Tue 2024-Feb-27

Does Trump Pose a Danger to Courts, Jurors, and Witnesses?

Tagged: MathInTheNews / Politics / Statistics

Trump is facing a gag order in his NY trial, on the basis that he has previously threatened judges, clerks, attorneys, witnesses and jurors – including death threats. While this is obviously true, do we have objective evidence that this is the case? Why, yes: yes, we do.

Doomscrolling: A Bad Habit

A confession: I have a bad habit of doomscrolling.

(Yeah, I know: Long COVID-19 brain fog, then depression, and now doomscrolling. Somebody fix the world for me, please?)

Some of it is “technical” doomscrolling, where I fantasize that I can keep up with physics and statistics at the level I practiced before retirement. This is an impossible standard, and it is not good for me to hold myself to it.

But much of it is “doom” doomscrolling, looking at the polycrisis where it seems everything is falling apart. We deny that COVID-19 is still here, democracy is crumbling before stupid fascists, the deep ignorance of the US population is astounding (as in: they don’t know who the likely presidential candidates will be), abortion bans actually force doctors to be complicit in the murder of women in need of medical care, congressional Republicans conspire with Russian intelligence to sabotage US government with shutdowns and cutoffs of Ukraine weapons aid, and so on. This is also bad for me, though it still sticks in my head that it is the duty of a responsible citizen to be at least somewhat informed about these matters.

But most of all, I watch the agonizingly glacial slowness of the Trump trials. I want so badly for this guy to be in prison forever, disqualified from politics, and his followers utterly disillusioned with, and ashamed of, their fascist turn. Yes, this is schadenfreude. Yes, it is not a good look. No, I cannot resist.

In particular, I tend to watch the YouTube highlights of the previous night’s news programs on MSNBC: Stephanie Ruhle, Lawrence O’Donnell, Jen Psaki, Rachel Maddow, Joy Reid, Ari Melber, Joe Scarborough/Mika Brzezinski, and others.

About That Gag Order…

Today’s case in point came up in Lawrence O’Donnell’s “Last Word”, about 5 minutes into the “highlights” (the video to the right should start there). [1]

It seems that in Trump’s latest criminal trial, NY District Attorney Alvin Bragg has filed notice of a motion to request that Trump be gagged, i.e., prohibited from talking about the trial or the people involved, for the duration of the trial. This is because Trump has a clear and persistent record of threatening judges, their clerks, attorneys, and jurors. This results in death threats, people moving to secret places, and having to hire bodyguards.

O’Donnell’s talking about an affidavit near the end of a recent court filing, which we’ll get to below. But first, let’s have a trawl through the rest of the filing.

NY DA Alvin Bragg: Notice of intent to file motion for protective gag order Bragg’s filing [2] makes for interesting, if voluminous (331 pages!), reading. The gist, of course, is simple (emphasis in the original):

Defendant has a long history of publicly attacking individuals involved in legal proceedings against him, including witnesses, jurors, judges, and prosecutors; and those attacks are often followed by harassment, intimidation, and threats. (p 4)

Defendant’s history of attacks create a reasonable likelihood of witness intimidation, juror interference, and harassment of other participants in this criminal proceeding. (p 22)

He then provides ample, even damning, evidence that Trump’s spray of bile leads to his followers making credible attempts at murder.

That’s the first 35 pages.

There follow about 300 pages of exhibits, showing Trump’s social media posts, speeches, and books full of inflammatory statements from which follower violence predictably erupts. It’s the predictability that matters: Trump can’t claim he couldn’t predict what other people would do; he spoke out because he knew they would use violence on his behalf!

There are veritable pleas from a dozen or so jurors in other Trump cases not to release their personal details, because they and their families fear for their lives. Included are chilling images of the hand-scrawled, semi-illiterate death threats.

Example of obscene, racist, anti-Semitic threats left on Judge Engoron's chambers telephone Example of specific murder threat against DA Alvin Bragg There are also amazingly crude threats left on Judge Engoron’s phone, showcasing the foul-mouthed anti-Semitism, sexism, racism, homophobia and general insanity of today’s Republicans (see image here, one example from many on pp. 260-261). Other threats are specific, actionable, promises of murder even down to the choice of weapons and preference for a head shot (see image here, one example from many on pp. 270ff). There are many such examples.

