Read on Twitter
I’ve seen a few tweets floating around claiming a statistical technique called Benford’s Law proves the Biden campaign committed voter fraud in some key states. Thought I’d dig into the claim a bit. So…
A quick thread about math and voter fraud: (1/8)
A quick thread about math and voter fraud: (1/8)
In a lot of datasets, when we chart how often certain numbers appear as the leading digit, an interesting pattern emerges. We see 1 appear around 30% of the time, 2 appear around 18%, and so on. This tendency is called Benford’s Law. (2/8)
Now we don’t see this pattern in all datasets. It only happens when a few criteria are met. For example, the original data has to be positively skewed, meaning there’s more data on the right tail than the left one. (3/8)
What does all this have to do with voter fraud? Well, it turns out the number of votes a candidate receives per precinct tends to be positively skewed. So regions where a candidate’s vote totals don’t line up with Benford’s Law tend to raise eyebrows. (4/8)
But this is key! Voter fraud is not the only explanation for these anomalies. Thanks to the awesome power of computer simulations, we can generate a range of possible datasets and see which ones have more Benford-like qualities. (5/8)
Let’s say we use a log-normal distribution to approximate vote totals. We’ll give it a fairly tight standard deviation (I used sdlog = 0.5) and try some different means. Turns out, as votes/precinct enter the 200-range, leading digits becomes a lot less Benford-esque. (6/8)
Keep the simulation going, and you’ll find the Benford distribution doesn’t reemerge until around the 900-1000 mark. (7/8)
In other words, a candidate who runs strongest in areas with larger precincts probably won’t follow a Benford distribution. Given rural/urban voting tendencies, we shouldn’t be surprised Trump votes conform with Benford’s Law better than Biden’s do. (8/8)
