Iran’s Election Results: “The Devil Is in the Digits”
Jun 20th, 2009 | 4 responses
We have all heard by now of the allegations of massive fraud in the counting and reporting of the recent election results in Iran.
There is telltale “suggestive evidence” that tends to confirm such allegations:
* The unrealistically high votes for Mahmoud Ahmadinejad in urban areas, including Tehran and Tabriz where he is not very popular.
* The surprisingly poor performance by opposition candidates in their own home cities and provinces.
* The “eyebrow-raising” consistency, according to the Washington Post, “in Ahmadinejad’s vote share across Iran’s provinces, in spite of wide provincial variation in past elections.”
But, is there any statistical evidence to corroborate these suggestions?
And, is the Iranian regime really that stupid as to believe that its massive fraud would go unnoticed and unchallenged?
The Washington Post’s answer to the first question is “Yes.”
My own answer to the second question is also “Yes.”
My answer is totally speculative and perhaps flippant.
However, The Washington Post’s answer, as posed today in an eye-opening article by Bernd Beber and Alexandra Scacco, Ph.D. candidates in political science at Columbia University, is based on data, statistics, probabilities, and even psychology.
In “The Devil Is in the Digits,” they agree that the suggestive evidence does point “in the direction of fraud, to be sure,” and that such evidence has “led experts to speculate that the election results released by Iran’s Ministry of the Interior had been altered behind closed doors.” But, more important, that “we don’t have to rely on suggestive evidence alone. We can use statistics more systematically to show that this is likely what happened.”
And they certainly do, using cognitive psychology, statistics and, specifically “frequencies of last digits” and “the lack of non-adjacent digits” in the vote counts, to support their conclusion that:
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.
Whether you are statistics or numbers-inclined, or not, read the persuasive analysis provided by these two bright Ph.D. candidates, who will be assistant professors in New York University’s Wilf Family Department of Politics this fall.
Upon reading, and whether or not you agree with my answer on the Iranian regime’s naiveté, I believe you’ll agree that there is at least some statistical evidence to corroborate the strong suggestion of election fraud in Iran.
Image Courtesy realestateofftheleash.com
4 Responses to “Iran’s Election Results: “The Devil Is in the Digits””
[...] Iran’s Election Results: “The Devil Is in the Digits” | The Moderate Voice DORIAN DE WIND [...]
The article is definitely interesting, but the statistics are bogus unless there's some specific reason to expect one high-frequency number and one low-frequency number in the last digit in a fraudulent election. Thousand-to-one “patterns” appear in any similar set of 116 random numbers. Go check out the 2008 election results that the authors use here as an example of the expected result in a non-fraudulent election. Look at the second-to-last digit in the election Wikipedia entry for Obama and McCain; 20% of these 102 numbers are 7s and only 5% of them are 8s. This is less likely than the pattern identified in this article (1.5% chance) but that doesn't mean that there's a 1.5% chance that the election was stolen.
Interesting. Perhaps the authors may want to comment on this.
Honestly I doubt they would. If you look at their earlier work, they applied a different statistical test to elections in Nigeria – there they looked for an overabundance of the numbers 1, 2, and 3 and an a lack of higher numbers in the last digit. They also looked for fewer than expected repeated digits in the last an penultimate digits. They didn't find any problem with nonadjacent digits in Nigeria.
Anyone with a passing familiarity with statistical tests (which generously describes my knowledge) knows that you can't change your test to fit the data. The fact that they used a different test in this work than in their previous work is solid evidence that they saw lots of sevens and few nines in the last digit and then set about calculating the probability of that occurring. That doesn't fly.