Electoral Court (TSE) for the 2018 Brazilian presidential election to assess suspicious vote count patterns deploying five techniques commonly used to detect fraud: a) the second-digit Benford's law test; b) the last digit mean; c) frequency analysis of last digits 0 and 5; d) correlation between the percentage of votes and the turnout rate; and e) resampled Kernel density of the proportion of votes. RESULTS: The results show that the second-digit distributions for the three most voted candidates – Jair Messias Bolsonaro (PSL), Fernando Haddad (PT), and Ciro Gomes (PDT) – conform to Benford's law. We also find that last digit means and last digit frequency are within normal parameters, indicating no irregularities. Similarly, the fingerprint plot indicates a correlation coefficient that is consistent with the theoretical expectation of a fair election. The resampled Kernel density suggests that the vote count was performed without statistically significant distortions. These results are robust at different levels of data aggregation (polling station and municipality). CONCLUSION: The joint application of digit-focused tests, regression-based techniques, and patterns in the distribution of vote-shares provide a more reliable method for detecting anomalous cases. Relying on this unified framework, we find no evidence of electoral fraud in the 2018 Brazilian presidential election. These results advance our current understanding of statistical forensics tools and may be easily replicated to examine electoral integrity in other countries.