One of my former PhD students shared with me a mathematical argument confirming that the July 28 election in Venezuela was fraudulent. The National Electoral Council announced the results based on around 80% of the electronic votes that same evening. Usually, results are given in percentages rounded to two decimal places, which corresponds to a precision of one-hundredth of a percent, or one ten-thousandth. Out of 10 million votes, this means a precision of around 1,000 voters, which seems reasonable. This time, the committee announced the results to a single decimal point: Nicolas Maduro (officially) received 5,150,092 votes, or 51.2% of the 10,058,774 votes cast, and his main rival, Edmundo Gonzalez, (again, officially) received 4,445,978, or 44.2%.

Do the math: These percentages are too perfect. By calculating 51.2% and 44.2% of 10,058,774, we get the exact number of voters announced, rounded to the nearest unit! How is this possible? The month strongly suggests that the percentages 51.2 and 44.2 could have been chosen somewhat arbitrarily to produce an acceptable result for Maduro. It implies that the administration might have calculated the number of Maduro and Gonzalez voters without worrying about the fact that there was absolutely no reason for these percentages to align so precisely. A clever fraudster would have changed the figures by a few thousand units to make them seem more realistic.

Let's imagine for a moment that the total number of voters is exactly 10 million. If we multiply this number by a percentage with a single decimal place, we'd only get multiples of 10,000. For the percentage to be exact, the number of supporters of each candidate would have to end with four zeros. This occurrence happens once in 10,000 for each candidate, and, therefore, once in 100,000,000 for it to occur for both at the same time. If the number of votes is not exactly 10 million but 10,058,774, as in this case, I'll let my readers convince themselves that this doesn't make much difference. The chance of this Venezuelan coincidence occurring is approximately once in 100,000,000. It's tempting to conclude that the election was fraudulent. Let me remind you that there is about one chance in 20 million of winning the Lotto jackpot.

An almost certain fraud

American mathematician Terence Tao, a Fields Medalist in 2006, recently published an article on his blog in which he lucidly explained the contributions of probability theory in such situations. In Maduro's case, the fraud was indeed almost certain, even though it was impossible to assign a probability with so many unknowns.

You have 24.83% of this article left to read. The rest is for subscribers only.