What Probability and Statistics Have to Say About an Election in Venezuela

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Mark Weisbrot
Al Jazeera English, May 10, 2013
En Español

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Probability and statistics were not on the favorites list of most college graduates who were required to take a course in the subject – all those permutations and combinations and probability distributions generally leave a lot of heads spinning.   But their real-world relevance has been growing in recent years as political polling becomes more widespread and sophisticated. Nate Silver of the New York Times and Sam Wang of the Princeton Election Consortium have shown eloquently that this branch of applied mathematics, combined with a good array of polls, can be an excellent predictor of election-day results. Silver became America’s most famous geek: Jon Stewart proclaimed him “the lord and god of the algorithm.”

But what about an election that has already happened?  Can we use probability and statistics to determine whether a close vote count was stolen through fraud? Normally a close election result would be difficult to second-guess with pre-election or exit polls.  But there is one election in particular where statistical analysis gives us an answer that is vastly more certain than any collection of polls.  And it happens to be a subject of some controversy. 

On April 14 in Venezuela, Nicolás Maduro of the governing party won with a closer-than-expected margin of 50.8 percent of the vote versus 49 percent for challenger Henrique Capriles. This was a margin of about 270,000 votes.  Capriles immediately demanded a full “recount,” and the Obama administration joined him, saying that it would not recognize the new president until there was a 100 percent audit of the paper receipts produced by Venezuela’s voting machines.  Capriles first agreed to, then rejected, an audit by the National Electoral Council, but many people not only in Venezuela but throughout the world have doubts about whether the vote count showed the true winner.

Should they?  Actually, no.  There is really no doubt at all about the outcome, because there is a relatively simple statistical analysis that can be done on the basis of what happened on the day of the election.  After going through a very thorough identification that includes their fingerprint, Venezuelans make their choice on a computer touch screen.  They then receive a paper printout that confirms their vote, and place the paper receipt in a sealed box.  When the polls close, a random sample of 53 percent of the machines is selected, with at least one machine at each polling place.  The paper receipt count is then compared to the machine count to make sure that they match.  This is done in front of witnesses from both sides, as well as election officials; members of the community are also invited to watch.

There has not been a single reported allegation of a mismatch between the machine count and the paper receipts. Capriles and his campaign have not produced even one allegation of such a discrepancy.

So the question is, how likely is it that this audit of 20,825 machines could produce no errors, if in fact Capriles were the true winner? The answer, as described in our new paper, is that it is far less likely than one chance in 25 thousand trillion.  There is really no way around this conclusion, and it does not depend upon any assumptions other than what tens of thousands of people witnessed in the vote audit of the 20,825 machines.

The results are intuitive: if there was a fraud big enough to move 135,000 votes from one candidate to another, it would have been discovered in some of those 20,825 machines.  But it wasn’t.  So you have a choice:  you can believe that the world witnessed something so improbable that it cries out for supernatural explanation on April 14:  an audit result that had far less than a one in 25 trillion chance of occurring.  That is what Capriles and his supporters are asserting when they claim that an audit of the remaining machines would change the election result.  Or, you can believe that Maduro actually won the election.

Nate Silver triumphed over his critics and the pundits who insisted that the 2012 U.S. presidential election was “too close to call,” correctly predicting the results in 50 out of 50 states.  But the actual result of the Venezuelan election is much simpler than any prediction, and vastly more certain.  Why, then, is it treated by so many as an uncertain result?


Mark Weisbrot is co-director of the Center for Economic and Policy Research, in Washington, D.C. He is also president of Just Foreign Policy