The Devil Is in the Digits - Statistical analysis of the Iranian election results

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These pieces of the story point in the direction of fraud, to be sure. They have led experts to speculate that the election results released by Iran's Ministry of the Interior had been altered behind closed doors. But we don't have to rely on suggestive evidence alone. We can use statistics more systematically to show that this is likely what happened. Here's how.

We'll concentrate on vote counts -- the number of votes received by different candidates in different provinces -- and in particular the last and second-to-last digits of these numbers. For example, if a candidate received 14,579 votes in a province (Mr. Karroubi's actual vote count in Isfahan), we'll focus on digits 7 and 9.

This may seem strange, because these digits usually don't change who wins. In fact, last digits in a fair election don't tell us anything about the candidates, the make-up of the electorate or the context of the election. They are random noise in the sense that a fair vote count is as likely to end in 1 as it is to end in 2, 3, 4, or any other numeral. But that's exactly why they can serve as a litmus test for election fraud. For example, an election in which a majority of provincial vote counts ended in 5 would surely raise red flags.

Why would fraudulent numbers look any different? The reason is that humans are bad at making up numbers. Cognitive psychologists have found that study participants in lab experiments asked to write sequences of random digits will tend to select some digits more frequently than others.

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Type: Discussion • Score: 11 • Views: 6,623 • Replies: 70

[+3] - Robert Gentel - 06/22/2009[quote="Setanta"]I don't see any reason to continue to say that "the western media" jumped to a conclusion of fraud.[/quote] That is your prerrogative, but most of the...

@Robert Gentel,

The premise for the study is simple, the last digits of the results should be random but if a human invented the results they are less likely to be.

I have not examined their evidence in detail, so I can't vouch for their conclusions but I've been taking a hard look at the evidence for fraud in the Iranian elections and this is an interesting way to seek to establish evidence for it.

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@Robert Gentel,

It is an interesting method of analysis, but I think it's too abstract to carry much weight (unfortunately).

Besides, at this point, I think Iran's internal grievances have gone beyond the election (as perhaps they always were). The problem now is that the basic process involving the Guardian Council has been exposed as a non-viable (at least non-democratic) governing body.

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Why should they count the ballots if their intention was to declare the winner regardless of the vote.? Why would they bother counting the ballots if they intended to appoint the winner?

I wouldn't be at all surprised if it was possible to see the ballots in the ballot boxes had never been unfolded and counted. I don't think the ballots were counted rather than stuffing the ballot boxes. They could not have possibly counted forty million ballots within the time frame of the outcome announcement. They didn't have electronic voting, only paper ballots.

They don't want a recount because if the ballot boxes were opened, they would find the ballots had not been removed from the boxes, unfolded, counted, and posted on talley sheets. I don't think talley sheets exist.

I've always thought the outcome was based on the percentages of the poll that was taken about three weeks before the election. The election results appear to match the poll percentages.

I wonder how long before it is discovered that the ballot box contents and disappeared and been burned?

BBB

BBB

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@rosborne979,

rosborne979 wrote:

It is an interesting method of analysis, but I think it's too abstract to carry much weight (unfortunately).

I think it's pretty straightforward, and the reservations I have about it have more to do with the extent of their sampling than the method itself.

What do you find abstract about it?

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Besides, at this point, I think Iran's internal grievances have gone beyond the election (as perhaps they always were). The problem now is that the basic process involving the Guardian Council has been exposed as a non-viable (at least non-democratic) governing body.

If you meant that it wouldn't be something that would influence Iranian leaders I'd agree, but I'm just looking to settle the question for myself as to whether or not the results reflect the will of the Iranian people.

The Western media jumped to the conclusion of fraud right away, and I want to see more evidence about that. This is an interesting approach and there are other statistical analysis being done that I think are promising. If this kind of statistical analysis checks out, then I think it would be enough of a smoking gun for me to accept as evidence of fraud.

