There is a body of science and psychology that deals with numbers that people choose when trying to create a random series. Hint -- they are rarely truly random and you can use statistics to see the difference. From the Washington Post, Bernd Beber and Alexandra Scacco take a look at the Iranian election returns:
The Devil Is in the Digits
Since the declaration of Mahmoud Ahmadinejad's landslide victory in Iran's presidential election, accusations of fraud have swelled. Against expectations from pollsters and pundits alike, Ahmadinejad did surprisingly well in urban areas, including Tehran -- where he is thought to be highly unpopular -- and even Tabriz, the capital city of opposition candidate Mir Hussein Mousavi's native East Azarbaijan province.
Others have pointed to the surprisingly poor performance of Mehdi Karroubi, another reform candidate, and particularly in his home province of Lorestan, where conservative candidates fared poorly in 2005, but where Ahmadinejad allegedly captured 71 percent of the vote. Eyebrows have been raised further by the relative consistency in Ahmadinejad's vote share across Iran's provinces, in spite of wide provincial variation in past elections.
These pieces of the story point in the direction of fraud, to be sure. They have led experts to speculate that the election results released by Iran's Ministry of the Interior had been altered behind closed doors. But we don't have to rely on suggestive evidence alone. We can use statistics more systematically to show that this is likely what happened. Here's how.
We'll concentrate on vote counts -- the number of votes received by different candidates in different provinces -- and in particular the last and second-to-last digits of these numbers. For example, if a candidate received 14,579 votes in a province (Mr. Karroubi's actual vote count in Isfahan), we'll focus on digits 7 and 9.
This may seem strange, because these digits usually don't change who wins. In fact, last digits in a fair election don't tell us anything about the candidates, the make-up of the electorate or the context of the election. They are random noise in the sense that a fair vote count is as likely to end in 1 as it is to end in 2, 3, 4, or any other numeral. But that's exactly why they can serve as a litmus test for election fraud. For example, an election in which a majority of provincial vote counts ended in 5 would surely raise red flags.
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.
They conclude that the numbers combinations seen would only statistically occur four out of 100 times. They then look at the McCain/Obama and the numbers there are 70 out of 100. There is a parallel study that looks at the first digits of a number -- Benford's Law is a fun read. An interesting example of its use in financial fraud detection can be found in this article from the Journal of Accountancy.
