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

Adds the obvious, hoping against that.

Elegant idea!

I suspected you might like it, has the ring of Levitt to it and that's an economist I bet you are a fan of.

I don't think the practical outcome of such an argument would change much if the argument was more compelling. Power, not deliberation would have a much greater influence.

That said, there's nothing wrong with the statistical reasoning. It's the same reasoning the FDA uses to establish that a new pharmaceutical is significantly more effective than a placebo would be. "Significant", as statisticians use the word in medical trials, means that a placebo would have a chance of less than 5% of curing the same number of people in this clinical trial. If that's good enough for us to bet our lives on the medication, why wouldn't we bet that the outcome of an election is forged if only 0.2% of clean elections would yield a statistical result like it?

Benford's law is irrelevant to this case, because it applies to the first digits of numbers in lists, which aren't uniformly distributed. By contrast, the statistical analysis Robert cited in the initial post concentrated on the last digits of the numbers for this very reason.

Indeed I like Levitt.

After reading the paper itself, which differs from the article mainly in that it contains references, the only qualm I can find is that the sample size is small.

I still wanna see someone else less lazy than me check the math though.

The sampling size is small, but the deviation from a normal distribution is large enough to make up for it. I see no mistake in their reasoning, and trust two political scientists to have a statistics program that crunches the numbers correctly for them.

My major point of mistrust is not the math, it's reporting bias. Professional, state-of-the-art statistics programs can have libraries with hundreds of canned tests for sanity-checking statistical data. Given enough strange things that can happen, some of them will. So for all we know, the authors could have run 200 tests and reported only the two whose outcome turned out to be suspicious. If that was the case -- and I have no opinion on whether it is -- the election could look flawed when it isn't, and we as readers would have no way of knowing.

Some folks on reddit (or some place I've read recently) expressed the same reservations about not disclosing tests that didn't deviate but I've got mixed feelings about whether that should affect my take on the results.

We already know that this could just be a coincidental outlier, and I imagine that many of the other tests not showing deviation is a result that is not mutually incompatible with fraud. Or put another way, without knowing what the other tests are, if this test shows that there's an X% chance of this result naturally occurring I'm not sure how other tests not showing abnormal results would refute that conclusion even while I understand how it would seem that much less remarkable of an outlier to have been discovered by brute force.

The conclusion that there has been fraud is irrefutable by statistical tests. A smart counterfeiter of election data could easily manipulate results in ways that don't leave any suspicious statistical traces. (Leave the insignificant digits unchanged to pass the Washington Post test; change the significant digits by a more-or-less constant factor to pass the Benson's law test, etc.) You can find evidence of fraud with those tests, but you can never find evidence of honesty.

PS: Now that I think of it, the attacks of Ed Felten et. al. on American voting machines would have passed the statistical tests in the Washington Post and in the blogs you cite. Did you follow what happened to the voting machine story by any chance?

So...you're saying the result IS fraudulent?????

No. I'm on the fence on whether it's fraudulent, because I don't know about the statistical tests the results have cleared, and hence have not been published in the Washington Post.

What I'm saying in my last post is that there's no way to prove statistically that an election was honest.

He's saying that you can't disprove fraud with statistical analysis because it's easy to commit fraud without triggering any outliers.

A very easy way is to just swap the names if you just need to change the winner. The assumption behind all the statistical analysis is that for some reason they didn't take care to do so, and some popular theories are that they didn't want a runoff (and therefore had a need to exaggerate the vote to a specific threshold) because Moussavi was a late bloomer who was surging in popularity near the elections and/or that they initially didn't care who won because they approve the candidates but became worried about Moussavi donning the mantle of reform and panicked.

But to answer your question, this statistical analysis can't prove it's fraud either. It can just state a probability of the result occurring naturally.

Looks like I was late with my reply, hadn't seen yours.

To answer your earlier question, I didn't follow the voting machine thing too closely. It was too technophobic a debate for me to enjoy, what with all the people against electronic voting itself.

Thanks guys...I can't sit long enough to read your posts properly...so gracias for the short versions.

It's a fascinating subject.

Oh, so ehBeth did squeeze you to hard with that hug, didn't she.

Only that the probability is so low, it's really unthinkable that it wasn't a fraud.

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I truly do not think there's a way to commit fraud and not being caught by numerical analysis. For instance, percentage distribution of votes can be bimodal, but the "high" mode cannot be around 100%. Then there's electoral dynamics: some regional change of trend is to be expected, but not a counter sway precisely in some opposition's strongholds.

Iranian electoral fraud was ill-thought. In order to get away with it, you rig elections almost entirely in the zones where you're strong, not everywhere, and you can't overcook the rigging. Ahmadinejad should've asked for advice from old PRI Mexican experts (called "racoons" over here).

More savvy from Fb. Thanks.

Let's keep my goddam back off any but one thread!!!

Interesting.
And sad.