Benford’s Law anomalies in the 2009 Iranian presidential election — Boudewijn F. Roukema

Abstract: 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 ≤ 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 ∼ 4×10^-6, 7×10^-9, and 1.2×10^-2 respectively. M’s distribution is not significantly skewed.

It’s a 14 page academic pdf.

Questions for the statistically-capable lazyweb:

• Have people applied Benford’s Law to election results before?
• Is the empirical variant of Benford’s Law a standard technique, or something Roukema has made up?
• Do the stats calculations look legit? (I didn’t do that much stats, and I’ve forgotton it all anyway.)
  • (pp7-8) Why is assuming that the 36 samples are independent considered conservative?

Via Andrew Sullivan.