Was the Iranian presidential election stolen?

I don’t normally stray far from my area of expertise in these posts, but a couple of you have asked whether political science can shed any light on the events occurring in Iran, specifically the allegations of vote fraud.  Although I have little expertise in Iranian politics, I have been following the work of some of my colleagues in this area, and thought I’d provide a brief summary of their findings.  By way of background, as most of you know Iran held its presidential election on June 12. The incumbent, Mahmoud Ahmadinejad, was declared the victor in what purportedly amounted to almost a landslide, but the main opposition candidate, Mir-Hossein Mousavi (as well as other opposition candidates) is arguing that the results were tainted by fraud. (According to official government results, Ahmadinejad won more than 62 percent of the vote, compared with 34 percent for Mousavi, his closest challenger in a four-person race. That is almost identical to the percentage Ahmadinejad won four years ago in a two-person race, but that result came in a runoff election. Seven major candidates participated in the first round of voting in 2005 — when no incumbent was running — and Ahmadinejad got 19 percent.) During the week since the election was held, there have been widespread demonstrations among both candidates’ supporters and the situation remains volatile. Yesterday, in an effort to put a lid on the continuing protests (see story here), Iran’s religious leader, Ayatollah Ali Khamenei threatened to crack down on opposition leaders should the demonstrations continue.

So, was the election fraudulent?  Those who believe it was point to a number of indicators, including the apparent speed with which the paper ballots were tabulated, and violations in protocol for recording votes at polling stations (see here).  Beyond these impressionistic indicators, however, is there any other evidence of fraud?  Political scientists typically use a couple of statistical methods to detect vote fraud more generally. One (somewhat controversial) method is to look at the polling results and see if the distribution of the digits in the electoral totals conforms to statistical expectations.  Interestingly, in many data sets – like street addresses – digits are not randomly distributed; there are far more addresses beginning with one than nine, for instance (this is called Benford’s Law, after physicist Frank Benford, although he wasn’t the first to come up with the idea).  Some argue – but there’s no consensus on this that I know of – that in election results that are the result of natural processes, certain numbers should occur more frequently in the listed vote totals.  (The controversy partly has to do with how the methods by which votes are registered [say, by machine versus paper ballot] influence the distribution of digits in the vote total).  So if reported results don’t conform to this expectation, it suggests someone manipulated the results. Unfortunately, since the Iranian results have been aggregated at the level of townships (that is, results from polling booths have been combined in each township) the standard tests designed to see whether voting results conform to the statistical expectations of Benford’s Law probably can’t be used because of the “mixing” of polling booth data that washes out these patterns.

A second method is to compare results across successive elections, to see how well votes in the first election predict the results in the second, taking into account the dynamics of both elections.  For example, if one wishes to explain Bush’s vote totals in the 2004 U.S. presidential election, a good predictor is to take the 2000 results and simply add about 3% across the board among all voting demographics supporting Bush, and you’d come up with a pretty accurate approximation of Bush’s 2004 votes.  This is because there wasn’t much deviation in the underlying voting coalitions across the two elections; Bush drew on the same voting groups in 2004 as he did in 2000, but he increased his support among those groups.  In fact, the correlation between Bush’s vote in 2000 and 20004 is about .97.  That is, the best predictor of how Bush did in 2004 is to look at who voted for him in 2000.

University of Michigan political scientist Walter Mebane has applied this method to study the Iranian results (see the Mebane paper here).  For the less statistically-inclined, a straightforward discussion of Mebane’s analysis is contained HERE, at the Pollster.com website.  But essentially what Mebane does is compare the town-level results in the 2005 Iranian presidential election with the town-level results in 2009.   (The analysis is slightly complicated because in 2005 there was a run-off election between Ahmadinejad and his main opponent following the first round of elections, whereas in 2009 there was no runoff election, since Ahmadinejad purportedly won a majority of the votes in the first round of elections.)   So Mebane is really comparing the second-round results in 2005 with the first round in 2009.  Mebane expects, given the high turnout in 2009 (supposedly close to 85% of voters) and the apparent surge of support for the opposition candidate in 2009, that in towns that did not support Ahmadinejad in 2005, his proportion of the vote total would go DOWN in 2009.  Conversely, one would expect Ahmadinejad to perform best in 2009 in those same towns that voted for him in 2005.  In fact, however, Mebane finds that this is not always the case; there are numerous outliers that do not conform to expectations.  Mebane concludes:  “More than half of the 320 towns included in this part of the analysis exhibit vote totals for Ahmadinejad that are not well described by the natural political processes the model …represents. These departures from the model much more often represent additions than declines in the votes reported for Ahmadinejad. Correspondingly the poorly modeled observations much more often represent declines than additions in the votes reported for Mousavi.”  Mebane’s bottom line: while the data are not conclusive, he suggests there is “moderately strong support for a diagnosis that the 2009 election was afflicted by significant fraud.”

