Benford's Law

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Benford's Law in the 2020 presidential election.png

Benford's Law is a principle of statistics discovered in 1938 which states that in a naturally occurring collection of numbers, the size of the leading digit (1 or 2 or 3, etc.) occurs with decreasing frequency starting with 1. Specifically, the number 1 will appear as the leading digit roughly 30% of the time, the number 2 less so, and on down to the number 9 which will appear as the leading digit only 4.5% of the time.

This law is often used in forensic accounting to determine if fraud has taken place, and has been accepted in criminal cases as evidence.

This law is useful to determine if fraud has taken place in an election, such as the United States Presidential Election of 2020, where Benford's Law helped detect fraudulent votes for Biden in the key counties of Allegheny County, Pennsylvania, Chicago, and Milwaukee (in Wisconsin).[1][2] This law also helped analyze suspected fraud in the Iranian election of 2009.

This logarithmic distribution of the leading digits has been observed in numerical tables since at least 1881 (then by Simon Newcomb).