Benham’s law just captures the probability phenomenon that populations are log-normally distributed in nature. At least in the natural sciences, this phenomenon is undisputed: with a sufficient sample size of a representative* population, log-normal distributions are expected.
To answer your question, the chance of ANY of these three Biden distributions happening in a representative* population asymptotically approaches zero. Such significant deviations from the log-normal distribution (orange bars) are virtually unheard of in nature UNLESS the population has been manipulated. That Biden’s data in ALL three of these cities fails to follow inarguable statistical distributions found everywhere in nature is a HUGE red flag to me that fraud is unequivocally present.
Does anyone have the raw data used to produce these plots? The meaning of the binning is still fuzzy. I really don’t understand your statement that the “measurements (Y axis) are the number of votes for each candidate.” Simplifying bin 1 of the Biden Milwaukee plot, does it mean Biden got 1 vote in 60% of precincts when he should have only received 1 vote in 40% of them??
Benham...Benford...
Per the description I received, the y-axis value in Bin 1 is the percentage of precincts across that state where the vote tally started with a “1”.
The analysis just looks at the reported numerical values for each precinct. As an example, if precinct A reported 1200 votes for President Trump, and 3900 votes for Joe Biden, the size of the bar in the chart for President Trump for an X value of 1 would increase by 1 unit.
Similarly, in the chart for Joe Biden, the size of the bar in that chart with an X value of 3 would increase by one unit.
The analysis just looks at a set of numbers to see how they relate to an expected pattern found in many instances. The original physical meaning of the data is unimportant.