Looking at the Iranian Elections

Whoever made up numbers apparently forgot about Benford’s Law:

The results of the 2009 Iranian presidential election presented by the Iranian Ministry of the Interior (MOI) are analysed based on Benford’s Law and an empirical variant of Benford’s Law. The null hypothesis that the vote count distributions satisfy these distributions is rejected at a significance of $p e 0.007$, based on the presence of 41 vote counts for candidate K that start with the digit 7, compared to an expected 21.2–22 occurrences expected for the null hypothesis. A less significant anomaly suggested by Benford’s Law could be interpreted as an overestimate of candidate A’s total vote count by several million votes. Possible signs of further anomalies are that the logarithmic vote count distributions of A, R, and K are positively skewed by 4.6, 5.8, and 2.5 standard errors in the skewness respectively, i.e. they are inconsistent with a log-normal distribution with $ p sim 4 imes 10^{-6}, 7 imes 10^{-9},$ and $1.2 imes 10^{-2}$ respectively. M’s distribution is not significantly skewed.

For those unfamiliar, here’s wikipedia on Benford’s law.
Three years ago, I looked at the decimals in the Dow’s daily close. I didn’t test them but it looks like they could follow Benford’s law.

Posted by on June 17th, 2009 at 2:16 pm


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