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I don't see any reason to continue to say that "the western media" jumped to a conclusion of fraud. Within hours of the polls closing, Persians on twitter were p0inting out that government sources had released certain figures of the votes for Moussavi, and within hours were reporting different, lower vote totals for Moussavi in the same districts. I don't think there is anything wrong with media outlets pointing out that there have been accusations of fraud from within Iran since the polls closed. I also don't think there is any reason to adopt a condescending attitude toward media outlets for reporting the information they have received rather than a recondite theory of numbers. I believe it is correct to point out that western media have been reporting since election day that there have been accusations of fraud. Those media don't have to prove that fraud has taken place in order to be truthful and accurate in saying that there have been such accusations.

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@BumbleBeeBoogie,

BumbleBeeBoogie wrote:

Why should they count the ballots if their intention was to declare the winner regardless of the vote.? Why would they bother counting the ballots if they intended to appoint the winner?

I have not seen any evidence to support this claim. In fact the prevailing narrative is that they had no intention to pick the winner, after all they get to pick the candidates and shouldn't have had a problem with any of them. But one candidate became transformed into a "reformist" by his followers and then they hastily decided to fix the election based on the late-campaign transformation.

That's the prevailing wisdom and even that doesn't have much to support it yet, not sure what you are basing your claims on, but it doesn't seem to make much sense. If they get to pre-approve the candidates why wouldn't they plan to count the ballots and make a nice dog and pony show about the democratic process?

I'd buy the hastily-decided-upon fix more than that.

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I've always thought the outcome was based on the percentages of the poll that was taken about three weeks before the election. The election results appear to match the poll percentages.

It doesn't match the poll exactly, but more importantly this contradicts the rest of your position. The results matching the independent poll taken three weeks before the elections would be an argument that the results are the legitimate will of the people.

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I wouldn't be at all surprised if it was possible to see the ballots in the ballot boxes had never been unfolded and counted.

[...]

They don't want a recount because if the ballot boxes were opened, they would find the ballots had not been removed from the boxes, unfolded, counted, and posted on talley sheets. I don't think talley sheets exist.

[...]

I wonder how long before it is discovered that the ballot box contents and disappeared and been burned?

Well, your imagination is as good as the media's has been, so this guess is as good as any. But I'm a bit speculation-weary and have been looking for more concrete evidence.

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@BumbleBeeBoogie,

BumbleBeeBoogie wrote:

Why should they count the ballots if their intention was to declare the winner regardless of the vote.? Why would they bother counting the ballots if they intended to appoint the winner?

Exactly. If they did an actual count (nonrandom), the last two digits should be random. If the digits are not random, it suggests they were fabricated.

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@Setanta,

Setanta wrote:

I don't see any reason to continue to say that "the western media" jumped to a conclusion of fraud.

That is your prerrogative, but most of the Western media clearly believe fraud to have occurred even if they admit the lack of clear evidence for it.

The more nuanced types caution against wishful thinking influencing this opinion and I share their caution (not condescension, I don't have any qualm with reporting accusations of fraud and in case you haven't noticed this thread started with an attempt to support that conclusion through statistics).

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I don't think there is anything wrong with media outlets pointing out that there have been accusations of fraud from within Iran since the polls closed.

Nor do I, but I do think there is a danger that the West will see what they want to see. Already in Lebanon the favorable (to the West) results are accepted without much fuss even though there are clear flaws in the democratic process there that allocate less weight to a Muslim's vote than a Christian's vote.

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I also don't think there is any reason to adopt a condescending attitude toward media outlets for reporting the information they have received rather than a recondite theory of numbers.

I can see why you'd want to corner the market on condescension given that it is your only stock and store but quite frankly I don't give a rat's ass what you think. You aren't very well informed on this subject and haven't anything useful to contribute in way of information. So you can spare your criticism for someone who cares about what you have to say.

