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[GavJ]

you'd be forcing a certain percentage of the population to get vaccinated and not the other.

It's not arbitrary though. If it turns out you do want to aim for some specific %, you'd want to start with trying to encourage the most at risk individuals for getting sick. Whereas the last people on the list might be healthy 25 year olds living out on farms or something.

The more vulnerable people or people in high risk areas get more benefit from the vaccine, while the risks are more likely to be more similar across the board. So overall the at risk people get disproportionate benefit for themselves (and from other people vaccinating), so it is more fair to also have them shoulder more of the risk in exchange.

On a side note, maybe we should try to run a risk/reward analysis on our risk reward analysis.

Presumably, danger (if there is any) of vaccines scale linearly as the population that is vaccinated increases.

The danger of the disease however, does not. It scales relatively slowly, until suddenly the herd immunity is no longer sufficiently and you cause an epidemic.

So it might be better to err on the side of caution.

I agree. That's what I was saying a couple pages back.  You'd ideally want to choose either:
1) The point at which risk balances reward OR
2) A point at just a reasonable safety buffer from the disease getting out of control

Choose by picking whichever one of those two involves the higher vaccination rate (assuming you did know enough to figure out any of that)

[Helgoland]

I think GavJ may have a point, even if he's clearly not communicating it well. Maybe my rudimentary knowledge of economics can help!
Let's take a disease that also occurs in animals, so that eradication is impossible, but let us ignore (for simplicity) the danger of being infected by an animal. Let the percentage of vaccinated people be p.
Let's call the benefit of herd immunity to a given individual h(p), and the benefit of a vaccination on top of that vaccination v(p).
Obviously h is strictly monotonous and increasing, while v is strictly monotonous and decreasing
Let the danger of vaccination be d. d is independent of p. Let p* be so that d=v(p).
A rational individuum will be indifferent to getting a vaccination or not when d=v(p*). At this point the dangers of vaccination are equal to the benefit gained from them. Thus p* is the vaccination level we as a society should try to reach.

There are some problems with this, though:
1) We have assumed perfectly rational and informed individuals. This is obviously not the case; rather each individuum i has its own functions h_i, v_i and d_i of perceived danger and benefit. (Interestingly these are even functions of time, as perception changes; but we'll try to keep the model simple.)
2) We do not know what these functions look like. This is only a model, we'll need hard data for it to produce results.
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. They are a significant part of the population! Let this part be q. They can be modeled by an additional constraint of p+q less than or equal to one. Keep in mind that if p*+q greater than or equal to one, all people who can be vaccinated should be!
And now I'll sit back and pray I haven't made any mistakes.
Edit: Most of this appears to have already been said; maybe just view this as a sort of summary.

[Phmcw]

GavJ I think you simply misunderstand how herd immunity work : no vaccine protect you 100% of the time.

An epidemic is like an explosion :  for it to happen, the disease must be able to spread faster than peoples die/heal. Heard immunity is the fact that by lowering the chance for the disease to spread, you stop the epidemic in its track. If enough peoples are vaccinated, one or two peoples will contract the disease then the epidemic will disapear. If not, a significant portion of the population will catch it. For me, it's a matter of national security or rather of national health, which is above personal health.

[Sergarr]

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!

[GavJ]

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%

[Neonivek]

I...just realized the relevance of GavJ's avatar to this conversation XD

Totally! No current vaccine for dysentary, guys!

It helps though not to swallow lungfuls of dirty river water because your asshole parents tried to ford a 30 foot river for fun.

Isn't that because dysentery like the common cold is not a single disease but a multitude of diseases that are highly mutable?

[Tiruin]

I...just realized the relevance of GavJ's avatar to this conversation XD

Totally! No current vaccine for dysentary, guys!

It helps though not to swallow lungfuls of dirty river water because your asshole parents tried to ford a 30 foot river for fun.

Isn't that because dysentery like the common cold is not a single disease but a multitude of diseases that are highly mutable?

Different causes. Many. Different. Causes.
I'm feeling extremely unsure about this thread other than it aims to...connect vaccination risk vs benefit in pure, sole terms of math.

Which misses out many things in between (like...the post above the quote :S There are many kinds of [virus] that cause the 'same' disease, as a basic note). It's like using the result without looking at the cause.

And the backing of the...err, 'anti' vaccine thing? It's very incomplete. Lacking detail. Seems superficial.

[Sergarr]

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%

Then, how much do you need? Please state some factual information about how much vaccination do you need to kill the viruses.

