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Comment by corpMaverick | Hacker News Reader

Benford's Law has been widely criticized as a technique to detect election fraud. A political scientist wrote a paper describing a variation. http://www-personal.umich.edu/~wmebane/pm06.pdf He used some data from the 2006 election in Mexico just to illustrate the proposed technique.

The paper has been used extensively by critics of the election as a proof of fraud. But they haven't been able to prove fraud any other way. The paper was never meant to be used as a strong proof of anything, it was mostly exploratory.

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Several years ago, I was chatting with a forensic accountant in a pub, and he was explaining about the use of Bendford's law in their work. I'd never heard of the law before, which is partly why it piqued my curiosity at the time. He explained that it was often used as a very quick sniff test for them, but not as proof of innocence or guilt.

Given the relative ease with which it could be calculated and analysed, it essentially became the first thing that they'd do once they'd got hold of the books. They'd do a quick analysis of the numbers, look at the distribution, and then use the outcome to give hints at where something unusual was going on. In his experience some 70-75% of the time, if Benford's law suggested something was odd, it was actually odd.

The 2004 Venezuela referendum is proved to be fraudulent without using the Benford distribution (it is not a law). On that election the opposition votes where invented based on the number of signatures requesting the recall vote per voting table, yet these same votes follow Benford quite well. On the other hand the government votes not only not follow the Benford distribution but have a flat (uniform) distribution.

What I am trying to say is that the Benford distribution is very useful, but it is not a definite proof of anything. It can point you to where you should dig deeper.

For more info about the 2004 Venezuela fraudulent election see: http://esdata.info/pdf/medina-es.pdf (Spanish) http://esdata.info/papers

Benford's law does not apply to unary systems such as tally marks.

Does that mean Benford doesn't work for counting things like votes or people?

This site tests Benford's Law on 30 different public datasets.

http://testingbenfordslaw.com/mexico-population-by-county

Looks to me like Benford works just fine for tally-type data like votes and populations.

Per your example. The numbers fit the population by municipality. Probably because the counts span several orders of magnitude. Some have millions (e.g Delegaciones in Mexico city). Some have hundreds( e.g Oaxaca ) However voting places are roughly the same size.

> Benford's law does not apply to unary systems such as tally marks. > Does that mean Benford doesn't work for counting things like votes or people?

Follow the links in the bit you quoted. It means numbers that are represented in a particular way, not those that represent the number of a particular thing.

Isn't Benford's law just a phenomenon that indicates fit to a power law distribution? I'm probably missing something, but why not just try to fit the data to a power law and use the goodness of fit as the measure?

> sn't Benford's law just a phenomenon that indicates fit to a power law distribution?

I think so. From the wikipedia article...

> Benford's law tends to apply most accurately to data that are distributed uniformly across several orders of magnitude.

In this case they are using the second-digit Benford's law. Which just makes it more mysterious. At least to me.

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