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Comment by blueintegral | Hacker News Reader

I thought this would just be an application of Benford's law, but they note in the beginning that using Benford's law doesn't work for elections (citing this paper: http://www.vote.caltech.edu/sites/default/files/benford_pdf_...)

Does anyone know why Benford's law doesn't work here but does work for other made up numbers in applications like accounting?

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Benford's law applies when the underlying distribution is approximately exponential. Because candidates with an exponentially small chance to win are not likely to run, it wouldn't make much sense for elections to have an exponential distribution. Much more plausible distributions are (truncated) normal or uniform, neither of which satisfies Benford's law.

I like to visualize it as throwing random darts at graph-paper that has logarithmic marks on both axes.

For Benford's law to apply, the numbers (the non-fabricated numbers) need to be coming from a source/distribution covering several orders of magnitude. The fabricated voting percentages are limited to between 0 and 100.

Raw vote totals then?

We ran a test for one of the problem sets in a course I was TAing. Raw vote counts did follow Benford's law in 2000 US presidential elections. We did not portray it as a tool to detect or disprove fraud, however.

Perhaps the sizes (number of eligible voters, and also number of people who actually voted) of the voting districts follows the law? Then you could take the total vote counts, and distribute them back to the candidates in a lot of artificial ways (e.g. always 50-50, a random percentage between 30 and 70, say) and probably obtain data that still follows the law.

Benford's law best applies to data that spans multiple orders of magnitude.

Isn't it that Benford's law applies when parts of data are being multiplied by other parts (like in most things in real world)? I.e. two uniform distributions multiplied together give a non-uniform distribution?

I have seen Benford's law applied to voter turnout, where the distribution could be expected to be closer to exponential (but still not truly, due to districting practices).

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