Update: Iran's Numbers Even Fishier Than Previously Reported

By Allison Bond | June 22, 2009 5:48 pm

numbersJust a few hours ago, we reported that two political scientists from Columbia University analyzed the voting results released by the Iranian government, and that they found that there was only a 1 in 200 chance that a certain numerical pattern would occur in a clean election. Their analysis was based on examining the last digits of vote totals for each candidate from each province.

We’ve recently learned that the chances that the election was not tampered with are even lower than the 0.5 percent the researchers reported in their Washington Post op-ed. That was thanks to an emailed tip from Douglas Keenan, a former Wall Street mathematical researcher and financial trader who now studies independently—a correction that was confirmed by the Columbia political scientists.

Keenan found that there is only a .13 percent chance that, based on the numbers in question, Iran’s election was not rigged—significantly lower than the 0.5 percent originally reported. According to Keenan and the authors, a computational error led to the error.

To come up with the probability that the election was not rigged, the researchers used the Monte Carlo method, which uses repeated random computer simulations to calculate real-world probabilities. While an error was made in the original calculation, the bottom line of the analysis remains the same: It is very unlikely such numerical patterns would occur in a clean election.

For more details on the methods used, see excerpts of the emails below and check out the annotated version of the Washington Post article from the authors’ web sites [pdf].

An excerpt from the emails between Keenan and Bernd Beber, one of the Columbia University political scientists:

From Keenan: “I thought that it might be interesting to replicate your analysis…. For each test, I got the probabilities stated in your article: a little less than 4% and 4.2%. Then I combined the tests. I got 0.13%, rather than a little less than 0.5%. My conclusion, then, is that the evidence is even stronger than given in your article.”

From Bernd Beber, co-author of the study: “You’re correct. Since the last and second-to-last digits are independent…. the joint probability is simply the product of the marginal probabilities, so it’s quite a bit lower than .005.”

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Image: flickr / Pink Sherbet Photography 

MORE ABOUT: corruption, Iran, statistics
  • http://slipr.com Christopher Mims

    I really hope people in Iran know this.

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  • Steve

    Has anyone checked the election results for Benford’s law? Is there any reason that shouldn’t apply here?

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  • Albert Bakker

    And sure, everyone’s a neocon when it comes to Iran. (Of course we should exclude ueber neocon Daniel Pipes, who in a rare moment of honesty said outright he would vote for Ahmadinejad if he could.)

    So what if the elections were rigged? Ahmadinejad might still have won but maybe he or someone for him stupidly chose to be rather sure than sorry.


    This in itself should not suprise us as US President nr. 43 came to power in rigged elections and then was rewarded with a re-election after he committed genocide. He might just a have thought it not necessary the second time as opposed to Ahmadinejad. (They were so secure that Cheney still thinks he is president.) Ahmadinejad like Bush is also a rightwing moron running on the platform of standing up for the common folk, the difference is mainly that Ahmadinjad did not start multiple wars of choice under false pretences, not even one actually. Which would be something of a unicum of such a thing happened under an American president.

    The whole thing is a farce though, sexed up by foreign policy interests with the tragic consequences we have seen televised, like the girl being shot and who probably died.
    Which is really odd come to think of it, not the shooting of demonstrators but if you compare the reactions to this with imagery of demonstrations against what we call in political parlance “moderate” regimes like Egypt for instance, where targeted demonstrators are equally dead but somehow far less popular in Western media. I won’t even mention Palestinian protesters who are shot dead all the time, because they don’t appear at all, lest the damn paper be accused of antisemitism. But then again same goes for Lebanon as long as they shoot dead the right kind of people, which would be Palestinan refugees.

    Same goes for rigged elections or even the absence of elections by favoured or otherwise known as “moderate” regimes. Or accepting the outcome of uncontested elections if like in Gaza, the people make the wrong choice. In that case you try to start a civil war by arming the opposition or something like that.

    In Iran too the whole simple good guys vs bad guys mold in which this crap is being chewed and then regurgitated for Western consumption is very, very sad. Mousavi is as much a “reformist” let alone a liberal dissident, as Ahmadinejad is a “conservative” as George Bush is an intellectual as Obama is an anti-torture peacenik.


  • Pingback: Can Number-Crunching Reveal Whether Iran’s Election Was Rigged? | Discoblog | Discover Magazine()

  • http://scienceblogs.com/cognitivedaily Dave Munger

    As I point out in a comment over on Cognitive Daily, the probability should be even lower for the specific digits 7 to be over-represented and 5 to be under-represented. If we are making the specific prediction that 5 should appear less frequently than 10 percent of the time and 7 should appear more frequently, that’s extremely unlikely, and would decrease the probability that this result is due to pure chance by two orders of magnitude, to less than 0.05 percent, or 1 in 2,000, for just the last-digit test. Combine that with the other test and you’re looking at a probability of less than 1 in 50,000.

    That’s a reasonable prediction to make, since we know from other research that when humans pick “random” numbers, they pick 7 more frequently and 5 less frequently than chance.


  • Zach

    @Dave Munger

    Except, in the authors’ previous work, they postulate that the numbers 1,2, and 3 are overrepresented in human attempts at random sequences while the numbers 6,8,9, and 0 are avoided. The numbers 7 and 5 aren’t mentioned. The observation in Iran flies in the face of their earlier work, and it’s telling that they mention the cognitive psychology behind their non-adjacent numbers observation but don’t mention the research they’ve previously identified regarding number frequency.

    The correct null hypothesis to test here is, “the last digit is randomly selected from a uniform distribution of the numbers 0 through 9.” I tested this – http://alchemytoday.com/2009/06/24/is-the-devil-in-the-digits/ – and found that it was impossible to confidently reject the null hypothesis.

    The fact that the authors apparently can’t even make a simulation that properly captures the probability of their observation is troubling. It’s trivial to show that the two events they identify (the 17%/4% and non-adjacent events) are completely independent, and that the probability is the product of the individual probabilities (3.5% * 4.2% ~= 0.15%).

    The authors imply that this means there’s only a 1 in 200 chance that the election was fair (1 in 600 or so actually). This is completely wrong. They looked at the last digit frequencies after the fact, and calculated the probability of one number being too frequent and one being too infrequent. Had they seen two numbers be too frequent, they would’ve written the same article. Had they seen two numbers be too infrequent, they would’ve done the same. Had all the numbers occurred 11 or 12 times out of 116 (10%), this would suspiciously lack the variance expected in a random sequence. It’s trivial to think of dozens of equivalent observations, and the odds of one of them happening are 100%.

    The authors use the last digit of the 2008 Obama/McCain race as an example of what a fair election should look like. Well, in a fair election with numbers that size the penultimate digit should also be random. If you look at the second-to-last digit in their data set, you’ll see 20% 7s and only 5% 8s. There’s a 1.5% chance of this occurring — over twice as rare as what happened in Iran and not much different than the 1 in 200 chance they see in Iran.


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