This joke-post is the kind of thing that should normally appear on The Babylon Bee satire site or similar, alongside such stories as “CNN calls Arizona 2024 for Biden” and “Trump locks himself in Oval Office, Swallows Key” (and I’d be only too pleased if they used any or all of mine gratis). However I felt we could all do with a little humour in these endlessly uncertain times. 🙂

=== BREAKING === BREAKING === BREAKING ==== BREAKING ===

**Breaking: Biden broke Benford’s Law**

In a controversial ruling, the US Supreme Court has found that Biden vote totals in key districts violate Benford’s law, which states that numbers the American people can be required to believe should start with 1 more often than 2, 2 more often than 3 and so on.

US liberals were not slow to denounce the court’s ruling. *“The crucial vote came from Amy Coney Barrett – the NINTH justice!”*, raged Alexandria Ocasio-Cortez. *“By Benford’s law, she should forbid us to believe herself.”* Replying, Justice Barrett said that 5-4 rulings were more in accord with Benford’s law than 9-0 ones, pointedly adding that she looked forward to many more such.

In a more nuanced version of AoC’s argument, a trio of California-based federal judges urged the decision be left to Justice Roberts (whose balanced, middle-of-the-road submission weighed the statistical improbability of the vote totals against the statistical improbability of orange hair in a president), on the grounds that Benford’s law should weight the first justice far above the ninth. However it was then put to them that, since they themselves served on the ninth circuit, these judges’ argument also overturned itself. Advised that the analysis of self-referential statements belonged to another, yet more abstruse, branch of mathematics than Benford’s law, one of the judges promptly shot himself in despair, while the other two endorsed Kamala Harris’ statement that the size of the supreme court must immediately be raised from the unacceptable number 9 to a more Benford-friendly total.

President Trump immediately went on televison to boast of being *“number one”* – but took the fifth when a New York Times reporter claimed that Trump’s true wealth violated Benford’s law. *“You tell the American people you are worth ten billion dollars, but I know from my secret IRS source that the true value is only nine billion!”* Meanwhile, Joe Biden also appeared on TV to explain that Benford’s law had no relevance to elections but, despite help from both his wife and the teleprompter, became hopelessly confused – which caused many Americans to say he was a good representative of the average guy, since Benford’s law confuses them even more than lockdown rules. (Later, professors at the University of California presented a statistical analysis demonstrating that counts of Biden’s gaffes obeyed Benford’s law, which therefore showed that whatever he had been trying to say was the truth.)

Elsewhere in academia, Professor Lawrence Tribe, expert in constitutional law, pointed out that there was no mention of Benford’s law in the constitution or any amendment. *“I find it disgusting that biased justices feel they can casually re-‘interpret’ the constitution to suit modern ideas. This law was not even suggested until a century after the constitution was ratified, and not given a mathematical proof till over a century after that. The founding fathers never even imagined such a thing!”*

The NeverTrumper ‘Lincoln Project’ denounced the ruling’s indirect endangering of the 9th amendment (which says that the enumeration of certain rights in the consititution shall not deny or disparage others retained by the people) as a typical example of the way in which Trump’s “pyrrhic” victories were defeats for true conservatism, and promised to spend the vast sums they raised in this election cycle on overturning the result.

LATE UPDATE: The New York Times has published a special insight article on Benford’s Law, explaining that mainstream media’s calling of the election for Biden came first, so outweighs the USSC ruling, which came second. It is rumoured that social media giant Mark Zuckerberg tried to agree – but was censored by the Facebook algorithm he put in place days ago to suppress any mention of Benford’s law. Here in the UK, media concurrence was marred by a Guardian article’s repeated references to ‘Bentham’s law’, suggesting they thought the USSC had ruled that Trump’s re-election would made for the greater net happiness – which, Guardian commenters said, was not the case for them.

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So much for satire. Anyone who would rather have had a serious discussion of Benford’s law can start with this intuitive example, then look at this application of it to huge amounts of data. (The really keen can download these Excel-oriented DIY instructions.) FWIW, my earlier comment on the story that prompted this is here.

[ADDED LATER: for those who read the comments and follow their links, it is worth being aware that Benford is normally used on the first digit of the data, but Mebane used it on the second digit (different ratios, as 0 is now included) and uses the more demanding ‘false discovery rate’ test, not just ordinary chi-squared (I agree with checking the higher bar of the FDR). The issues of the technique’s value at various granularities, and usefulness beyond identifying *some* places to look further at, are prudent to be aware of. (Returning to humour, it is also ‘prudent’ to be aware that Mebane himself was swift to go on the web and deny everything the moment the question arose of applying this to the Trump 2020 election instead of to the Bush elections of 2000 and 2004. The man holds an academic post, which he would doubtless rather retain – another thing it might be prudent to be aware of. 🙂 )]

Douglas Adams’ masterpiece The Hitchhiker’s Guide to the Galaxy was prescient, it seemed as if it was written with certain American judges in mind, e.g. in a copyright dispute, my emphasis added:

And we have the running software issue which seems to transmute Trump votes into Biden votes, across many States. (Around the 9 minute mark).

Sorry, but I’ve been running a question on Quora regarding Benford’s law. The comedy is there, but mostly in the denials.

https://www.quora.com/Some-election-observers-have-noted-that-certain-Biden-results-violate-Benfords-law-and-thus-should-be-viewed-with-suspicion-How-much-weight-do-you-put-on-statistical-evidence-of-election-fraud

Confirmation that at all levels minds have been made up and nothing is going to change them.

