More on Statistical Stupidity at SCOTUS

Yes, the nonsense in Texas AG Paxton's lawsuit is as bad as it first appeared

As I noted yesterday (here), Texas AG Ken Paxton's suit asking the Supreme Court to overturn the certified election results in GA, PA, WI, and MI (thereby throwing the election to Trump) purports to show that:

The probability of former Vice President Biden winning the popular vote in the four Defendant States—Georgia, Michigan, Pennsylvania, and Wisconsin—independently given President Trump's early lead in those States as of 3 a.m. on November 4, 2020, is less than one in a quadrillion, or 1 in 1,000,000,000,000,000. For former Vice President Biden to win these four States collectively, the odds of that event happening decrease to less than one in a quadrillion to the fourth power (i.e., 1 in 1,000,000,000,000,000^4). See Decl. of Charles J. Cicchetti, Ph.D. ("Cicchetti Decl.") at ¶¶ 14-21, 30-31. See App. 4a-7a, 9a. 11.

Although I had not yet read the Cicchetti Declaration when I posted my comments, I assured you that it did not, and could not, demonstrate what Mr. Paxton claimed it demonstrated, and that it was nonsense of the highest (or lowest) order, and I promised a more complete explanation once I had read Ciccheti's full analysis.

Well, now I have read it (see the Appendix posted here), and it's as bad as I knew it would be. [h/t Jonathan Adler]

Here is how that idiotic "one in a quadrillion" estimate was derived.

First, Cicchetti shows that if the voters in 2020 had the same Dem vs Rep preferences as they had in 2016, the chance that the results would show Biden out-performing Hillary Clinton to the extent reported in the certified results is virtually zero. That is correct. Here's his analysis.

"10. In 2016, Trump won Georgia with 51.0% of the vote compared to Clinton's 45.9%, with more than 211,000 votes separating them.  Clinton received 1,877,963 votes and Trump received 2,089,104. In 2020, Biden's tabulated votes (2,474,507) were much greater than Clinton's in 2016.

11. I tested the hypothesis that the performance of the two Democrat candidates were statistically similar by comparing Clinton to Biden.  I compare the total votes of each candidate, in two elections and test the hypothesis that other things being the same they [i.e., Clinton and Biden] would have an equal number of votes. . . . I can reject the hypothesis many times more than one in a quadrillion times that the two outcomes were similar.

Statistics textbooks and statistics professors love to state problems with reference to balls in urns, so we can restate what Cicchetti has actually shown this way:  Suppose you have many millions of balls in an urn; 51% of the balls are red and 45% of them are blue (the 2016 distribution). You now draw 5 million balls out of the urn (the 2020 election). The chances that 2.5 million of them (50%) would be blue is, indeed, virtually zero (one in a quadrillion).

So we can reject the hypothesis that Cicchetti testing: that "the performance of the two Democrat candidates [i.e., Clinton and Biden] were statistically similar [and] that other things being the same they [i.e., Clinton and Biden] would have received an equal number of votes." As he shows, the two performances are not "statistically similar." If the voting population in 2020 had exactly the same distribution of preferences it had in 2016, Biden could not possibly have out-performed Clinton as substantially as he is reported to have done.

Second, he demonstrates that if the population of voters using mail-in ballots had the same preferences as those voting in person, the chance the mail-in ballots could have turned the tide for Biden in the manner reported is also virtually zero. That is also correct.

"14. At 3:10 AM EST on November 4 the Georgia reported tabulations were 51.09% for Trump and 48.91% for Biden…. On November 18 at 2 PM EST, the reported percentages were Trump 49.86% and Biden at 50.14%.

15.  [T]he votes tabulated in the two time periods could not be random samples from the same population of votes cast…. There is a one in many more that quadrillions of chances that these two tabulation periods are randomly drawn from the same population.  Therefore, the reported tabulations in the early and subsequent periods could not remotely plausibly (sic) be random samples from the same population of all Georgia ballots tabulated."

That, believe it or not, is it.  (A) If the 2020 voting population had precisely the same party preferences as the 2016 voting population, Biden could not possibly have won; and (B) if the mail-in and in-person voters had precisely the same party preferences, Biden could not possibly have won.

Wow! Man bites dog!!  Who would have believed it!!  If the 2020 voting population had the same Repub/Dem split as it had in 2016, Trump must have won!! If mail-in voters had the same preferences as in-person voters, Trump must have won!! And if my aunt had four wheels, she'd be a motorcar!!

Dr. Cicchetti, in other words, has falsified two hypotheses that nobody in his/her right mind could possibly have believed might actually be true. Garbage in, garbage out.

I would remind Dr. Cicchetti—and, more importantly, Texas AG Paxton—that we periodically conduct "elections" precisely because voter preferences may change over time, and some people who voted for the Democratic candidate in one election might choose the Republican in the next, or vice versa. Were this not the case, I suppose we'd still have a Federalist as Chief Executive.  ["Your Honor, the chance that Thomas Jefferson carried Maryland in 1800, as has been reported, is less than one in 8 million billion quadrillion!!  (assuming that voter preferences haven't changed since the 1796 election …)"]

And I would urge Dr. Cicchetti to re-do his analysis, but instead of comparing Biden's performance to Clinton's he should compare Mitt Romney's performance in 2012 to Donald Trump's in 2016. This, of course, would prove conclusively that Donald Trump could not possibly have carried Pennsylvania or Michigan or Wisconsin (given voters' 2012 preferences) … one in a quadrillion!

And as far as the mail-in vs in-person distributions is concerned, only about 2.48 million pundits and prognosticators predicted, before the election, that mail-in ballots would likely skew Democratic. So there, too, Cicchetti's findings are hardly a surprise.

Dr. Cicchetti's analysis—for which, I assume, he was paid handsomely—is merely silly, irrelevant, and a total waste of time.

Attorney General Paxton, though, is another story; his use of Ciccetti's analysis is mendacious and misleading and, I believe, unethical.  Recall what the Motion he filed at the Court asserts:

The probability of former Vice President Biden winning the popular vote in the four Defendant States—Georgia, Michigan, Pennsylvania, and Wisconsin—independently given President Trump's early lead in those States as of 3 a.m. on November 4, 2020, is less than one in a quadrillion, or 1 in 1,000,000,000,000,000. For former Vice President Biden to win these four States collectively, the odds of that event happening decrease to less than one in a quadrillion to the fourth power (i.e., 1 in 1,000,000,000,000,000^4). See Decl. of Charles J. Cicchetti, Ph.D. at ¶¶ 14-21, 30-31. See App. 4a-7a, 9a. 11.

No, no, no, Mr. Paxton—that is most definitely not what Cicchetti demonstrates. You have omitted the critical qualifier: that probability is less than one in a quadrillion assuming the distribution of voting preferences is exactly the same in the two populations (mail-in vs. in-person voters).  If those distributions are not the same—and there is absolutely no reason to think they are—the Cicchetti Declaration says absolutely nothing at all.

In the long history of misuse of pseudo-statistics and probabalistic mumbo-jumbo, about which many books have been written (my personal favorite being "The Drunkard's Walk" by Leonard Mlodinow—highly recommended), this surely has pride of place. It is a disgraceful performance, and I would hope that the voters in Texas would take note.

And if, as several of the commenters on my earlier posting suggested, Paxton (who is currently under indictment for securities law violations) is doing all this just in order to get a pardon from Trump, that is—to put it mildly—a gross abuse of the power entrusted in him by the good people of Texas.