Benford's Law anomalies in the 2009 Iranian presidential election

Details Benford's Law anomalies in the 2009 Iranian presidential election Benford's Law anomalies in the 2009 Iranian presidential election

2009-06-16

arxiv.org/abs/0906.2789v3

Statistics

Applications

25 pages, 17 figures, 4 tables; v2: 3 of 6 biggest cities satisfy K7; v3: simulations give p=0.0007, K7a distribution is odd

Scientific paper

The vote count first digit frequencies of the 2009 Iranian presidential election are analysed assuming proportionality of candidates' votes to the total vote per voting area. This method is closely related to Benford's Law. A highly significant (p ~ 0.0007) excess of vote counts for candidate K that start with the digit 7 is found (41 observed, 21.2--22 expected). Using this property as a selection criterion leads to the following coincidences. (i) Among the six most populous voting areas, this criterion selects those three that have greater proportions of votes for A than the other three. The probability that the two sub-groups are drawn from the same distribution is p ~ 0.1. (ii) K's vote counts for these same three voting areas all have the same second digit. The probability of this is p ~ 0.01. (iii) Most (75%) of the vote counts for K in voting areas with 70 to 79 votes for K are odd, and every even number occurs exactly once. The probability of the latter is p ~ 0.0005. Interpreting the big city effect (i)+(ii) as an overestimate of the true vote, assumed to be roughly 50% to match other data, while retaining constant total vote numbers and increasing votes for the other three candidates in proportion to their average voting percentages, would imply that the difference between A's and M's vote totals would drop by about one million votes. These results do not exclude other anomalies.

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