Numbers Don’t Lie

According to the Benford’s law, the first digits in many real life data follow a particular pattern such that the number 1 will be the most common as the first digit, number 2 will be the next most common, then 3 and so on. For example, one out of three times you will see 1 as the first digit. Click here to see the likelihood for all single digit numbers. This trend can be found in real life data, such as financial statements, birth and death rates.

This means that a simple frequency distribution check on, for instance, accounting reports, can be used to detect fraud – because the botched numbers tend to violate the distribution.

That’s exactly what someone did to verify an anomaly in the ballot numbers from 2009 Iranian presidential elections. And guess what, according to this paper, the results indicate a possible overestimation of the winning candidate’s votes by several million! (Apparently, as compared to the expected distribution according to the Benford’s law, there was an access of 7’s in the vote counts for Mousavi, and access of 2’s and lack of 1’s in the vote counts for Ahmadinejad.)

P.S. Andrew Gelman, whose blog I visit often, is not convinced about the methodology, by the way.

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