Before accepting Mebane’s analysis, let me add two caveats: first, as he readily acknowledges, Mebane is no expert on Iranian politics.  He doesn’t read Farsi (Persian), has no understanding of the local political dynamics in the towns whose data he analyzes, and he is relying on data provided to him by someone else with no way of verifying its accuracy.  Second, his “naturalistic” model assumes that the surge in voter turnout reflects an increase in support for Mousavi. But it’s quite possible that the dynamics of this election reflect a surge, particularly in more rural areas, for Ahmadinejad as well. More generally, without independent confirmation, there is a lot of uncertainty built into the assumptions underlying Mebane’s model, as he freely admits.  We cannot dismiss the possibility that Ahmadinejad did, in fact, win a commanding victory.

Of course, many observers in the U.S. are hoping that Mousavi – as the more “moderate” candidate – won, and therefore are inclined to support the idea that the election was tainted, despite the uncertainty.  We shouldn’t let our ideological predispositions influence our assessments of the facts, however. (As a quick test of our willingness to do so, consider the following: how many of you believe that by intervening in the 2000 presidential election and stopping the statewide recount, the Supreme Court prevented Al Gore from winning Florida?  Quite a few of you, I’d wager, although we now know this is not the case. )

There is a larger point, here, however: viewed by “western” standards, the electoral system in Iran is fraudulent, regardless of the outcome.  There is no truly independent media, and the results, in the end, must satisfy the ruling theocracy to stand. In this respect, I would argue, there is little debate: the Iranian election WAS tainted, regardless of whether Ahmadinejad or Mousavi truly received the most votes.

NOTE: I am on deadline to finish my book on White House staffing and therefore (as I hoped you’ve noticed!) will be blogging much less frequently throughout the summer.  However, if you have questions or topics worthy of a blog posting, do send them along and I’ll try to respond in a somewhat timely manner.


  1. Matt, Doesn’t the fact that that the government tried to shut down the email and other communication systems suggest that the government had something to hide?

    As well, the protests have been relatively peaceful, but the Supreme Leader is threatening dire consequences. What does he have to fear about a recount if the results were so overwhelming?

    I think the circumstantial evidence is “beyond a reasonable doubt”.

    A question for you: Do you think Obama should take a stronger line in this matter, as the Republicans suggest?


  2. Thank you! I wondered what your take would be. I gave up reading op/eds by statisticians on the Iranian election because they began to sound, well, a little political. Or metaphysical, anyway.

    I think you also nailed it at the end. It’s not about accuracy, it’s about legitimacy. There is something funny about how a “winner” wins in this situation. Poll his supporters, and I am sure you will find that a majority of them do not particularly care if elections are free and fair. So who is the regime kidding when they take a vote? Guys, either you’re a banana republic or you’re not.

    Any reactionary clique worth its salt knows this is too much of a hassle. Just have a real vote, hand the opposition a defanged executive, and ride a popular backlash back into power. Then you get to declare democracy a failed experiment, and rewrite the rules all over again.

    Best of luck on your manuscript, Matt.

  3. Jack – Not necessarily. It’s pretty apparent that Mousavi’s supporters are convinced the election was stolen, and they will dismiss any recount supervised by the ruling elite that suggests otherwise – even if the recount is accurate and confirms that Ahmadinejad did win. The demonstrations have long since transcended questions regarding the accuracy of the vote count – what we are seeing now is a struggle for power and governmental control. The legitimacy of the ruling regime is potentially at stake, something Ayatollah Ali Khamenei clearly realizes. He’s not about to sit by and watch these demonstrations morph into a pro-democracy movement that could threaten the ruling regime.

    Marty – I think under the “normal” election rules, you are absolutely right – the idea that these elections constitute an exercise in popular control is a farce. However, I do think Khamenei is worried that these demonstrations might spark a movement toward legitimate democracy – with real oppositions, free speech, etc. That’s what’s driving the crackdown.

    Obama is getting pummeled from both the Right and Left for his lukewarm response to the crisis to date, but he’s in a very difficult position. I’m going to devote a separate post to this, but my short answer is I don’t think he has very many options. Once again, he is finding that campaigning is not very good preparation for governing. In this instance, if he condemns the crackdown, he plays into Ahmadinejad’s and Khamenei’s argument that the U.S. is inciting the demonstrations and meddling in Iranian affairs. He also potentially makes it more difficult to engage in a dialogue with the Iranian government regarding nuclear weapons.

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