ABSTRACT
The goal of this paper is to verify the applicability of Newcomb-Benford Law for the Second Digit on elections auditing, through an empirical analytic and descriptive study, having as the background the analysis of the election for President of Brazil in the year 2006. Back in 1881, astronomer and mathematician Simon Newcomb, observed in experimental measurements, that the most significant digits (the ones most to the left), didn’t have their quantities equally distributed between 1 and 9. Around 30% of those numbers started with digit 1, and lowering gradually until gets to digit 9 with only 4,6% of occurrence. In 1938, such a phenomenon was checked independently by physicist Frank Benford. Such observations caught attention of the scientific community, because they contradicted common sense at the time. Therefore, Newcomb-Benford Law was created. Step-by-step, scholars noticed its power to detect frauds in groups of numbers. By the end of the 20th century, Newcomb-Benford Law started to be put in use successfully in financial and accounting audits. Recently it was used in election audits in the United States, Mexico, Venezuela and Iran. Due to its unique characteristics, Brazilian bibliography is almost non-existent on this field of research. This way, it was necessary to make some adaptations on methodologies already used in other countries to the Brazilian case. The data used on this paper was provided by the Tribunal Superior Eleitoral –TSE, Brazilian highest electoral court of law. It consisted on the total of votes of all of the 3034 electoral zones scattered throughout the country and overseas to the candidates for Brazilian presidency in 2006. Since Newcomb-Benford law can be divided into two parts, Law of the First Digit and Law of the Second Digit, for each of these situations, it was taken a different hypothesis test, using Z-test statistics, Qui-square, and FDR criterion for false positives, with significance level α = 0,05. This way, there’s the probability of 95% to make the right decision. Nevertheless, as predicted on the researched bibliography, the results found were only favorable to the Law of the Second Digit, because all of the 99 test statistics that were made none had exceeded their correspondent general critical value. On the other side, when the Law of First Digit was concerned, among all 90 tests made, 22 kept out of the pre-established parameters. It was concluded that the Law of Newcomb-Benford for the Second Digit can be used to search for frauds while auditing Brazilian electoral system, therefore, assisting in the maintenance of democracy.
Keywords: Newcomb-Benford Law. Election Audits. Election Fraud. FDR Criterion.
Download the paper here: Monografia
Francisco Alves Júnior 