On August 1, 2024, the online newspaper El Mostrador published an opinion piece by Dr. Andrés Navas, an academic at the University of Santiago, Chile, entitled “Mathematical autopsy of Maduro's results: 99.99999% fraud.”
The text presented an arithmetic and probabilistic analysis that utilized figures to demonstrate how percentages were manipulated to match the number of votes cast, concluding that this numerical exercise in the Venezuelan elections would have been crude and traceable.
The study by Dr. Navas found the official vote figures to be suspiciously precise. As he explained in his column, with 10 million total votes, obtaining vote percentages exact to one decimal place requires vote counts that are precise multiples of ten thousand. Given that real-world vote percentages are usually approximate, this statistically negligible probability points to data manipulation.
While the researcher initially rushed to disseminate the information days before the Venezuelan election without peer review, he subsequently developed the work over the following weeks, which led to this formal publication.
To gain a deeper understanding of this interesting analysis from a mathematical perspective for addressing social context situations, we spoke with a distinguished professor from DMCC-Usach.
Professor Navas, what is the article published in Argentina about?
The scientific publication, titled "Election results and an elementary exercise in probability," is the formalized version of a column in El Mostrador that first presented the clear and well-justified observation of figure manipulation in the first vote count of the 2024 Venezuelan presidential election. Since the El Mostrador column lacked academic peer review, I developed the analysis into a more rigorous paper, which was later submitted to a journal managed by colleagues in Argentina.
How did the opportunity to publish in the Revista de Educación Matemática arise?
I had doubts when I published the article in the online newspaper, as it was the first time in my career that circumstances required me to disclose findings without prior peer review. I therefore decided to develop the work into a more formal academic paper. This provided a valuable discussion opportunity with the journal's advisors, who deemed it an atypical case and initiated a double peer review process. The editorial committee first provided pertinent comments and requested modifications, which I accepted. Subsequently, an external referee reviewed the article and requested additional adjustments.
Is this work replicable in the upcoming presidential elections in Chile?
I don't believe this manipulation is reproducible in Chile because our country has maintained solid institutions since the return to democracy, including an exemplary electoral system. It's rare globally to have nearly 80% of results available within two hours of polls closing, allowing us to know the winners that same night, save for tight races. In my article, I compare these two systems. In Chile, we convert votes into percentages given to two decimal places. Rounding to only one decimal place would make the count too coarse, risking errors in close elections often decided by a tenth of a percentage point. This two-decimal precision makes it very difficult for results to be determined by a hundredth of a percentage point. The suspicious precision of the Venezuelan figures—which were presented to one decimal place but were not rounded—is what triggered my doubt. From a mathematical perspective, this lack of rounding is extremely rare. I explained this in my article, demonstrating that the probability of the data provided being reliable was incredibly low: 99.9999% in the worst possible mathematical modeling scenario pointed to unreliability, not reliability.
What is the relevance of this article?
I made these initial observations just two days after the election, and the article was published in the press four days later. In that publication, I clearly stated that the figures had been manipulated. The subsequent events confirmed my analysis: there was never any promised institutional correction of the figures or official data delivery. Everything points to the Venezuelan election having been a fraud.
It is crucial to emphasize that this article appeared in a mathematics education journal, not a mathematics research journal. It was intentionally written using pedagogical language with teachers in mind. The core idea is for this article to serve as a useful document, enabling educators to analyze contingent events and reality itself from a clear mathematical perspective. Ultimately, the aim is to shift the public image of mathematics—to demonstrate that it is not a crude, technical, and arid discipline, but an extraordinarily relevant science that provides clear and rigorous constructs for analyzing any situation within the social sphere.