Detecting Fraud

A fascinating statistical law was brought into play to substantiate claims that the Iran election was rigged

Walter Mebane of the University of Michigan has based his claim on an interesting statistical anomaly called Benford’s law. The law states that for some type of statistical data the numbers from 1 to 9 do not occur as the first digit with equal frequency. In simple terms, when any quantity grows with a uniform rate then going from 10 to 20 involves a jump of 100 per cent, from 20 to 30 a jump of 50 per cent and from 80 to 90 only 12.5 per cent. So the quantity is likely to be stuck in the 10s, where the first digit is 1 for far longer than in the 20s or 80s where the first digit is respectively 2 and 8.

Refining this procedure, the law predicts that for such data the digit 1 will occur as the first digit a staggering 30.1 per cent of the times.

The frequency of the other digits is given in the table as is their occurrence in some real life data. The match between the law and observed data is striking and improves with the number of samples, as there are only a few hundred river basins, but there are millions of tax returns. Mebane claims, after studying election data from the US, Russia and Mexico, that even vote counts tend to follow Benford’s Law in the second digit. Based on this he has concluded that in Iran “the evidence is so strikingly suspicious, (that) the credibility of the election is in question until it can be demonstrated that there are benign explanations for these patterns.” 

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