A genuine mystery

A week or so ago, a posse of Texas Democrats fled their legislative session in Texas to go to Washington, D.C. in order to deny a quorum needed for legislation to be passed.  Some legislation passed, but the most contentious pieces lacked the necessary quorum.  The Governor is threatening to keep calling new sessions until they return.  Or to arrest them and force their return.  There is a lot of theater going on.    

According to this source, 50 Democrat legislators joined the field trip as well as six staff members.  The Texas Democratic Caucus has claimed all 56 posse members were vaccinated.

The Republicans have had a field day with the hypocrisy after the Democrats posted a picture of a few dozen of them, maskless and not social distancing, on a private jet for their trip to D.C.  In conservative circles there has been some inside humor to the effect that AGW must not be so serious if it is acceptable to fly a half full private jet to Washington, D.C. for a field trip.  And lockdowns must also be irrelevant if the Democratic delegation is fine with no masks and no social-distancing.

But what followed has excited even more comment.  Six of the delegation of 56 (11%), have come down with Covid-19, apparently spreading it further at meetings held by the legislative desperadoes on Capitol Hill.  

What I have not seen is any commentary on that 11% infection rate among those supposedly already vaccinated.  

According to Vox, there is only a 0.003 percent chance of reinfection leading to serious conditions.  According to the Covid Symptom Study, there is only a 0.03% of infection at all.  Very crudely, there are some 80 million remaining unvaccinated adults and the rolling average daily rate of infection has been about 35,000.  0.04%.  

Which leaves us with a mystery.  All the Democrats were supposed to have been vaccinated.  The fact that they were maskless and not social distancing supports that assertion.  11% have already come down with Covid-19, fortunately none so far with serious symptoms.  We would have expected at most 0.03% to have become sick, not 11%.

How can this be?  The easiest answer is that the Texas Caucus was lying - they were not vaccinated.  And maybe that's all there is to it.  However, most of the posse are old enough for them to have been inclined to be vaccinated anyway regardless of partisan inclination or philosophy.  And then also, their behavior seems consistent with a belief that they were safe (presumably because of vaccination.)  Maybe some weren't vaccinated but almost certainly half would have been.  Heck, at least half of Republican legislators are vaccinated.  You would not expect less of Democrat legislators.  

We are left with a mystery.  All things being equal, I am perfectly comfortable assuming that the Texas Democratic Caucus is simply lying.  They were not all vaccinated.  On the other hand, I am pretty confident at least some of them were, probably the majority, maybe even a large majority.  

But if that is the case, we shouldn't see more than a single infection at most.  How is it that 11% of them are infected?

Are our statistical data that wrong?  Wrong, perhaps.  That wrong?  I doubt it.

The only wiggle room I see for everyone telling the truth is that perhaps a large number of the delegation of 56 did all get at least one vaccination (making "They are all vaccinated" true) but that some large number, or all of them, either have not received the second vaccination or they left on the trip sooner than the advised 14 days after the second shot.  

That would increase the probabilities for at least one infection, but it would still be low.  

Perhaps there is another very improbable but also reasonably plausible explanation.  Institutionally, social distancing and masks are really second and third order mitigations.  They are only pertinent in very specific circumstances.  The single biggest intervention, and little remarked upon, is improved air filtration systems in any enclosed public space.  Hospitals, Hotels, Office buildings, airplanes, etc.  I know a lot has been done in this field but I have not seen any sort of measures of progress.  My sense is that the most exposed (hospitals, airplanes, maybe office buildings) have been significantly retrofitted.

Since it appears that the jet that took the posse to Washington seems to have been a private jet (from the accounts I have seen), I am guessing that perhaps it is possible/probable that the owner of that jet has not gotten around to upgrading the air filtration system as has been required on commercial jets.

I am also guessing that perhaps not all the delegation was vaccinated, and that certainly there must have been at least one member unvaccinated and ill, though perhaps asymptomatic.  My far-fetched but plausible theory is that with at least one infected person on board and perhaps a half dozen or more others with only recent first injections, the circumstances might have been right for a spreader event if the plane's air filtration system had not been upgraded.  The whole delegation might have been breathing low filtered air carrying infection during the three hour flight from Austin to D.C..

Setting all the mockery for hypocrisy aside, and even conceding that perhaps it was a complete lie that any of them were vaccinated, we still have a larger outbreak than would be statistically likely.  

What is going on?  And why is the press not discussing it?