[zerojunkie]

So someone ran the election results through Benford's Law. The math is way beyond me, but here's a description of it from Wikipedia.

Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty. This distribution of first digits arises logically whenever a set of values is distributed logarithmically. For reasons described below, real-world measurements are often distributed logarithmically (or equivalently, the logarithm of the measurements is distributed uniformly).

This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). The result holds regardless of the base in which the numbers are expressed, although the exact proportions change.

It is named after physicist Frank Benford, who stated it in 1938,[1] although it had been previously stated by Simon Newcomb in 1881.[2]

Here are the results. The candidates are referred to by the first letter's of their last name.

Conservatives

* Mahmoud Ahmadinejad, the President of Iran
* Mohsen Rezaee, former Commander of the Iranian Revolutionary Guard

Reformists

* Mehdi Karroubi, former Speaker of the Majlis
* Mir-Hossein Mousavi, the last Prime Minister of Iran (Campaign article)

Conclusion. The vote counts per voting area published on 2009-
06-14 by the Ministry of the Interior of the Islamic Republic of Iran for
the 2009 presidential election show a highly significant excess of the first
digit 7 for candidate K, compared to the expectations either from a uniform
Benford’s Law or from an empirically derived equivalent of Benford’s Law.
Given that the test was applied for all four candidates, for all nine possible
first digits, the null hypothesis that the first digit in the candidates’ absolute
numbers of votes are consistent with random selection from a uniform, base
10 logarithmic distribution modulo 1 is rejected at a significance of p ≤
0.0069, i.e. 1 − p ≥ 99.3%.

Less significant anomalies suggested by Benford’s Law can be interpreted
using an alternative hypothesis in which a few dozen vote counts for candidate A in the range 10,000–19,999 had an extra digit added, shifting them
to the 100,000–199,999 range, and/or a few dozen vote counts in the 20,000–
29,999 and 200,000–299,999 ranges were artificially added to these ranges.
Corrections for these would-be anomalies would amount to several million
votes.

The highly significant excess of 7’s for K and the speculative alternative
hypothesis could be checked by examining the credibility of the total
vote numbers (and likely voting patterns) for those particular voting
areas with these numerical characteristics. The voting areas’ names are
listed in the table published by the MOI (MOI Iran 2009a; MOI Iran 2009b;
MOI Iran 2009c).

A possible clue for further investigation is that all the candidates’ logarithmic
vote count distributions are highly skewed, especially R’s vote counts,
which are positively skewed by about 5.8 standard errors, except for M,
whose logarithmic vote counts are skewed (negatively) by less than one standard
error. Any demographic models of Iranian voting patterns will need to
either reproduce these statistical characteristics, or else make hypotheses
regarding systematic anomalies in the data.