Too many 7s make 2 students certain that Iranian vote was rigged
Two PhD candidates at Columbia University have written a statistical review of the Iranian election results. According to the authors, their data suggest with 99.5% certainty that the reported voting totals for Iran's provinces were made up by a human.
The study uses the vote counts released by the Ministry of the Interior for 29 Iranian provinces. The authors focused on the final two digits of the reported totals for each candidate in each province. As the article explains, these numbers can indicate whether humans interfered in the final tallying of votes:
Why would fraudulent numbers look any different? The reason is that humans are bad at making up numbers. Cognitive psychologists have found that study participants in lab experiments asked to write sequences of random digits will tend to select some digits more frequently than others.
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.
Based on their analysis, which appeared on the Washington Post's Opinion page Saturday, the authors claim that the probability of Iran's election data being genuine is less than .005, or a 1 in 200 chance. Although some critics have expressed concern over the small sample data (116 numbers), the article certainly raises some interesting questions regarding the validity of Iran's reported election results.
The complete annotated article can be found here.
-- Brendan Bigelow
Photo: Iranian supporters of defeated reformist presidential candidate Mir-Hossein Mousavi demonstrate June 16 in Tehran. Credit: Getty Images