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@Robert Gentel,

Robert Gentel wrote:

rosborne979 wrote:
It is an interesting method of analysis, but I think it's too abstract to carry much weight (unfortunately).

I think it's pretty straightforward, and the reservations I have about it have more to do with the extent of their sampling than the method itself.

What do you find abstract about it?

It's just that I imagine it would be difficult to argue with an Iranian leader that he should give up his power and position because the last two digits in various polling numbers didn't agree with predicted statistical standards. I suspect that argument would not be compelling.

Robert Gentel wrote:

If you meant that it wouldn't be something that would influence Iranian leaders I'd agree, but I'm just looking to settle the question for myself as to whether or not the results reflect the will of the Iranian people.

The Western media jumped to the conclusion of fraud right away, and I want to see more evidence about that. This is an interesting approach and there are other statistical analysis being done that I think are promising. If this kind of statistical analysis checks out, then I think it would be enough of a smoking gun for me to accept as evidence of fraud.

It's interesting that you place such a high value on statistical analysis.

For myself, I require a preponderance of evidence. No single source does it for me. And at this point I'm still not sure what happened over there, which is why I started my other thread to ask how voting fraud may have been done and how it can be hidden so effectively.

I have virtually no first hand information on anything in Iran, nor do I understand that area of the world well enough to feel confident proclaiming the results as fraud.

One thing I am convinced of however is that a lot of Iranians are very angry, and I figure they know their country better than I do. And that piece of information, along with a handful of other suspicious aspects of the vote count (including what you have listed above), as well as an inherently flawed verification process in place over there (the Guardian Council) make me think that the election results are probably (but not definitely) inaccurate.

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@rosborne979,

rosborne979 wrote:

It's interesting that you place such a high value on statistical analysis.

Well I did said "if it checks out". I can't buy the claims made in the article without a lot more research than I have time for right now (thankfully I am following some smart folk who do).

There was an earlier claim for statistical evidence of fraud based on Benford's Law that I didn't find very convincing. Here's the paper on it:

BENFORD’S LAW ANOMALIES IN THE 2009 IRANIAN PRESIDENTIAL ELECTION By Boudewijn F. Roukema [pdf]

And here is a very good analysis of it's relevance by Nate Silver that contributed greatly towards my rejection of it as a form of evidence. Even so, it was an interesting hypothesis because it tied together with another bit of evidence (about the turnouts being greater than 100% in many cities).

So I don't know whether the claims they made in the article I posted this thread about check out they seem to on the surface but these kinds of things often are spoiled by "gotchas" that weren't immediately obvious (at least in my experience). However if they are correct in saying that the results they analyzed should only happen 4% of the time naturally I would find it compelling evidence, together with the rest, that it is likely to have been fraudulent.

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For myself, I require a preponderance of evidence. No single source does it for me. And at this point I'm still not sure what happened over there, which is why I started my other thread to ask how voting fraud may have been done and how it can be hidden so effectively.

I'm leaning toward fraud based on the other bits of evidence I posted to your other thread, and frankly I am a lot more suspicious about statistical analysis being able to conclusively say whether it was fraud one way or another than anything else in this election. I've seen miracles where such conclusions are teased out of the data but this is a case where there's just not much of the data itself to work with.

But the biggest reason statistical analysis can't be conclusive is because it simply can't rule out many kinds of fraud. They could just switch the names on the results for very natural numbers that would conceal the fraud against statistical analysis nicely.

However I have seen statistical analysis give very solid conclusions about fraud using similar techniques, and I know it can be done. I just am not very hopeful that it can in this particular case. But if their claims check out, and the odds of these results being natural are 4% I would take that into consideration and yes it would be the last straw that leads me to believe that fraud did occur.

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One thing I am convinced of however is that a lot of Iranians are very angry, and I figure they know their country better than I do. And that piece of information, along with a handful of other suspicious aspects of the vote count (including what you have listed above), as well as an inherently flawed verification process in place over there (the Guardian Council) make me think that the election results are probably (but not definitely) inaccurate.

