Benford’s Law By Chris Knight

Benford’s law is a mathematical construct which applies to much more than voting patterns, but applies to a wide range of phenomena:

https://en.wikipedia.org/wiki/Benford%27s_law#:~:text=Benford's%20law%2C%20also%20called%20the,life%20sets%20of%20numerical%20data.&text=If%20the%20digits%20were%20distributed,about%2011.1%25%20of%20the%20time.

“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. 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.

The graph to the right [see website] shows Benford's law for base 10, one of infinitely many cases of a generalized law regarding numbers expressed in arbitrary (integer) bases, which rules out the possibility that the phenomenon might be an artifact of the base 10 number system. Further generalizations were published by Hill in 1995 including analogous statements for both the nth leading digit as well as the joint distribution of the leading n digits, the latter of which leads to a corollary wherein the significant digits are shown to be a statistically dependent quantity.).

It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, and physical and mathematical constants. Like other general principles about natural data—for example the fact that many data sets are well approximated by a normal distribution—there are illustrative examples and explanations that cover many of the cases where Benford's law applies, though there are many other cases where Benford's law applies that resist a simple explanation. It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which is common in nature).

The law is named after physicist Frank Benford, who stated it in 1938 in a paper titled "The Law of Anomalous Numbers", although it had been previously stated by Simon Newcomb in 1881.”

 

https://www.inzichten.nl/contact/images/benford_law.pdf

 

“It has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unre- lated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that indi- vidually are without relationship are, when considered in large groups, in good agreement with a distribution law-hence the name " Anomalous Numbers." A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies. An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc. The equation also gives the frequency of digits in the second, third - place of a multi-digit number, and it is shown that the same law applies to reciprocals. There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.”

 

Now apply all of this to the US election:

 

https://www.naturalnews.com/2020-11-13-benfords-law-proves-biden-didnt-win-election.html

“ Though many are unfamiliar with it, Benford’s law is a computational system that has been used time and time again to unearth election fraud. It was used in the 2000 and 2004 presidential elections, for instance, as well as in the 2003 California gubernatorial election. It has also been admitted as evidence in criminal cases at the federal, state and local levels.

When plugging in data straight from the city of Detroit’s election results page, for instance, Benford’s law shows that something very unnatural occurred on the Biden side, while Trump’s side showed a natural distribution of votes.

In laymen’s terms, Biden’s vote totals do not make any logical sense apart from fraud. Using Benford’s law calculations, his final numbers in Michigan do not match at a 99.999% significance level, meaning they are obviously and almost undeniably fraudulent.

While a legitimate election would show a relatively even distribution of votes within the Benford’s law model, the 2020 election prominently shows an anomalous distribution of votes for Biden, even as Trump’s votes followed a normal distribution pattern that is suggestive of legitimacy and honesty.

“I conducted a Chi-test comparing Michigan’s precinct vote counts to Benford’s law and found that Biden/Harris votes returned a 0.000017% (statistically significant, especially with a very large sample) whereas Trump/Pence votes returned a score of 53.059791% and whilst looking at my data set I noticed there were 0 write-in votes in Michigan,” wrote an alt media reader who conducted these calculations himself using a Benford’s law spreadsheet.

“Very odd stuff.”

No, Joe Biden did not win Michigan

This would seem to serve as proof that the mystery ballots dropped off by suspicious vehicles in Michigan during the early morning hours of Nov. 4 did, in fact, skew Biden’s vote totals to the point that they show up as blatant fraud using the Benford’s law litmus test.

Keep in mind that any score below 0.05 using Benford’s law is considered to be statistically significant. This means that Biden’s score of 0.00000017 is very significant, and hopefully something that is brought up in the legal proceedings that aim for election fairness.

Since Benford’s law is widely considered to be sound science, the left will not have an argument against its use in cases like this, especially since the left is the so-called “party of science.” If Democrats are to remain consistent in their convictions, then they must take seriously these findings as they open a huge can of worms for Biden’s alleged election win.

When the courts dive into this and other mounting evidence, things could shift back in favor of Trump very quickly – and many are expecting this to happen in a matter of weeks, or even days. At least half of the country is now aware of the fact that the election results are not legitimate, which means the Democrat Party is going to have a whole lot of explaining to do.

“I don’t need Benford’s law to tell me that fraud and cheating was rampant in this election cycle,” noted one commenter at The Gateway Pundit. “Joe Biden said on video that Democrats built the biggest ‘voter fraud’ operation in history.”

“That comment by Joe is so arrogant and brazen,” responded another. “They think that their power is absolute and that nothing can be done about it. I hope they are wrong.”

https://www.youtube.com/watch?v=vIsDjbhbADY

https://www.tandfonline.com/doi/full/10.1080/00029890.2020.1690387

https://mathworld.wolfram.com/BenfordsLaw.html

 

 

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Monday, 04 March 2024

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