‘Iran’s election was fixed,’ say number crunchers - June 22, 2009
UPDATE: Some are now questioning the maths behind this analysis. See: John Graham-Cumming, Times.
It is widely acknowledged that humans are very bad at making up random numbers. If we weren’t we wouldn’t have invested so much time in developing random number generators.
Now some work by political scientists Bernd Berber and Alexandra Scacco, of Columbia University, suggests that fact hasn’t reached certain key individuals in Iran. As the country struggles with the violent aftermath of its recent hotly contested election, Berber and Scacco say the results of that election seem highly suspicious.
They used the results published by the Ministry of the Interior and examined the last two digits of the votes reported for the four main candidates.
“The numbers look suspicious,” they report in the Washington Post.
There are far too many 7s, for a start, and not enough 5s. Such results would occur in fewer than four in 100 non-manipulated election results, they write.
That would not rule out Iran’s election being fair. But Scacco and Berber go further. They note that previous work has proven that humans have trouble generating “non-adjacent digits”, ie: 27 as opposed to 23, or 36 rather than 34. Non-manipulated results should be approximately 70% non-adjacent digits; Iran’s results are 62% non-adjacent.
The probability of that happening in a fair election is less than 4.2%, they write.
Their conclusion:
Each of these two tests provides strong evidence that the numbers released by Iran’s Ministry of the Interior were manipulated. But taken together, they leave very little room for reasonable doubt. The probability that a fair election would produce both too few non-adjacent digits and the suspicious deviations in last-digit frequencies described earlier is less than .005. In other words, a bet that the numbers are clean is a one in two-hundred long shot.
In other Iranian election news, the New York Times says that authorities have acknowledged that the number of votes cast in 50 cities exceeded the number of actual voters in said cities.
Image: last two digits from election results / source: Wikipedia
Comments
There was a minor error in the calculations of Beber & Scacco. The correct probability for the combined tests is not 0.005, but 0.0013. I pointed this out to the authors, and they concurred. See further the update at Discover Magazine:
http://blogs.discovermagazine.com/discoblog/2009/06/22/update-irans-numbers-even-fishier-than-previously-reported/
Posted by: Douglas J. Keenan | June 24, 2009 02:31 PM