I am cautious against bias on the part of the Iranians as well. They were distributing a very dubious-looking document that purported to be a letter to Khamenei with the "real" results and they too might be engaging in wishful thinking as well. Maybe the progressives have just had enough of the regime while still being in the minority and due to the lack of political transparency are lashing out at the validity of the results.

In many such political systems with little transparency the losing party alleges fraud almost invariably. Hell, even in the US you'll have huge swaths of people who believe in fraud at times even with all the checks and balances we have. I can just as easily envision this anger taking place with or without fraud if the narrative that the educated metropolitan folk were outnumbered by the rural folk is true.

But you bring up a good point here, in that they are angry and don't feel adequately represented and maybe that's all that matters. If enough believe it was illegitimate then that may just create the facts on the ground. I for one wouldn't mind if the regime finally cracks over this accusation even if it wasn't true.

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@Robert Gentel,

What evidence do you have that "most of the Western media believe fraud to have occurred?" You seem to wilfully ignore the distinction which i made between reporting that there has been fraud, and reporting that there are allegations that fraud has occurred. If you have something to back up that claim, i'd be interested to hear it.

The remarks about the Lebanon are not germane to a discussion of whether or not fraud can be shown by a statistical analysis. You might note that i have not challenged that claim, because you have not really developed it. As for your snotty remarks about condescension, it shows the force of your argument that you'd rather make personal reflections on my character and behavior than to back up your claims. You could start by showing that "the western media" clearly believe that fraud has occurred. I'm not denying that is the case--i am saying that absent proof, you have no case. But before that, i was saying that i haven't seen the evidence of it, making a distinction between claims that fraud has occurred on the part of western journalists, and reporting by western journalists of claims that fraud has occurred. If you can come up to scratch on your claim about western media, it might redeem your otherwise puerile response.

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While essentially doing RG's leg work for him, which is to say while looking around to see if there were an anecdotal basis for stating that clearly the western media believe there was fraud--i came across an interesting article at CNN-dot-com.

Was the Iranian Election Rigged?

I can't speak to the issue of whether or not CNN as a western media organization "clearly" considers that fraud has occurred. I will note that this page quotes the source, Amir Taheri, saying more than once that he cannot prove fraud. It would seem to me that if CNN at least had an interest in alleging that fraud had occurred in the Persian elections, they would have been more careful about quoting someone who believes it, but acknowledges that he cannot prove it.

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Another article on the same subject is Statistical Evidence for Iranian Election Fraud?. It has a link to a description of Benford's Law on the distribution of initial integers in lists.

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If the Supreme Leader is really the person that has the power, what is the concern about a President that may be a titular head of state? It seems to me that the protests might be some sort of mass denial that Iran is not a democratic country. Meanwhile the centrifuges are going. And, the military might be getting ready for some other country's effort to prevent Iran from going nuclear? How much of this is just diversionary theater?

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@Setanta,

Setanta wrote:

What evidence do you have that "most of the Western media believe fraud to have occurred?"

I can't prove what they believe unless they choose to state it, but I've read a couple hundred articles from the press in the last few days on the subject and my impression is that the majority do believe that fraud occurred even while admitting they lack specific evidence for it.

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You seem to wilfully ignore the distinction which i made between reporting that there has been fraud, and reporting that there are allegations that fraud has occurred.

I've never claimed they have failed to report responsibly, I just think the preponderance of articles examining "why the results might be fraud" and the paltry few examining what evidence exists to the effect that it was not a fraud indicate what they find more plausible. I haven't kept a strict count but in my readings I'd estimate that it is more than 90/10 in fraud's favor when it comes to the open speculations.

Sure, they don't come out and claim they know it to be fraud but I never claimed they did, and I never claimed I have any problem with them reporting the reports of fraud.

