Benford’s law and the 2020 election. A Limerick on fraud.

Elections and fraud in this nation

cannot stand a close observation.

Zero Trump votes are added

but Joe Biden’s are padded

an act of the left’s desperation

This is a map of the extent to which Dominion voting machines software is presently used. When votes are tallied it produces results that are not credible according to statistical science.

Joe Biden’s votes violate Benford’s Law, President Trump’s do not.

Benford’s law or the first-digit law, is used to check if a set of numbers are naturally occurring or manually fabricated. It has been applied to detect the voting frauds in Iranian 2009 election and various other applications including forensic investigations.

Benford’s Law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small. For example, in sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time. Benford’s law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.

Plots of the first digits of counts in various precincts and wards for selected counties/cities.

This is Pittsburgh.

But even cities where we know the outcome, the numbers have been manipulated such as

When this fraud is corrected the electoral map will look quite different, and may even swing a few house and senate votes.

Published by


Retired engineer, graduated from Chalmers Technical University a long time ago with a degree in Technical Physics. Career in Aerospace, Analytical Chemistry, computer chip manufacturing and finally adjunct faculty at Pennsylvania State University, taught just one course in Computer Engineering, the Capstone Course.

13 thoughts on “Benford’s law and the 2020 election. A Limerick on fraud.”

  1. Hello. Is it possible to do the graphs for MI? I do not believe for a second Biden won MI. Over night Biden pulled out like 300k votes while we were sleeping to take the lead. Before that, Trump was up over 10%. Thank you!

      1. Hi there,

        Thank you for this. I have a rough understanding of the concept, but it’s not clear what is being measured. Can you clarify what the frequencies stand for please?


  2. What produces the first digit whose frequency is being measured in the election results? I don’t understand what is being measured.

  3. Jimmy Carter said in 2009 that vote by mail was a bad idea and there would be wide spread fraud, looks like he was right.

  4. can really see the anomaly, the curve of total results not even close for Biden/Harris. Wonder what a 3d graph of results over time, say every 6 hours, for the first 4 days would look like? There would have to be an hour of day AHA! moment.

  5. I am afraid I don’t get the numbers. Could someone translate this into something that a layman like me can grasp? What does frequency of the leading digit mean in the context of ballot counting.

    1. First, Benford’s law is applied to audits … most auditor tool sets include it. Also, Benford was a Physicist studying mathematical theory of leading digits.

      “Specifically, in data sets, the leading digit(s) is (are) distributed in a specific, nonuniform way. While one might think that the number 1 would appear as the first digit 11 percent of the time (i.e., one of nine possible numbers), it actually appears about 30 percent of the time (see figure 1). Nine, on the other hand, is the first digit less than 5 percent of the time.”

      “The theory does not hold true for data sets in which digits are predisposed to begin with a limited set of digits. For instance, Benford’s Law will not hold true for data sets of human heights, human weights and intellectual quotient (IQ) scores.” I.e., many weights start with a “1” for example.

      “Benford’s Law is legally admissible as evidence in the US in criminal cases at the federal, state and local levels. This fact alone substantiates the potential usefulness of using Benford’s Law.”

      Interesting, huh?

      So, it is not “political”. It’s PHYSICS! Hooah!

      Election example, 2009 Iranian election.

      “Roukema noticed a strange anomaly in the votes for Mehdi Karroubi from the National Trust Party, who came in third place. He found that the number seven occurs as a first digit more often than would be expected by Benford’s law.

      He found that this anomaly occurs in three of the six largest voting areas and, moreover, that Mahmoud Ahmadinejad had a greater proportion of votes in these three areas than the others.

      Roukema concludes that this could suggest an error in the official count of around one million votes.”

      Above from:

      1. First of all, it’s not PHYSICS it’s mathematics *facepalm*. And guess what, just because it’s legally admissible as evidence, doesn’t mean for a second that it’s actually useful: see lie detector tests. Benford’s law is only useful in detecting election fraud under very particular circumstances; it does not fit everywhere (like Chicago)!
        Read the following from
        “This essay, however, argues that, despite its apparent utility in looking at other phenomena, Benford’s Law is PROBLEMATIC AT BEST [emphasis added] as a forensic tool when applied to elections. Looking at simulations designed to model both fair and fraudulent contests as well as data drawn from elections we know, on the basis of other investigations, were either permeated by fraud or unlikely to have experienced any measurable malfeasance, we find that conformity with and deviations from Benford’s Law follow no pattern. It is not simply that the Law occasionally judges a fraudulent election fair or a fair election fraudulent. Its ‘‘success rate’’ either way is essentially equivalent to a toss of a coin, thereby rendering it problematical at best as a forensic tool and wholly misleading at worst.”

  6. How many of the last 58 presidential elections has benford law shown no fraud? If it shows fraud for the majority of elections does that mean all of then have had fraud from one side or the other? Does this prove that election system needs to be changed at its foundation to eliminate fraud? What would satisfy benfords law using datasets for presidential election? Trumps and Bidens votes are dependent on each other. If trump got 10 votes and biden 5, there is no way for biden to get more votes, since the total votes is 15. If trump has all the 1’s, then biden can’t have the 1’s since they don’t exist for him.

  7. Since Bendford’s law is admissible in federal courts, do you know if it might be used by the Trump team for this election? I’ve seen a few references to it and the data look compelling but never hear if they intend to present it to a Federal judge.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.