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Other fun I've had with Benford's Law.

1. Spotting odd things in MPs' expenses: http://blog.jgc.org/2009/06/its-probably-worth-testing-mps.h...

2. Spotting odd things in BBC executives' expenses: http://blog.jgc.org/2009/06/running-numbers-on-bbc-executive...

3. The Iranian election: http://blog.jgc.org/2009/06/benfords-law-and-iranian-electio...

4. New Age mumbo jumbo: http://www.jgc.org/blog/2008/02/any-sufficiently-simple-expl...



Benford's law does not apply to some of those things! In particular not to expenses.

Benford's law only applies to things that experience exponential growth, things that obey a power law distribution, and things that are totals of random processes.

Expenses are none of those.


Benford's Law has for some time (years, in fact) been used to look for anomalies in expenses and other corporate financial data: http://www.journalofaccountancy.com/Issues/1999/May/nigrini


It's going to apply to anything that has a probability distribution that is monotonically decreasing at any rate, exponential or not.

This is pretty obvious: the probability of the number 1 will be greater than the number 2, and so on up to 9.

The probability of the range 10-19 will be greater than the range 20-29, and so on.

The probability of the range 100-199 will be greater than the range 200-299, and so on.

And so on... The probability of the ranges starting with "1" will always be higher.

Also, I have no idea why anyone would think this is "arcane". It's very simple and obvious and a good example of where intuition can go wrong.


How could expenses not have a power law component to their distribution? Sometimes you're buying an expensive thing, and sometimes a cheap thing, and you don't buy something between $999 and $200 dollars nine times as often as you buy something between $199 and $100.


If you have a 40$ meal limit on your expence reports you would expect to see a lot more 3X$ meals than 1X$ meals.


Yes, you will certainly get artifacts at the top of what you can expense. You will probably also get distortions at the bottom where you'll have some threshold of "not worth expensing." There will almost certainly be distortion around the boundaries, but as long as you have a big enough range you should be able to see a Benford's law effect in the middle.


It applies to most quantities that can be represented in multiple units or where no unit is a natural one.




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