I am merely very interested in getting as much information as I can so that I can make my own decision. It is not about "condescending" to the media for me, no matter how much you wish to make it so.

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The remarks about the Lebanon are not germane to a discussion of whether or not fraud can be shown by a statistical analysis.

I never claimed anything of the sort. So your reply is "not germane to what I have posted".

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You might note that i have not challenged that claim, because you have not really developed it.

I clearly state that I have severe doubts about the election being able to be shown as fraudulent or not by statistical analysis so it is probably a good thing that you didn't jump the gun on this too and try to get me to argue it.

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As for your snotty remarks about condescension, it shows the force of your argument that you'd rather make personal reflections on my character and behavior than to back up your claims.

No, it shows the dim view I hold of you based on how you interact with others here and my own lack of self-control in expressing my distaste for you. It has nothing at all to do with the "force of my argument". I just think you are a jerk.

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@Setanta,

Setanta wrote:

Another article on the same subject is Statistical Evidence for Iranian Election Fraud?. It has a link to a description of Benford's Law on the distribution of initial integers in lists.

In an earlier post I link to a very well-explained refutation of this analysis by Nate Silver that you might be interested in.

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@Setanta,

Setanta wrote:

While essentially doing RG's leg work for him, which is to say while looking around to see if there were an anecdotal basis for stating that clearly the western media believe there was fraud--i came across an interesting article at CNN-dot-com.

Was the Iranian Election Rigged?

I've read that article dozens of times (because of the way CNN does their updates to the same damn article and because I have been searching and landing on it from different urls0, I have no qualm with it. It was useful speculation about the possibility of fraud that launched a lot of my research.

If you want anecdotal evidence then you might consider that the others who have come to the same conclusions as I have in regard to the "wishful thinking" I spoke of. Hell I just put in "iran wishful thinking" in Google and was able to unearth similar views:

'Extraordinary Amount of Wishful Thinking' by US

http://www.spiegel.de/international/world/0,1518,630552,00.html

Wishful thinking from Tehran

http://www.guardian.co.uk/commentisfree/2009/jun/13/iranian-election

Iran Vote: Fraud or Journos' Wishful Thinking?

http://www.alternet.org/blogs/world/140625/(updated)_iran_vote:_fraud_or_journos%27_wishful_thinking/

But like I've already said, I can't prove that the majority of the Western media believes there was fraud because there are simply no scientific polls asking their opinions as of yet. I have seen some polls (though none that I consider scientific) already showing that the West in general largely believes there to have been fraud but until someone polls the media I just won't have the data on what they personally believe.

What leads me to conclude that they largely accept that narrative is that the Western coverage has speculated endlessly about the fraud with lots of "top ten reasons the results are suspicious" articles and I have yet to see one such list of why the results shouldn't be and when trying to decide for myself as to the legitimacy of the results I am having a much harder time finding devils advocates to the fraud scenario. The speculation has been pretty one-sided in my own reading.

I too lean towards fraud but that is the narrative that I, and the West, wants to believe but it is my nature to be deeply skeptical, especially when I perceive bias. I was not condescending to the media, and I don't really care to try to prove the bias I see in their coverage so much as simply get as much information as I can for myself out if it and play devils advocate against the bias I perceive to ensure I don't adopt it myself. This, if it stands scrutiny, would be a compelling bit of evidence to me and I wanted to share it and discuss other statistical models that might shed light on the probabilities of the results being natural.

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The last digit analysis has proven very useful on assesing not only electoral fraud, but also the possible scale of the fraud.
It doesn't prove that the protesting candidate won, but this would call for new elections in any respectworthy nation.

Now even the mullahs have found an excess of 3 million votes.

For them now it's either repeat the elections and lose or get a bloody revolution, hold a while and lose, after a huge bloodshed.
They'll choose the latter.

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@fbaezer,

My surmise as well.

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The Devil Is in the Digits - Statistical analysis of the Iranian election results

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