I love small little math-related factoids that explain the way the universe works through statistics. There's a lot of that in Anathem, if you've read it. And I love this piece in the Washington Post that demonstrates the likelihood of fraud in the Iranian elections - not by examining voter patterns, political ideology, or ballot methodology - but by examining how bad people are at making up random numbers. So cool.
Stumble This
Reddit!
Read Anathem? Cover to cover bro. Just kidding. Dude, the thing is coming out like late August according to Amazon. How'd you read it? This one of those sneaky Brit tricks? Furthermore it's 1000 pages. Anything that can't be written in less than, say, 500 pages isn't worth saying.
Beber and Scacco said, "We expect each digit (0, 1, 2, and so on) to appear at the end of 10 percent of the vote counts."
That is the last thing we expect. That would be a dead giveaway that the numbers aren't random. A result like that would be more unlikely than their example of too many sevens and not enough fives. Which does prove their point that randomness is not instinctive for humans, even human Ph.D. candidates.
"Beber and Scacco said, "We expect each digit (0, 1, 2, and so on) to appear at the end of 10 percent of the vote counts."
That sounds reasonable to me, assuming you have enough votes counted. Can't prove it though.
E, it sounds reasonable to most people, because we know that before the event each digit has an equal chance of appearing. But an unmanipulated series of counts will not distribute evenly over the ten digits. The problem with the Iranian counts is not that they vary from the mean, but the extreme degree by which they vary from the mean.
Later in the article they talk about the McCain/Obama variation from the 10% mean: "The frequencies of last digits in these election returns never rise above 14 percent or fall below 6 percent, a pattern we would expect to see in seventy out of a hundred fair elections."
"But an unmanipulated series of counts will not distribute evenly over the ten digits."
Not perfectly evenly, but if you pick a number 1-10 randomly, with each having a equal chance of being picked, and you record enough (beacoup) trials, I'd expect they'd come out *roughly* equal. In the same way if you flipped a fair coin 1000 times in a row you'll have strings of heads or tails but overall you should be *close* to half heads, half tails. That's my understanding.
That said, they examined 116 numbers. In which case having some numbers show 17% of the time doesn't seem surprising. You're right.
My head hurts.
I agree while you wouldn't expect them to be completely evenly distributed, given enough trials the divergence from equal distribution indictated the likelihood of fraud. Is 116 a large enough sample size? I suspect the answer is yes, but that's not about what your gut tells you, it's what the formula requires to be able to derive a significant result.
Speaking as a non statistician but as a magician, I can confirm one contention in a this story, because a preponderence of sevens is exactly what you get when you ask people a to select a "random" number between one and ten. Try it yourself - ask 20 ppl a number between one and ten, and see if more that 2 answer with a 7.
Maybe people in Iran live in groups of 7.
Best way to alter election results is to add to them. Add some factor of 1,000 to each district and you don't affect the final digits or the adjacent digits. You can even add strings of 7's and you'll just rotate the digits. And it's much easier. You can have your PC do it. For a country with the Bomb you'd think they would have figured that out.
I'm not sure they have the bomb per se, just the Holy Hand Grenade of Antioch