The theme of this text is delicate and dangerous to such an extent that it has become one of the taboos of our society. We are not talking about hunger, as Josué de Castro did in the preface to his main book. We are talking about the delicacy of the only government regime capable of resolving conflicts without the need for physical violence: democracy.
According to Our World in Data, 7 out of 10 people live in autocratic systems, that is, where it is not possible to choose political representatives from free and fair elections. In this article, we argue that the 2022 Brazilian presidential elections were neither free nor fair. There is robust evidence that the presidential candidate, Jair Bolsonaro, used government institutions politically and abused economic power in order to obtain electoral gains, in addition to having intentionally degraded the population’s confidence in the vote tabulation system. The deliberate attempt to corrupt the electoral process took place on some fronts, let’s get to them:
On October 29, Silvinei Vasques, then director of the Federal Highway Police (PRF), asked for votes for Bolsonaro on social networks. The following day, the PRF launched 549 vehicle inspection operations throughout the national territory, which represents a 70% increase in relation to the first shift. During the approaches, 610 public transport vehicles were stopped, contrary to the order of the Superior Electoral Court, which prohibited actions capable of obstructing the movement of voters. Interestingly, most of the operations took place in the Northeast, the main electoral stronghold of the Workers’ Party (PT) and the only region in which Lula received more votes than his opponent. Here we have the first stab against the notion of free and fair elections since there are objective records of the political use of the PRF to suppress votes against Lula.
A few months before the elections, Bolsonaro sanctioned Proposal for Amendment to the Constitution No. 15/2022, which increased social spending during the election year, as well as expanded the letter of payroll-deductible credit for Auxílio Brasil beneficiaries. That’s exactly what you just read: the Constitution was amended to make it legal to distribute money during the election period. Here we have the second strike against the idea of a free and fair dispute.
In addition, Bolsonaro tried to undermine the population’s confidence in the integrity of the digital vote counting system. According to him, and most of his followers, electronic voting machines are subject to fraud. These speeches have been repeated over and over for the past four years. In numbers: there were 18 public speeches about electoral fraud and distrust of electronic voting machines, as shown by our survey. However, neither the TCU nor the OAB found evidence of irregularities. Even the long-awaited Armed Forces report was unable to identify any anomalies.
Below, we report the results of an ongoing survey on voter fraud. Our analysis is based on a fundamental assumption: the intentional manipulation of votes leaves traces that can be detected through statistical analysis. That is, the accomplices of electoral fraud fail to forge results that appear to be the product of the free and spontaneous exercise of suffrage. Following the best international methodological practices, we employed five different procedures. Image 1 illustrates two of them, using Newcomb-Benford law and the fingerprint graph as techniques. The first technique analyzes the relative frequencies of the second digits observed in the total vote count, while the second tool compares the relationship between the voter turnout rate and the proportion of valid votes for the winning candidate.
One way to find suspicious statistical patterns is to examine how often certain digits of the vote count are repeated across municipalities or sections for a given candidate. In fair elections, the values of the first, second and last digits of the accumulated votes tend to follow a predictable distribution. According to the Newcomb-Benford Law, in a set of spontaneous numbers, it is more likely that the first digits (1, 2, 3, etc.) appear more often than the last ones.
This mathematical curiosity was originally discovered by the astronomer Simon Newcomb when leafing through a book of table of logarithms, he observed that the initial leaves were significantly more worn than the final ones. This numerical regularity was rediscovered by Frank Benford in an article published in 1938. In it, Benford calculated the expected frequency of digits from a wide variety of data distributions and demonstrated that we were indeed dealing with a law: smaller digits appear more often than larger digits. From then on, this procedure began to be used to detect suspicious patterns in data.
Figures 1 and 2, for example, demonstrate that the frequency of the second digit (illustrated by the bars) approaches the expected pattern (represented by the red line) for the best voted candidates. This correspondence between what is observed and what is expected increases confidence in the fairness of the electoral process. The techniques that focus on the first and last digit also did not detect anomalies.
Another procedure is to analyze the relationship between the percentage of voters present and the proportion of votes for the winning candidate. Under free and fair elections, the theory holds that there should be no voting dominance of a winning candidate garnering the vote of everyone present. This is because, assuming that abstention should vary more or less evenly between polling stations, the expectation is that the vote for a given candidate will be independent of the turnout rate. The fingerprint graph is a tool that shows this type of trend through the accumulation of points in the upper right corner. If this happens, it may be a sign of manipulation of the electoral result, since the votes of absentee voters would be artificially transferred to the winning candidate. We did not find any minimally suspicious patterns (see figure 3).
Forensic electoral analysis is a recent field of study and faces some challenges. It is known, for example, that strategic voting produces statistical anomalies that can be easily confused with deliberate attempts to tamper with the vote count. With that in mind, we employed different investigation techniques in order to increase the reliability of the results. It is one thing to corrupt the vote tally by obeying a known mathematical regularity, such as Benford’s Law, for example. It’s another thing to be able to circumvent the system in compliance with multiple statistical tests in an extremely short time span, about three hours. Something that would only be possible in a fictional universe like “The Paper House” or “Mission Impossible”. Furthermore, the public availability of data and computational codes ensure the transparency and replicability of our study. Thus, anyone can corroborate or refute our inferences with minimal logistical effort.
In summary: we found no traces of fraud in the electoral results of the 2022 presidential race. None of our forensic investigation procedures corroborate the thesis that the votes were manipulated. The Michaelis dictionary defines myth as a fantastic story that cannot be proven, usually starring supernatural beings. The mythical candidate, now defeated, seems not to have understood that his magical fable has come to an end.
Coauthors: Cláucia Piccoli Faganello (PUC-RS); Pedro Cardoso Saraiva Marques (UFPE); Nelson Goular (UENF); Quemuel Baruque de Freitas Rodrigues (UFPE); Bernardo Rangel Tura (INC-MS); Renato Lira Brito (UFPE); Artur Quirino (UFMG); Lucas Silva (UNCISAL); Ananda Marques (UFPI/ESPMA); Hesaú Rômulo (UnB/UFT); Ana Carol Aldapi Vaquera (UFPB).
With a wealth of experience honed over 4+ years in journalism, I bring a seasoned voice to the world of news. Currently, I work as a freelance writer and editor, always seeking new opportunities to tell compelling stories in the field of world news.
