### Thursday, August 13, 2009

## Iranian election statistics

I've written a number of things about the Iranian election, but one topic I never addressed was something called the Chatham House study (pdf), a study by two researchers in Scotland which is used by critics of the election to "prove" that fraud occurred.

Let's start with simple (but significant!) math errors in the paper. In trying to explain how it could be possible that Ahmadinejad got 13 million more votes than conservative candidates got in the 2005 election, the authors offer three possible explanations:

• The approximately 10.6m citizens who did not vote in 2005, but chose to vote in this electionHere's the problem. Their own statistics show that in 2005 there were 28.1 million votes cast, with a 63% turnout, which computes to 44.6m total registered voters. That means there were

• The 6.2m citizens who voted for the centrist Rafsanjani in 2005

• The 10.4m citizens who voted for reformist candidates in 2005

*16.5 million*voters who didn't vote in 2005, not 10.6m. Kind of a large error. [

**Update/semi-correction**: They do say "who...chose to vote in this election," which means their 10.6m figure is actually the difference in the number of voters, and is correct. So math-wise, they are correct. But conceptually, they still aren't, because the fact remains that there were 16.5m more registered voters. The ones who

*didn't*vote in 2009 are not necessary the same ones who didn't vote in 2005. In any case it's a minor point; the major point is made below.]

Then there's the fact that they miss an obvious fourth source of more votes - a larger electorate, as would be naturally expected in a country with population growth. Indeed, the 2009 vote total was 39.1m votes and 83% turnout, which calculates to 46.6m total registered voters, an increase of 2 million people. Thus there were actually 18.5 million more people voting, from whom Ahmadinejad needed to draw 13 million votes, even assuming he drew no votes from Rafsanjani voters or reformist voters from 2005.

By far the most quoted line in the study, however, and the "gotcha'" quote for many people, is this one, which is repeated no less than three times in the paper:

In a third of all provinces, the official results would require that Ahmadinejad took not only all former conservative voters, all former centrist voters, and all new voters, but also up to 44% of former reformist voters.There are multiple things that are wrong or misleading about that statement. That "44%" figure sure sticks in your mind, doesn't it? You probably skipped right over that "up to" that precedes it. In fact, if you look at the authors' Table 3, you'll see there is exactly one province with that 44% figure. There's one with 35%, three with 25%, and after that the outliers drop off the 10% and then 5%. So the 44% figure is misleading right off the bat. Then of course there's that "third of all provinces" figure, which again one tends to skip right over. Of course that means that in

*two-thirds*of all provinces, Ahmadinejad needed

*no*votes whatsoever from former reformist voters.

There's one more factor. Unsurprisingly, just as in with the states of the United States, provinces in Iran have very different populations. 8 of 30 provinces have one million or more people voting for Ahmadinejad, representing 63% of all Ahmadinejad voters. Of those, exactly *one*, Fars province, is in that third of provinces where, according to the authors, Ahmadinejad needed to pick up reformist voters, and the percentage in that province is 5%, a far cry from 44%. Let's look at the statistics another way. *Every single vote* that Ahmadinejad received in those "third" of provinces where he had to pick up "up to 44% of former reformist voters" amounts to 5.9 million votes. If Ahmadinejad did not receive a single vote in those ten provinces (obviously a preposterous hypothesis), he still would have won the election by 5.4 million votes!

Now consider Tehran province, by far the largest. There were, according to the Iranian government, 3,819,495 Ahmadinejad voters in that province in 2009. In 2005, Ahmadinejad received 1,500,829 votes in that province and other conservative candidates got 860,548. There were 2,424,653 non-voters in that province in 2005, which means that in the most populous province in the country, not only didn't Ahmadinejad need to pick up any reformist votes to achieve his total, he didn't even need a single vote from former Rafsanjani voters either, just 64% of those who didn't vote in 2005 (taking into account the 2009 turnout and population growth), a number entirely commensurate with his overall vote.

Does this analysis prove there was *no* fraud of any kind in the election? Obviously not; proving a negative is rather difficult, and, furthermore, we can pretty much expect *some* fraud in elections in every country in the world. But does the Chatham House study provide the "definitive proof" of fraud that some claim? Not if you actually look at the numbers.