No less chillingly, but more amusingly, we can see relevant extracts from Trump’s books (exhibit 11, pp. 304ff). (Side note: some poor schlub in the DA’s office drew the assignment of reading this sewage.) A few bits that justify gagging Trump for the duration of the trial:

When somebody hurts you, just go after them as viciously and as violently as you can. Like it says in the Bible, and eye for an eye. (p. 308, excerpted from Trump: How to Get Rich)

I love getting even when I get screwed by someone – yes, it is true, people still try to take me for a ride, and sometimes they succeed, rarely, but when they do I go after them. (p. 315, excerpted from Think Big)

To any sane person, this should be enough: numerous threats to maim, torture and murder along with Trump’s stated policy of encouragement of this. It’s happened so many times – apparently in the low hundreds of times, documented here – that Trump simply cannot blame this on others. He knows what he’s doing, and has written that this is how he operates.

Either you gag him, or gag orders are meaningless and can never be used again.

The Evidence: Statistical Significance & Strength of Effect

Yes, to any normal person that should be more than enough.

Pastilli affidavit: rate of threats against DA, pre-Trump vs post-Trump But then we come to exhibit 13 (pp. 316 - 321) [3], and it contains some hard data that is quite a doozy, statistically speaking. It’s only 5 pages, but… boy is it worth reading.

This is an affidavit by Nicholas Pistilli, a Sergeant in the NYPD, who is the commanding officer of the security detail (“Threats and Protection Unit”, or TAPU) for DA Alvin Bragg.

He has… thoughts. In particular, he has numbers, and there’s no better way to get nerdly attention than quantifiable stuff like this. He tells us in 2022 (pre-Trump) and 2023 (with Trump) the number of threats his group processed, and the number of those that were against the DA, his employees, or his family.

After 2023-March, the volume went up so much they had to ask for help from outside the unit protecting the DA. Also, the severity went up enough that in just the 3 weeks after 2023-Mar-20, they had to open several threat cases (basically referral for prosecution).

So, of course, we wrote an R script to analyze it! [4]

The Numbers and Estimates of DA Threat Frequency

Here’s what we found from his affidavit, giving the frequencies of threats in 2022 (pre-Trump) and 2023 (after Trump proceedings began). He tells us the total number of threats, and the number of threats specifically against the DA, his employees, and their families.

We’ve marshalled his report into a table; for now just concentrate on the first 3 columns:

Year NThreats NDAThreats pDAThreat MedpDAThreat LCLpDAThreat UCLpDAThreat
2022      483          1    0.0021       0.0035       0.0005       0.0115
2023      577         89    0.1542       0.1550       0.1271       0.1860

Note that the total threats go up by about a quarter (483 to 577), and that the DA-specific threats go up a lot (1 to 89). We can get a rough measure of the probability that a given threat will be made against the DA by:

\[\mbox{pDAThreat} = \mbox{NDAThreats} / \mbox{NThreats}\]

We see in column 4 that this measure went from 0.21% before Trump to 15.5% after Trump, a very, very sharp increase by a factor of about 73 times!

Bayesian Posterior Estimates of the Distribution of DA Threat Probability

We can also, briefly, think like a Bayesian. Start by considering the probability $p$ that a given threat is specific to the DA. Well, that’s a random variable, so we can ask how it’s distributed.

  • Before seeing any data (a “prior”), we choose a uniform distribution, i.e., we’re indifferent and think $p$ could be anything in $[0, 1]$.
  • After seeing some data (a “posterior”), we find from Bayes Theorem that $p$ should be distributed according to a Beta distribution, with parameters calculable from the counts ($N$ = number of threats, $k$ = number of those that are DA-specific) by some trivial arithmetic: $ p \sim B(k + 1, N - k +1)$.

Uniform prior, posterior Beta distributions for probability that a threat is a DA threat Those distributions are shown here. (Columns 5-7 of the table above report the median and the 95% credibility intervals, as discussed here and shown on the plot.)

  • The blue curve shows what we should think about $\Pr(p)$ pre-Trump.