Unless you can acquire such information and prove that it is true beyond any doubt, the best vaccination is 100% vaccination.

[Tiruin]

Isn't dysentery a symptom more than a disease?

It's a result.

[scrdest]

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%

Then, how much do you need? Please state some factual information about how much vaccination do you need to kill the viruses.

Unless you can acquire such information and prove that it is true beyond any doubt, the best vaccination is 100% vaccination.

Globally, average time between separate infections needs to exceed the maximum time a virus can survive outside a host.

[GavJ]

Then, how much do you need? Please state some factual information about how much vaccination do you need to kill the viruses.

Unless you can acquire such information and prove that it is true beyond any doubt, the best vaccination is 100% vaccination.

1) I don't know.
2) No, that doesn't mean you DO know that 100% is the right amount by default.

There IS some actual answer out there, and if it happens to be, say, 80%, then if you do 100%, you are killing more people than have to die. And without any good information about risks (even attempting to keep good track of it outside of a court case reporting system would be a good start...), your fallback opinion of 100%, although no better or worse than almost any other guess, is still a random, arbitrary guess, nothing more.

And therefore you have no basis or right to lord it over people or tell them they're wrong if they decide on something different than you, unless/until YOU get data for your own opinion, just like me.

Until then, as I stated in the OP, it's just simply every man for himself armed with his own gut instincts, and we should not be dicks to each other no matter what the other person chooses for himself or his/her family, because you don't know your gut instinct is any better.

[scrdest]

Then, how much do you need? Please state some factual information about how much vaccination do you need to kill the viruses.

Unless you can acquire such information and prove that it is true beyond any doubt, the best vaccination is 100% vaccination.

1) I don't know.
2) No, that doesn't mean you DO know that 100% is the right amount by default.

There IS some actual answer out there, and if it happens to be, say, 80%, then if you do 100%, you are killing more people than have to die. And without any good information about risks (even attempting to keep good track of it outside of a court case reporting system would be a good start...), your fallback opinion of 100%, although no better or worse than almost any other guess, is still a random, arbitrary guess, nothing more.

And therefore you have no basis or right to lord it over people or tell them they're wrong if they decide on something different than you, unless/until YOU get data for your own opinion, just like me.

Until then, as I stated in the OP, it's just simply every man for himself armed with his own gut instincts, and we should not be dicks to each other no matter what the other person chooses for himself or his/her family, because you don't know your gut instinct is any better.

So you are if you fall short. Except overshooting has the added benefit that the whole dilemma for a particular disease stops existing from here on out, forever. You claim that it only matters for someone living '200 years from now' but this, again, is treating population as a snapshot. The first child born after 100% eradication gets zero risk and 100% benefit. And since people actually sometimes care about other people, it's additional thing to factor into utility calculation.

Also, the 80% rate might kill exactly the same amount of people as the 100% option.

[Tiruin]

Could I ask why the tone of being against vaccination? o_O

Until then, as I stated in the OP, it's just simply every man for himself armed with his own gut instincts, and we should not be dicks to each other no matter what the other person chooses for himself or his/her family, because you don't know your gut instinct is any better.

Please do note: the choice should be informed in the least. I'd respect an informed choice, however the respect of choice is also taken into note when the person going otherwise or for, does not know much (or has little understanding of) the choice being presented as a factor there.

Also percentages are really not a good thing to judge by itself whether you'd want someone vaccinated or not. -_-

[Helgoland]

Could I ask why the tone of being against vaccination? o_O

I guess it's just a matter of perception: GavJ is presenting the purely mathematical side of the problem (as detailed in my previous post), while practically everyone else is focusing on the practical side.

To put it in terms of propaganda: Even if a 100% vaccination rate is not the optimum (which is GavJ's point), we should still advocate a vaccination rate of 100% (which is, as far as I can see, the cause of everybody's discomfort with GavJ's post) to convince dumb people to vaccinate and get closer to the actual optimum.

[Neonivek]

The issue is some Vaccines are only effective if used on Mass.

GravJ essentially creating a chicken or the egg scenario.

Super low chance of being maimed or dying from the Measles? Well congratulations that was created by the vaccination.

As well ANOTHER benefit of the Vaccination is that you won't harm anyone else should you become contagious.

It isn't about GavJ using math. It is about where that math is coming from. In fact it is about where all his statistics come from.

Just unpack the statistics and you will easily see through them.