Saturday, November 7, 2020

Vox Popoli: The attack on Benford's Law

Given that Wikipedia is already changing its tune on the reliability of Benford's Law in detecting fraud, it's obvious that those utilizing it to analyze the election results are right over the target. This Twitter thread shows how statistical analysis demonstrates that the excessively pro-Biden electoral counts are obviously fraudulent.

Which, of course, is why Infogalactic is a much better source of information on the subject:

Benford's law, also called the first-digit law, is a phenomenological law about the frequency distribution of leading digits in many (but not all) real-life sets of numerical data. The law states that in many naturally occurring collections of numbers the small digits occur disproportionately often as leading significant digits. For example, in sets which obey the law the number 1 would appear as the most significant digit about 30% of the time, while larger digits would occur in that position less frequently: 9 would appear less than 5% of the time. If all digits were distributed uniformly, they would each occur about 11.1% of the time. Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution.

Accounting fraud detection

In 1972, Hal Varian suggested that the law could be used to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions. Based on the plausible assumption that people who make up figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's Law ought to show up any anomalous results. Following this idea, Mark Nigrini showed that Benford's Law could be used in forensic accounting and auditing as an indicator of accounting and expenses fraud. In practice, applications of Benford's Law for fraud detection routinely use more than the first digit.

Legal status

In the United States, evidence based on Benford's law has been admitted in criminal cases at the federal, state, and local levels.