The Devil Is in the Digits, an op-ed by Bernd Beber and Alexandra Scacco in Saturday's Washington Post.
This piece claims that the distribution of insignificant digits in vote totals in the recent Iranian election look funny, and that there's a good chance this is because the numbers were made up.
I haven't looked at the numbers myself, but this seems like an avenue worth pursuing.
A random walk through mathematics -- mostly through the random part.
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7 comments:
I suspect the Iranian results are false, but the statistical arguments given in that article reek of postdiction effects.
As Carl, above, says.
So the question is this: If the statistician only looked into these 2 measures, and discovered the described abnormalities, then the likelihood of fraud is very, very high.
If the statistician looked into a large number of potential disparities and reported these because they happened to be the farthest from expectations, then the article is bunk.
If you look at 20 things and find 2 abnormalities, that's normal. If you look at 2 things and find 2 abnormalities, that's interesting.h
Gelman's blog (well, there are a few other contributors there, but Andrew Gelman is the main poster so I think of it as "his") discussed this stuff in a couple of posts on the 20th
http://www.stat.columbia.edu/~cook/movabletype/archives/2009/06/the_devil_is_in.html
and then the followup
http://www.stat.columbia.edu/~cook/movabletype/archives/2009/06/combining_findi.html
The followup has some interesting discussion of detail from the authors of teh piece
I'm almost embarrassed to admit that I'm coming around to suspecting that the Iranian election results were approximately correct. And that the complaints about them being false are politics (and diplomatic maneuvering) as usual. The absence of a free press is an obvious problem with Iran but maybe not electoral irregularity.
Postdiction effects also apply when a large number of people look at the data and apply various tests to it. Only the ones who find significant results publish it. The problem has hounded elementary particle experiments for decades and now is taken quite seriously.
In a US presidential election, I have to choose 30 or 40 candidates for various offices among maybe 200 or 300 total. Of course it takes a long time to count. Iran's elections are simplicity itself. One election with maybe 6 choices. Of course they can count those quickly without any need for technology.
When I taught calculus, I found it was important not just to grade the tests fairly, but to mention how many points I deducted for various errors. This makes the student realize that they have been graded fairly. They are much happier.
Iran should use some similar technique. I saw students burning stuff in the streets. When we did this in my youth (in the US) some of us also got shot. Kent State.
To have people shouting "death to" slogans is a pretty strong indication that someone has failed to understand human nature. Humans, especially youth, are ridiculously over concerned with fairness and the authorities need to take this into account.
Carl:
(a) We're long past the point where it matters whether the results were correct (though even if you disregard the low-order digits reasoning there's still the demographics to contend with). The problem now is that when the people stood up to say they didn't have faith in the system, the system told them to kindly go f*** themselves. The people's response (translated into Brooklynese) is "No, f*** YOU!" Whether the results are accurate or not, people need to believe that they're accurate.
(b) "Death to" is a classic mistranslation. Yes, the phrase they use literally means "death to", but idiomatically it's more like "down with". Or did you think that the protesters in the 1960s were literally calling for sexual intercourse with swine?
@CarlBrannen - You're absolutely right about postdiction; go look at the authors' previous work on Nigerian elections. They use the same technique but look at a different metric (not one number higher than X% and another lower than Y% in the last digit). If the authors had seen two overly frequent numbers in the last digit, they would've written the same editorial. It's trivial to extend this to dozens of apparent paradoxes, and I've got some great hidden prophecies in the bible to show people who believe this.
By their logic, every plane crash is an act of terrorism because the odds of a plane randomly crashing at that time and location are incredibly low. You can't see a rare event, calculate how unlikely it would be, and claim that's the probability that it arose from a random process. The 0.005 probability in the article is intended to convince people that those are the odds that the election was fair (beyond that, it's not even the right number -- it should be 0.0015).
I hope the authors are actually studying misguided accusations of election fraud as a means to support revolutionary movements and not planning on becoming involved in actual election monitoring.
Look at the penultimate digit in their McCain/Obama 2008 data. It should be uniformly distributed by the same logic, and it fails their "test" even more severely. It's also got a wider standard deviation (and standard error).
All that said, the Iranian results are bogus simply because of the rules of the game if nothing else. There's no reason beyond saving face with those it governs for the government not to have a new, monitored election... and that's a good trade-off for not having to kill a few thousand people to maintain your hold on power.
A look at some philosophical implications of the study is here:
http://www.analyticpolitics.org/2009/06/devil-is-in-statistics.html
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