Posted by Jay Livingston
Political scientists Bernd Beber and Alexandra Scacco have a simple test for electoral fraud in the Iranian election. Here are the results from Qom
- Ahmadinejad . . . . .422,457
- Karroubi . . . . . . . . . . 2,314
- Mousavi. . . . . . . . . .148,467
- Rezaee. . . . . . . . . . . . 16,297
But Beber and Scacco were interested in the right-most digits, the ones that we might throw out and round to zero. Here’s why:
When people try to make up numbers that appear to be random, they show certain preferences. Try it yourself. Think of any random number from 0 to 100. I’ll wait. Got your number? O.K. Chances are it’s an odd number that does not end in 5. More than likely, it does end in 7.*
In an honest vote count, about 10% of the final digits should be fives, and 10% should be sevens. If five is underrepresented, and if seven is overrepresented, someone is trying to make up numbers and have them seem random.
Beber and Scacco looked at the 116 results (four candidates x 29 provinces) and . . .
The numbers look suspicious. We find too many 7s and not enough 5s in the last digit. We expect each digit (0, 1, 2, and so on) to appear at the end of 10 percent of the vote counts. But in Iran's provincial results, the digit 7 appears 17 percent of the time, and only 4 percent of the results end in the number 5. Two such departures from the average – a spike of 17 percent or more in one digit and a drop to 4 percent or less in another – are extremely unlikely. Fewer than four in a hundred non-fraudulent elections would produce such numbers.
In a second test, Beber and Scacco also looked at the last two digits.
Psychologists have also found that humans have trouble generating non-adjacent digits (such as 64 or 17, as opposed to 23) as frequently as one would expect in a sequence of random numbers.Sure enough, the totals had fewer non-adjacent pairs than would be expected, especially in the province totals for Ahmadinejad. The two tests provide a fairly persuasive case for what most people think anyway – that the vote totals reported by the Iranian government were fabricated.
Beber and Scacco report their research in the Washington Post here.
*Street magician David Blaine uses this same tendency in one of his mind reading tricks. A lot of people pick 37.
Hat tip to Joshua Tucker at The Monkey Cage, which has links to the electoral data.