I have seen the argument advanced in a few places that getting lots of people vaccinated is actually more dangerous, because it creates a more likely opportunity for a super-variant of Covid to arise, one that overwhelms even vaccinated immune systems. While this is not so, it does have an element of truth in it that deserves refutation rather than mere dismissal.
Let us look for a moment at winning a lottery. A person who has bought a million tickets has a much better chance of winning than a person who bought only one, so his average expected winnings is a million times higher. But there aren't really "average" winnings in a lottery (a pure lottery. I am excluding the actual money-raising games that give lesser prizes for getting some of the numbers right). If you win the 10 million dollars, you win it, and if you don't you get nothing. The idea of average winnings is something of a statistical trick.
The rise of a supervariant is like a lottery in reverse, an enormous single bad-luck outcome. If everyone but one person were vaccinated, there would still be a chance, however minuscule, that the last person who contracted the disease carried a mutation that turned out to be the supervariant that overwhelmed everyone else. You can see how that might happen in theory, but no one is losing sleep over that possibility. Much more worrisome is the situation where there are many, many people carrying the virus. It's like millions of lottery tickets for that ugly reverse lottery. Even though the chance of a supervariant mutation is extremely low for each of those "tickets," in aggregate the odds are much greater. It is still small. There have been millions and millions with the virus, and only a couple of variants that have been problems. It may be that only the Delta is a big deal.There are likely many mutations out there already, but as well all know, most mutations make things work worse, not better. The many mutations simply sink beneath the waves.
But if there are a bunch of these mutations around, they have an enormous number of vaccinated targets. I am going to describe the situation as if the virus is "trying" to outwit the potential hosts, even though it is not sentient and trying to do anything. It's just with such enormous numbers it has that appearance, of an organism trying to get through defenses, like a hundred million squirrels trying to get through to the bird feeder by indefatigable persistence. When there are only a small number of variants, it's like there are fewer squirrels trying their hand at the obstacles. The odds of the squirrels in general succeeding and coming up with a strategy is low. But when there's lots of squirrels, the possibility that one might hit upon the one brilliant strategy is increased.
I don't know what the worst ratio is for that possible development of a supervariant is, but I have to think 50% vaccination - right about where we are now - might be close. With 95% vaccination, there just wouldn't be enough squirrels working at the feeder puzzle. But with 50%, there are a huge number of people carrying the virus, and they have a huge number of targets - both the easier targets of the unvaccinated and the hardened targets of the vaccinated. Or if you prefer, while one of the few unvaccinated in the 95% scenario might develop the winning ticket variant that is actually the losing ticket variant for us all, such a variant is more likely to arise in the scenario of only 50% vaccinated, because that would be like buying ten times more tickets for that lottery.
Even with all the unvaccinated counted together a supervariant might not arise. Even though it's ten times worse than the 95% vaccinated scenario it's still low. But remember, the original predictions months ago were that more powerful variants were unlikely - and we've already had one. Worse, the one we've got is still spreading, so a variant of that would only have to be a little worse to be a heightened risk. We don't actually know the likelihood. No one does. It may be unfortunate bad luck that we got even one Delta variant. Or we may have gotten lucky with ten almosts that just missed, with no reason to expect such good luck in the future.
It has some importance because of the insistence of the unvaccinated that they represent no danger to the vaccinated, and so should be left alone by all the busybodies. It is true in the limited sense that the potential danger of each unvaccinated person is low. Like lottery ticket low. Though someone does eventually win lotteries, and if you buy millions of tickets the aggregate danger is higher. At minimum, they increase the risk of danger for us all.
If someone has better math on this, let me know.