But maybe the vaccine is 100% effective against all outcomes! So long as it’s correctly transported and administered, that is. Except sometimes vaccines are left at high temperature for too long, the delicate proteins are damaged, and people receiving them are effectively not vaccinated. If this happens 5% of the time, then 95% of people are completely immune to Covid and 5% are identical to not be vaccinated. Whatever chance they had of getting severe Covid before, it’s the same now.
If all-or-nothing were true, you would expect the following equality in conditional probability distributions
This was already shown in the mass Pfizer study, but several other sources indicate the ratio of asymptomatic-to-symptomatic cases is increased for vaccinated people. In other words, vaccination works better against symptomatic Covid (more severe) than asymptomatic Covid (less severe).
The all-or-nothing vaccine hypothesis is:
If all-or-nothing were true, you would expect the following equality in conditional probability distributions
P(⋅∣infection=true, vaccine=true)=P(⋅∣infection=true, vaccine=false)This is not what we see:
Therefore, all-or-nothing cannot be true.
Am I missing something?
Nope, that seems roughly right. It is I who failed to propagate. Was a cached argument from before I’d looked at the data.
I’ll update the post shortly with this. Thanks for pointing it out.