Thursday, July 2, 2009

Human Number Generating Flaws

Chris Lloyd reviews some evidence that the Iranian elections may have been fraudulent. Here is one of his surprising points:
Humans are especially terrible at generating random numbers. And for a large voting count, for instance 325911 which was Ahmadinejad’s count in the region of Ardabil, the last few digits should be essentially random. On the other hand, if someone were making the numbers up and not concentrating too hard on the unimportant final digits, you might expect to see some tell-tale signs of non-randomness in the those final digits.

This idea is due to Alexandra Scacco and Bernd Baber who have suggested that there is indeed such evidence in the data. They claim that human generated random numbers tend to have too many 7’s and not enough 5’s. And looking at pairs of digits, they claim that human generated digits will have too many adjacent sequences such as 23 and 76.
Another cool numerical phenomenon is Benford's Law, which is that in lists of numbers from real life sources of data, the leading digit is the number one almost one-third of the time. Detecting crime and fraud in a quantifiable manner is really sweet.