## What are the Chances that Maduro Actually Won?

There's roughly a 1 in 100 million chance that the numbers given by the CNE would happen by chance, says a Columbia University expert. Ecoanalítica director says they’re almost as likely as winning the Powerball

Art by Joaquin Salim

It turns out the numbers that the Venezuelan electoral authority CNE gave on Sunday are not only disputed by Venezuela’s opposition—they also don’t make sense to statisticians.

First, some context: the Electoral Council said that with 10,058,774 votes counted, Nicolás Maduro obtained 5,150,092 for a 51.20%, Edmundo González Urrutia 4,445,978 for a 44.2% and the other candidates 462,704 for the remaining 4.6%. Add the percentages and of course you get a nice and correct 100%

Fine. But here’s the problem that was quickly spotted by statisticians and math enthusiasts: If you take a given portion, let’s say the 462,704 that the “other” candidates received and calculate what percentage it is from the total 10,058,774 you get exactly 4.60000. And, of course, the same happens if you do the math for the other portions as well, you get 51.20000 for Maduro and 46.20000 for González Urrutia. These are next to impossible round numbers in an election were millions voted.

By the way, Johanna rants about it:

Andrew Gelman, professor of statistics and political science at Columbia University, says this is reminiscent of the recent Iranian election, “ where the five different vote totals all were multiples of 3.” By the way, Iran was one of the first countries to recognize the Venezuelan results.

In Columbia’s “Statistical Modeling, Causal Inference, and Social Science” blog, Gelman did a probability model to try to prove how likely a result like that is. Let’s start by saying that he did specify that “the 51.2% for Maduro looks a bit sus, kinda like they wanted to put him over the 50% hump by roughly the minimal amount that it wouldn’t trigger a recount, also they didn’t want it to be an exact percentage.”

He started with the same 10,058,774 votes and divided them into 3 piles, then assigned “a vote proportion to candidate A that’s randomly distributed between 0.3 and 0.7,” and  “a vote proportion to Others that’s randomly distributed between 0.01 and 0.10.”

Here’s where it gets more technical (more technical!). For each of the options, he multiplied those proportions by 10,058,774 and rounded them to the nearest integer. And he did that a bunch of times. “For each simulation, take the proportion of votes for each of the three options, round to the nearest 0.1%, multiply by 10,058,774, and round to the nearest integer. If these are the same as the actual vote totals, it’s a win.”

The result? 0. “A million simulations, and not once does this rounding thing work out.”

He shared the R code he used, if you’re into that kind of stuff:

He also did a Bayesian analysis (def: a statistical paradigm that answers research questions about unknown parameters using probability statements).

For that, he said that “there are 1001 possible vote counts you can get by rounding vote percentages that are multiples of 0.01, and there are 10,058,775 possible vote counts you can get.” So the probability of both candidates getting the exact numbers the CNE gave by chance is “approx (1/10,000)^2”, or 1 in a 100 million.

Statisticians closer to home have similar thoughts. Alejandro Grisanti, a computer engineer with a PhD in Economics who founded Ecoanalítica, went to his X account and compared the probabilities of getting those numbers with those of winning the Powerball—and they’re not as far as one might think.

He first explained that the range of votes Maduro might have gotten goes from 5,145,063 (51,15%) to 5,155,121 (51,24%), based on the 52.1% that the CNE mentioned. “The probability of it being exactly 5,155,121 (51,24%) is 1 in 10,059.”

For Edmundo’s votes, the range goes from 4,440,949 (44.15%) to 4,451,007 (44,24%), so the same 1 in 10,059 chance. When you add the vote for the “Other” candidates into the mix, the chance of those numbers happening becomes independent—so the chance of getting exactly the numbers the CNE gave is 1 in 101,2 million.

“The probability of winning the Powerball is slightly lower, 1 in 292 million. This means the chance of the CNE result occurring is only 2.9 times higher than winning the Powerball. Simply impossible!”, he added.

The New York Times used a different methodology. They based their analysis on a sample they got from an independent group called AltaVista. AltaVista used a random sample of 1,500 voting machines across the country that proportionally would represent the whole country. And according to those numbers, Edmundo González Urrutia defeated Nicolás Maduro 66% to 31%.

They got it thanks to the opposition witnesses in those polling centers. As the NTY registers, “intimidation by government supporters, organizational lapses and patchy cellphone coverage prevented the researchers from obtaining all the tallies in the sample, but they collected and verified data for more than two-thirds of those precincts.”

Although the sample represents 5% of the country, it was verified as useful by a number of experts. Adam Berinsky, an expert in survey methodology at M.I.T, said that, if anything, given all the tactics we know the government uses to discourage voters, it could underestimate the number of votes the opposition received.

Dorothy Kronick, an expert on Venezuelan electoral data at the University of California, Berkeley, did find the sample to be slightly favored to the opposition-leaning areas, “but not nearly enough to explain the tremendous difference between the numbers claimed by the government and the opposition.”

If nothing made sense to you in the previous 862 words, here’s the crux, again, for those in the back: the chances of Maduro’s numbers being real are one in 100 million.