At this point, it seems clear that Venezuelan president Hugo Chavez won a definitive victory in the recall referendum that the country held a week ago Sunday. The opposition, though, continues to insist that there was massive fraud. There doesn’t seem to be any proof of this, but one piece of evidence that Chavez’s opponents seized on almost immediately was the curious fact that at hundreds of polling stations around the country more than one voting machine recorded the exact same number of “yes” votes (“yes” was a vote for Chavez’s removal). For instance, the Wall Street Journal reported that at one polling station in Bolivar, two machines each recorded 153 “yes” votes while recording 215 and 237 “no” votes.
The opposition argued that this was proof that the number of “yes” votes had been “capped,” so that after a certain number of votes had been recorded, every additional “yes” vote was changed to a “no” vote instead. (Venezuela uses computerized touch-screen voting machines.) And at first glance, this might seem suspicious. But at second glance, it seems like a simple product of chance, as the Journal pointed out:
Aviel Rubin, a computer-science professor at Johns Hopkins University, said he calculated odds of roughly one in 17 that two of three computers at a voting table would have identical results. That compares to about one in 15 that so far have shown similar results in Venezuela’s referendum.
In other words, with twelve thousand voting “tables,” many with multiple machines, it was inevitable that some would end up with matching scores. (It’s similar to the fact that if there are 23 people in a room, the chances are 50-50 that two of them have the same birthday.) Not surprisingly, then, when international observers audited a sample of the results, they found that while there were 402 tables with matching anti-Chavez votes, there were 311 tables with matching pro-Chavez votes, too. What seemed to be proof of fraud was most likely just a statistical artifact.
This is a classic example of what Nassim Taleb calls being “fooled by randomness,” in his intriguing book of the same name. We think that randomness means there will be no clusters or sequences of similar behavior, and therefore when we see them we assume they’re evidence of some hidden pattern. (You can see this in the way people interpret everything from clusters of cancer cases to hitting streaks in baseball.) But they’re really just evidence of the numbers working themselves out.