1) We have assumed perfectly rational and informed individuals. This is obviously not the case
In the first couple paragraphs of the OP of the thread, I said "this is how people should think about vaccines if we lived in a rational, scientific world." And my point is that people are being obnoxious due to not being rational enough about it. So ... yes, I know. That's what I'm saying need to change, at least a little bit.
Perceptual value can be changed by education. It's not something you're obligated to work around.
2) We do not know what these functions look like.
It doesn't matter for our purposes. It would if you had all the data and were actually trying to solve it, but talking generally here without data, as long as it's decreasing monotonal like you agreed it is for the benefit of vaccination, you end up at the same conclusion. I didn't include scaling constants on my graph on purpose. You can rescale it to make that curve any shape you want, as long as it's monotonal decreasing, and the conclusion will be the same.
Specifically, that there will probably be some point where d=v(p) in between 0% and 100%
3) We have ignored the existence of individuals that cannot be vaccinated, or are susceptible to the disease despite their vaccination, such as children, the sick, and the elderly.
GavJ I think you simply misunderstand how herd immunity work : no vaccine protect you 100% of the time.
I have not ignored these people or that vaccines don't work 100% of the time.
Notice that in my graph, the blue benefit curve does NOT reach zero. This represents the continued potential for disease in people who either cannot be vaccinated or where the vaccine didn't take. Thus there's still some benefit. If vaccines were 100% effective and could be taken by anyone, the curve would hit zero on the right side.
This issue only matters if you suspect that vaccine risks might be lower than even the lowest benefit of a vaccine with 100% of the possible-to-vaccinate population vaccinated, which is probably very unlikely, because it would have to be an even LOWER than 1/60,000,000 risk or whatever (we would have fewer than 100 cases a year springing up so all the math would shift it that much further out of reach.)
The best course of action thus be 100% vaccination, followed by 0% vaccination after the death of dangerous virus.
It would minimize the total damage inflicted by the virus!
I addressed this earlier and nobody really directly responded. This is the best course of action from the perspective of some guy 200 years in the future who didn't have to be there. But not for us. We need to consider the danger of the vaccines in the meantime, and since you don't actually need 100% vaccination for a virus to die out (once the world catches up), you can most likely save extra lives by hovering a little ways below that. How much, if any? Nobody knows, but conceptually, it is clear that there
might be an optimal level below 100%