Does Benford's Law work for "election data"? There are certain sets of data pulled from elections where Benford's Law could apply. The number of votes received in a precinct is not one of them. Benford's law for the first digit would not work. Benford's law for the second digit would not work. There isn't any controversy. There isn't any doubt. There isn't any serious debate.
I think Benford's Law can be used in this type of case. Because that is exactly what I did when I started reading about this.
But you have to apply it correctly. In looking at precinct data, what you get is a Benford curve combined with a bell curve. You have to adjust the Benford curve based on the number of possible magnitudes and then overlay the bell curve with appropriate weight.
I did this. Unfortunately I did not save it because there has just been too much. I have had way to many election-relate files going on and I ditched everything.
I had taken one of the counties where it was claimed Benford proved election fraud. I overlaid an adjusted Benford curve and an expected bell curve based on poll predictions. Well, sort of. The math is a bit beyond my ability, but I could approximate it with algorithms. Then I compared that to the actual numbers.
The results were uncanny.
This was a heavily Democratic county, so the poll predictions were about 65% Biden to 35% Trump. The average county size was a little under 1,000 with ranges from about 300 to 1,700.
For Trump, that would mean basically never going over 1,000. And some in single, double, and triple digits. So it should be mostly a Benford curve. But the curve of the actual count would be at about 300, which would mean for leading digits an overlaid bell curve going from 1 to 4 with a peak at 3. That means a prediction of a Benford curve that is accentuated higher in the lower numbers with an odd bump at 3. And that is exactly what is was.
For Biden, he could get over 1,000 in a number of precincts resulting in a higher number of leading digits of 1, but no other numbers. Very little chance of single or even double digits. So, not much of a Benford curve. Mostly 3 digit numbers peaking around 6 to match the projected vote count. But some Benford. With a bump at one for the over 1,000 votes. And that is exactly what it was. A bell curve peaking at 6, but a bit lower on high numbers and a bit higher on the lower numbers due to the overlay of the Benford curve, and a big number for the the ones because of the over-1000 possibility.
It is really creepy. I had no idea you could do things like this. But you have to do it correctly and not just apply a single basic formula. But when done right, it is spooky how it can match a certain curve in ways that you would not expect.