Iran’s Guardian Council has found that the number of votes cast in 50 Iranian cities exceeded the number of people entitled to vote.

Iranian State media reported that the additional votes “could be over 3 million and the council could at the request of the candidates re-count the affected ballot boxes.”

While the claim has been widely reported in Western media as well, far little analysis has been done on the numbers claimed in the report. A crunch of the numbers suggest that the number of fraudulent votes could be much, much higher than 3 million, but let me explain the math.

Voter turnout at the Iranian election was reported to be 85% (ref), a historic high in a country where voting is not compulsory. There are anywhere from 46 million eligible voters according to Iran’s Interior Ministry, to over 51 million according to Iran’s Center for Statistics (ref.)

Now the 3 million votes identified by the Guardian Council are votes cast above 100% of eligible voters, and yet turnout is reported at 85%. See the gap now?

Turnout figures are reported on a country wide average basis, and aren’t available on a city or polling booth basis (least not in English or via an easy to identify source.) We also don’t know which cities or ballot boxes were affected, but we can make some estimates.

An additional 3 million votes would mean that an additional 6.5% of votes were cast on top of the 100% mark based on the Interior Ministry number of 46 million eligible voters. If turnout was the average 85% in the effected cities, that would mean that up to an additional 6.9 million fraudulent votes may have been cast on top of the 3 million figure, bringing the total to 9.9 million votes.

Now the bad news is that 9.9 million doesn’t allow for the gap between Ahmadinejad and Mousavi, which was 11.3 million votes, but there could be more.

The 85% turn out figure is strange on a couple of fronts. Yes, there’s obviously a mood for change in Iran, but there’s some irregularities as well. The figure was first reported by Iran to be 70% (ref) until it was revised up to 85%. Both figures are historic highs as well, with voter turnout at the last round of voting in Iran in 2005 hitting only 48% (ref). 85% isn’t impossible, but could the additional 15% above 70% have been added to cover up even more widespread voting fraud?

If the actual turnout was 70%, the figures shift around, and presuming all fraudulent votes went to Ahmadinejad, Mousavi comes out at around 4 million votes ahead, and that of course would be game over.

Other sites are claiming that the Iranian Government simply made the figures up (and there’s some decent arguments in favor of that theory), but what if they didn’t just make the numbers up, but tried to cover themselves by stuffing the ballot box with physical votes for Ahmadinejad, after all, if you can show physcial votes, it’s easier to defend against claims of fraud. But what if they didn’t get it right, and over stuffed the ballot boxes, resulting in the 3 million votes they’ve admitted to today? Given the situation in Iran, it’s not impossible that this scenario may have taken place.

Update: a thought: we’re taking turnout figures as being accurate, but we can’t back those up, and if the election was rigged, so to could have been the reported turnout figures. We know turnout was high in Tehran due to the media coverage, but what if the real figure Iran wide wasn’t even 70%? What if it was something closer to 50 or 60%? the bigger the gap between actual turnout and reported turnout becomes, the bigger the fraud. It’s not inconcievable that in at least some Iranian cities, actual turnout could even have been below 50%.