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Benham's law is related solely to the frequency of digits appearing in data. Its shape is a function of the base of the number system, and the probability of each digit appearing. Originally it was derived from large sets of data where the points are randomly distributed over a power law function.

So the X-AXIS values have no physical meaning, they are just the digits 1 - 9. The Y-AXIS is the number of times that the digit appears in the set of measurements. In this case, the measurements are the number of votes for each candidate.

The reason I asked for FReepers with statistical analysis skills to look at this data is that we should be able to see if the distribution of digits in the polling place data is reasonable. In other words, are we really seeing the measurement of the voter's actions, or are we seeing the result of fraudulent activity.

I posted another analysis earlier of what values were present in the last two digits of the precinct data from the 478 precincts in Minneapolis. In that case one would expect a nearly random distribution of values, but the 00 value appears 14 times.

That may be just a statistical fluke, but figuring out the chance of that happening would be a worthwhile effort.

Doing similar basic analysis of data for consistency and reasonableness in contested areas would be a good idea.

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??