    The 1 case in 483 threats gives us a pretty low value, as shown by the blue curve saying most of the evidence indicates a low probability near 0. In fact, the posterior median estimate is $p \sim 0.4\%$, with a 95% credibility interval/confidence limit of 0.1% – 1.1%.

    That is, we’re 95% sure the true value of the probability that a threat is directed at the DA is somewhere between 0.1% and 1.1%.

  • Now consider the red curve, which covers the Trump period, i.e., $\Pr(p)$ post-Trump. It’s centered on a much higher value.

    In fact, the posterior median is $p \sim 15.5\%$, with a 95% CL of 12.7% – 18.6%.

This is clear visual evidence that the probability a threat is directed against the DA went up, and dramatically, after Trump was indicted and inflaming his followers.

Frequentist Analysis: Statistical Significance Testing & Strength of Effect

The relevant test here is a test of proportion, whether the 1/483 is different from the 89/577 in the pre-Trump and post-Trump years. The null hypothesis here is that the proportions are equal; our choice of alternate hypothesis was that the pre-Trump rate was lower.

The data rejects the null hypothesis, i.e., this is excellent evidence that the Trump era included more DA-specific threats:

	2-sample test for equality of proportions with continuity correction

data:  threatData$NDAThreats out of threatData$NThreats
X-squared = 76.416, df = 1, p-value < 2.2e-16
alternative hypothesis: less
95 percent confidence interval:
 -1.0000000 -0.1253086
sample estimates:
     prop 1      prop 2 
0.002070393 0.154246101 

The reported $p$-value of $2.2 \times 10^{-16}$ is just the smallest the R user interface will report without embarrassment. If you dig inside the test report, the actual value is $1.1 \times 10^{-18}$. Either way, this is ridiculously statistically significant: the effect is real, and there is no doubt that the DA threats went up after Trump came along.

Statistical significance tells us whether an effect is real, and it is. But to see whether it went up by a little or a lot, we need a parallel strength of effect analysis. For that, we resort to the Cohen’s $h$ statistic, which is the relevant strength of effect measure for proportions.

Cohen's h |       95% CI
0.72      | [0.60, 0.84]

The interpretive rule here is that $h \sim 0.2$ is a small effect, $h \sim 0.5$ is a medium effect, and $h \sim 0.8$ is a large effect. At $h \sim 0.72$, we’re either a very solid medium effect size, or just on the verge of a large effect size.

The effect is both real (statistically significant) and rather large.

The Weekend Conclusion

There’s extensive, and damning, evidence of threats of kidnapping, torture, and murder against judges, clerks, attorneys, and jurors.

The numbers show unequivocally and objectively that the rate of DA-specific threats went up dramatically. The difference statistically significant, i.e., real. Objective effect size statistics also show that it is a pretty large effect, i.e., actually dangerous.

Trump should be gagged.

Ceterum censeo, Trump should be incarcerated pending trial. [5]

Notes & References

1: L O’Donnell, “Lawrence: NYPD affidavit details threats after Trump’s ‘arrest’ post”, MSNBC YouTube channel, 2024-Feb-27.

2: AL Bragg, “NOTICE OF MOTION FOR AN ORDER RESTRICTING EXTRAJUDICIAL STATEMENTS”, Filing with Supreme Court of the State of New York, County of New York, Part 59, Indictment No. 71543-23, 2024-Feb-22. Archived here 2024-Feb-27, for future reference from original location, in case it gets ‘disappeared’ somehow.

3: N Pistilli, “Exhibit 13: Affidavit”, included in ref [2], pp 317 - 321.

4: Weekend Editor, “R script for analyzing Trump’s probability of threatening a DA”, Some Weekend Reading blog, 2024-Feb-27. There is also a transcript of running this, for you to compare to make sure we’re being honest about what it reports.

5: Not a fan of Cato the Elder, but I’m beginning to understand his frustration with political foot-dragging to avoid dealing with a clear and present danger to the republic.

So… Ceterum censeo Trump incarcerandam esse!

Published Tue 2024-Feb-27

Gestae Commentaria

Comments for this post are closed pending repair of the comment system, but the Email/Twitter/Mastodon icons at page-top always work.