Benford's law for fraud detection

[magna carta]

Does this have enough creds to be used in a court setting

[aposiopetic]

Pinging here too

[CommerceComet]

What is “naturally occuring” about vote counts? They are generated by man, using purely deterministic processes...

The phrase "naturally-occurring" eliminates man-made numbers like serial numbers, identification numbers, and other numbering systems where systematic alteration of the numbers might be introduced for identification purposes. For example, in a phone number, the first three numbers are a geographical indicator.

Numbers that represent measurements or simple counting are naturally occurring in this definition.

[Pearls Before Swine]

when fraud is not extinguished, it grows exponentially.

Is that why Benford's law is based on logarithms?

Just kidding. Agree with the comment.

[wintertime]

Why is the zero digit not listed?

I would think that would be important.

[Chaguito]

The Benford info may not be completely reliable, due to small sample size. It’s a lead, however.

[wintertime]

Ok, I have figured it out.

It is law governing **leading** digits, therefor this explains why there would be no zero.

[Stosh]

“Why is the zero digit not listed?”

It would be for a Benford’s analysis of a second or third digit (and those predictions exist as well), but not for an initial digit, because of course if zero is the first digit in a numerical value, it doesn’t really signify anything and it’s just discarded.

[Chaguito]

The x-axis is digit 1-9. The y-axis is the frequency that ted digit occurs at the first position of the numbers in the number set. The number set consist of all the tallies reported since 11/3/20 from the indicated voting precincts.

[freeandfreezing]

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.

[freeandfreezing]

Because they are actually definitely not random at all.

You sound like someone who is familiar with statistical analysis, so I urge you to start looking at the raw data published by the various election offices.

At the precinct level the actual count for any candidate has a random component, since the number of eligible voters in any precinct has a random component, and the number who turn out to vote does to.

As one example, I would expect that the turnout percentage by precinct would be a distribution around a mean, and certainly not a fixed, constant value.

The percentage of voters who choose a particular candidate in any precinct should also have some variability.

[freeandfreezing]

The Wikipedia article indicates that some courts have recognized analysis based on Benham's law for fraud matters.

It is just one tool that may be useful to determine if election results are likely to be legitimate.

At this point any FReeper with data analysis skills who has some extra time should grab some data and start looking to see if it appears legitimate.

[freeandfreezing]

Benham should be Benford - I can’t type tonight.

[SelfhatingMillennial]

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??

[SelfhatingMillennial]

Benham...Benford...

[DoodleBob]

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”.

[freeandfreezing]

The meaning of the binning is still fuzzy.

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.

[SelfhatingMillennial]

To see a graphical presentation of data and say the original meaning of it is unimportant is horrifying. This is how the media bamboozles data-ignorant America with plots, charts, and other half-baked statistics (exhibit A: everything related to COVID). Understanding WHAT is being captured in any graphic is extremely important, both for validating the legitimacy of the graphic (and its conclusions) and for being able to explain it to others.

For instance, a log-normal distribution IDENTICAL to the ones we’re talking about here could be created by plotting the birthdates of each precinct/ward captain using this bar chart distribution plotting method (except with bins 1-12). That data is obviously utterly meaningless, but the chart would tell the exact same story (at least as the honest Trump plots). Point being, WHAT is being plotted absolutely cannot be ignored. “Trust but verify” as someone famous once said, especially with pretty pictures.

Stepping down from my angry scientist soapbox (sorry), I now understand what is going on here, and the results are extremely compelling. I would like to know how many total data points there are, which I think would equal the total number of precincts/wards in each of the three cities. Curious if we’re talking tens or hundreds (probably not thousands) of individual election results. The more data points the stronger the evidence of fraud.

[Svartalfiar]

If you examine a large enough list of random numbers drawn from the range from, let's say, 0 to 999,999 then I would expect that the least significant digit would be distributed evenly; that is, there would be the same amount of each of the ten digits.

Except these numbers aren't randomly pulled from a list, they count, and they count up. Therefore EVERY count will start with a '1' at some point, but not every count will end up reaching a '9' for the same power of ten you end the counting in. That's why this works, if you start counting and are stopped randomly (what voting is, basically) every power of ten of votes (10, 100s, 1000s, 10Ms, 100Ms, 1MMs, so on) will fill in every chance to start with a '1', and each higher digit will be less likely to have been reached, but once you hit the XX999 and give each number an even chance to have been the final starting digit, the next count will go back to starting with a 1 and make that the most likely starting digit.

EG for your random result to be, say, 328, you will have had the opportunity to stop at 111 '1's (1, 10-19, and 100-199), 111 '2's (2, 20-29, 200-299), but only 39 '3's (3, 30-39, 300-328), and 0 '4'-'9's. Any 'random' number you pick, will always fill in the lower numbers' possibilities, but not the higher ones.

[Svartalfiar]

Please explain the PHYSICAL meaning of your description of the X axis. I’m an engineer and look at plots all day, but am befuddled by the X axis here. I don’t get the connection between precincts and 1- 9 scale. Probably over-thinking this...

It's not a connection between precincts specifically and the 1-9, it's the connection between the liklihood of counting numbers to start with a certain digit, and the fact that vote totals are a counting number. My post #59 gives some detailed example.