How Benford's Law Indicates Fraud in 2020 Presidential Election

There have been several allegations of election fraud in the 2020 presidential election, which caused one statistician to look at the numbers.

He took data from several precincts in Milwaukee in the critical swing state Wisconsin and analyzed them against a statistical model called Benford’s law. Benford’s law predicts that various sets of real-life numerical data will follow a specific pattern: the leading digit (in a three digit number like 372, the lead number is the 3) of the number has a roughly 30 percent chance of being a 1. It has a roughly 17 percent chance of being a 2, a roughly 12.5 percent chance of being a 3 and so on.

This is what you would expect in naturally-occurring numbers and a quick spot check on web traffic statistics from this website demonstrates this:

Out of this small dataset of 12 numbers, 10 of the leading digits are 1 (83.3%), one is 3 (8.3%) and one is 5 (8.3%). This makes sense because any digit in any column has to be 1 before it can be 2 and has to be 2 before it can be 3, so the lower the number, the greater likelihood.

This predictive model applies in several real-world situations including vote counts. And comparing vote tallies against what Benford’s law would predict can give an indication of election fraud.

As recently as 2016, Benford’s law has been used to determine if elections were fraudulent. Amid allegations of electoral fraud in the 2016 Russian elections, an article co-written by Kirill Kalinin and Mebane in The Washington Post observed that the mean of the second digit of the number of voters in each of the country’s 96,869 electoral precincts was equal to the expected mean (4.187) per Benford’s law. In addition, the mean of the last digit of the votes in each precinct for the triumphant party, United Russia, was equal to the expected mean (4.5) per Benford’s law. On the basis of other indicators of electoral fraud, Kalinin and Mebane suggest that these “perfect” statistics show that those responsible had deliberately rigged the votes to conform to the expectations of Benford’s law.

As you can see, Benford’s law (in red below) predicts fairly well what the distribution is like for the vote tallies for various candidates in Miami-Dade and Fulton Counties for the 2020 election:

But what these statisticians discovered was that the model breaks down in certain swing states, but not for every candidate, just for the Biden/Harris ticket.

In Milwaukee, Chicago, and Alleghany, PA, Benford’s law is predictive for every candidate except for Biden:

This is the Trump and Biden Milwaukee numbers compared a Benford’s projection in a line graph:

If these data are accurate, they would indicate a higher chance of data manipulation or fraud with the Biden numbers.

The name of the Post article mentioned about was “When the Russians fake their election results, they may be giving us the statistical finger.” It’s apropos because the distribution graph on the fraudulent numbers looks like the computer sticking up its middle finger. If there was fraud in the 2020 US presidential election, the perpetrators may have been doing exactly that to the electorate.

Sources

“Benford’s Law.” Wikipedia, Wikimedia Foundation, 7 Nov. 2020, en.wikipedia.org/wiki/Benford’s_law.

cjph8914. “cjph8914/2020_benfords.” GitHub, github.com/cjph8914/2020_benfords.

Kirill Kalinin, Walter R. Mebane. “Analysis | When the Russians Fake Their Election Results, They May Be Giving Us the Statistical Finger.” The Washington Post, WP Company, 18 Apr. 2019, www.washingtonpost.com/news/monkey-cage/wp/2017/01/11/when-the-russians-fake-their-election-results-they-may-be-giving-us-the-statistical-finger/.

Statsguyphd. “11 – In the End, Biden’s Vote Data from That Page Is Far More Anomalous than Trump’s. Here Is What It Looks like Visually: Pic.twitter.com/7qPivR9zQX.” Twitter, Twitter, 5 Nov. 2020, twitter.com/statsguyphd/status/1324356583304974339.