Also that it appears possible to make a plausible case for Benfords, to the tiny extent that I understand it, supporting whatever pre-held opinions one happened to hold.

These elections seem more to exemplify Conquest’s Three Laws. The first law, of course, is that everyone is conservative about what he knows best. This says a lot about the Left.

Murphy’s law

couldbe invoked.But of all the laws I’ve considered, Catch-22 seems to best satisfy Benford’s Law.

“Sorry, but I’ve been running a question on Quora regarding Benford’s law.”I thought the only interesting comment there was the one starting: “Here’s a somewhat contrived example to explain Benford’s Law, as it is being misused here.” It points to the way Benford’s law arises as the result of samples being taken from many different random distributions that collectively have to have a certain “scale-unbiased” or “base-unbiased” property. (See here for the proper maths.) If for some reason the distributions in the different wards are not unbiased in this way, then Benford’s law would be violated.

I consider the objection highly speculative – the commenter doesn’t show that the distributions are indeed biased in this way. His suggestion that precincts having similar-sized populations would lead to this I don’t think is right, and he doesn’t offer any other reasons for thinking it should be. But I’d not consider it a done deal until that technical debate has been worked through. And it’s going to take considerable mathematical expertise to even understand what the argument is about.

By the way, I found a link to the Milwaukee data and confirmed for myself that Benford’s law was violated.

Two questions come to mind:

1. did anybody apply Benford’s Law to previous US elections?

2. if so, what were the results?

I’d like to see someone run an analysis of past elections and how Benford’s law is preserved within them, paying attention to elections that had now-known fraud as a significant component.

Without that practical application, all most of us non-mathematicians can do is take sides and memorize their arguments without understanding.

“I’d like to see someone run an analysis of past elections and how Benford’s law is preserved within them, paying attention to elections that had now-known fraud as a significant component.”I’ve not read the paper, but the abstract seems relevant.

https://www.jstor.org/stable/23011436?seq=1

Great minds, and all that . . .

Certainly does, facially at least. Coin-toss territory? Guess I’ll have to steel myself and read it. Whether I understand it or not . . . .

“I was told there would be no math . . . “

One question for the mathematical illuminati:

If we assume that Benford’s law works as offered, does it indicate in which direction the fraud worked?

bobby b (November 8, 2020 at 5:32 pm), this PDF includes Benford’s law use in various reviews of US votes. (It does not make too many concessions to non-mathematical readers.) You would probably know better than I how to track down legal cases where it was used as evidence.

Nullius’ link is to a 2011 paper challenging use of Benford, which has itself been challenged.

Thank you NiV … but i was wondering specifically about the US context. I was wondering more specifically whether there was a comparable amount of fraud in 2016, but Trump did not bother because he won!

Previous elections are also of historical interest, of course.

We do have some evidence that, in some counties, Biden’s votes were made up, while Trump’s votes follow Benford’s Law. (Link is the same as the 1st link in the OP.)

That in itself does not mean that the fraud worked in Biden’s favor — but combined with the fact that Biden won those counties, it DOES mean exactly that. (Although i am not yet sure that the evidence is conclusive.)

Another qualification: that Trump’s votes follow Benford’s Law does not prove that Trump votes did not disappear: subtract a random number from Trump’s votes in each precints, they would still follow Benford’s Law. At least, that is my intuition: mathematicians might want to investigate this further.

For the original spoof, without the warning that this is satire, Poe’s law would be kicking in in spades.

For lack of a better place to put this, here’s an interesting article on how election litigation might proceed (if you have any interest in the legal arcana of the situation.)

https://macris.substack.com/p/how-might-election-fraud-get-litigated

A good example of voter fraud to start off with would be the 1982 gubernatorial election, Jim Thompson for the GOP vs. Adlai Stevenson III for the Dems. The Cook County Dems went all out to close the 10% gap, and were found out.

https://sites.duke.edu/pjms364s_01_s2016_jaydelancy/files/2016/04/Report-of-the-Special-Grand-Jury-US-District-Court-NE-Illinois-.pdf

What structural changes have been made since then to improve the voting process? Cos from where I stand, there doesn’t seem to be any.

I’ve been an election official in Sg, a lowly poll station officer, but even then I could be justifiably proud of our tight security procedures and handling. Sealing of the boxes with stickers once voting is done, tight security as we follow the boxes to the counting station, with further police escort.

No such thing as boxes appearing out of nowhere! Even the number of boxes at each polling station must be accounted for and tallied at the counting stations with observers on hand.

FWIW, Scott Adams said on his Periscope broadcast last Friday, I think it was, that he seems to have become a sort of rallying point for a large number of guys who, as he described them, are high-functioning autistics who really understand data and how to analyse it. They’re beavering away at the data and they are finding anomalies, apparently.

there was a comparable amount of fraud in 2016, but Trump did not bother because he won!Trump did try to launch an investigation into possible fraud in the 2016 elections. He claimed there were votes by undocumented immigrants (those who have no right to vote).

He demanded that the states hand over documentation about the election so that a Federal committee could investigate. The states refused, claiming that running elections is within exclusive authority of the states. Needless to say that the states who refused had Democrat administrations.

Hmm, as illustrated in Mystery Men: “We are number one! All others are number two or lower!”.