Thread by @jengolbeck

🧵Next week, you will see people using something called Benford's Law to try to prove election fraud.
⛔️These people are wrong⛔️
I am a scientist who has published on Benford's Law. Let me tell you what it is and why what they are doing is mathematically incorrect. 1/

Consider the 1st digit of a number (e.g. the 3 in 386). In lots of systems, the frequency of 1st digits follows a specific pattern. 1s are way more common than 9s. There's a formula that predicts it. For a first digit N, the frequency is log (N+1)-log(N). This is Benford's Law

All kinds of systems follow this. Lengths of all the rivers on earth. Atomic weights. Financial statements. Benford is so reliable it's admissible in court as evidence of fraud. If you want to know more, watch Ep 4 of Connections with @latifnasser on @netflix . I'm in it!

@latifnasser @netflix Benford's Law can detect fraud in some systems, but not elections. People have tried, but it is no better than random guessing. Here's an abstract from "Benford's Law and the Detection of Election Fraud": "PROBLEMATICAL AT BEST…WHOLLY MISLEADING AT WORST"
cambridge.org/core/journals/…

@latifnasser @netflix The reason Benford's Law doesn't work on elections, in part, is because there are certain things that must be mathematically true for it to work.
1. The numbers involved must be independent
2. They should span multiple orders of magnitude

@latifnasser @netflix Independence means the numbers don't depend on anything else. In elections, the numbers aren't independent.
Say we look at the Trump and Harris vote counts for each precinct. The # of votes each gets depends on the precinct size AND on the # of votes the other gets

@latifnasser @netflix If there are 1,000 voters in a precinct and Trump gets 600 votes, Harris's vote count can't be more than 400. It DEPENDS on the other two numbers. Benford's law doesn't work when there are these kinds of dependencies

@latifnasser @netflix Also, Benford's Law works when #s span multiple orders of magnitude (10s and 100s and 1000s and 10000s, etc). Precincts are all roughly the same size on purpose. So you don't get many vote totals in the small orders of magnitude or large ones. This makes it unlikely Benford works

@latifnasser @netflix In 2020, lots of Trump supporters watched that netflix show and got out excel and made charts like this to prove there was fraud. They were so so wrong. Let's look deeper

@latifnasser @netflix People incorrectly claim Trump votes follow Benford but Biden doesn't and thus there's fraud
They are wrong. NEITHER follow it…because Benford doesn't work on elections
For example, this post claims all candidates but Biden follow Benford
NONSENSE!
Look at all these deviations!

@latifnasser @netflix Benford's law isn't some general shape. It's a specific distribution given by the formula log(N+1)-log(N). Even if you reject the mathematical requirements for Benford to work, you can just do a statistical test. If you do, you'll see Trump doesn't match Benford in these cases

@latifnasser @netflix One guy claiming fraud in 2020 actually did this, found that neither candidate followed Benford, but then was like "but Biden doesn't follow it WORSE than Trump". That is absolutely not how Benford proves fraud. It's either totally statistically illiterate or intentionally lying

@latifnasser @netflix The people incorrectly trying to prove fraud are going to:
1. ignore the mathematical conditions necessary for Benford to work
2. refuse to run tests to show a statistical match to Benford (not that it would mean anything because of #1) and just show you a chart

@latifnasser @netflix And they are going to reject this thread and say "What about Walter Mebane?" (a scholar at Mich who studies this)
But these mathematically unsophisticated people will have failed to realize a few things. First, Mebane does SECOND digit Benford, seen here cambridge.org/core/journals/…

@latifnasser @netflix Second, Mebane applied his own methods to the 2020 election to show that the *correct* application of Benford does not find fraud. Here's his analysis (opens a PDF) www-personal.umich.edu/~wmebane/inapB…

@latifnasser @netflix You simply cannot use a first-digit Benford's Law analysis to prove election fraud, and even if it worked, the people applying it aren't even doing it right. Doing actual math and statistics requires very precise work, not just tossing some numbers into a spreadsheet

@latifnasser @netflix People get intimidated because Benford's Law sounds all mathy and obscure. Most people don't have the background to understand or challenge it. And it's intimidating because the liars get really mad and say mean things when you call them out

@latifnasser @netflix So bookmark this thread and if you see anyone trying to use Benford's Law next week, send them to me. My election-month hobby is good-faith, calm explanation of my statistical pet to seething mobs. I feed off their anger, secure in the knowledge that I can science and they can't

@latifnasser @netflix And if you want to check out any of MY work on Benford's Law (done correctly), here are the receipts:
journals.plos.org/plosone/articl…
journals.plos.org/plosone/articl…
firstmonday.org/ojs/index.php/…