There was a gallup poll recently that asked people what the risk of hospitalization was if you got infected.

95% of D voters overestimated the risk, 78% of them were more than 10x wrong, and 41% of them were more than 50x wrong. R voters did better, but still overwhelmingly overestimated the risks.

So we're having this enormous discussion on misinformation and how to combat it and making sure people get "trustworthy" news, and yet, Americans are completely fucking wrong about the disease. It's a giant elephant in the room that no-one is addressing!

No wonder you can't have a rational debate about weighing different risks against each other, if your opponents wrongly overestimate the risk by one or two orders of magnitude.

There is an elegant argument, due to Laplace, that says that if you have an urn containing red and blue balls, you extract N balls, and M of them are red, you should assume that the probability that the next ball is red is (M+1)/(N+2), and not M/N as one might naively assume. The general case requires integrating the beta function, which is kind of advanced, but the M=0 case can be done with elementary calculus, as follows.

Call X the probability of extracting a blue ball, which we view as a property of the urn. If we don't know anything about X, before we extract any balls, we should assume a uniform prior distribution P[X]=1 for 0<=X<=1 (this is the main and only assumption). The probability of seeing M=0 red balls after extracting N, for given X, is the same as the probability that all balls are blue, i.e., P[M=0|X]=X^N. But we care about P[X|M], not P[M|X]. By Bayes' theorem, P[X|M] is proportional to P[M|X]P[X], times a proportionality constant that makes the total probability be 1. Because we assumed P[X]=1, we have that P[X|M=0] is proportional to P[M=0|X]=X^N. The integral of X^N between X=0 and 1 is 1/(N+1), yielding P[X|M=0]=(N+1) X^N. The expected value of X is the integral for X=[0,1] of X P[X|M=0], which is E[X]=(N+1)/(N+2). This is the expected probability of a ball being blue, with 1-E[X]=1/(N+2) being the probability of a ball being red. QED.

Now say we have historically observed 1000 vaccines and they were all safe in the long term. It is still perfectly rational to assume that there is a 1/1002 chance that this vaccine is unsafe in the long term. Anybody claiming otherwise better have a cogent argument about why the prior probability should not be uniform. Saying that 1000 vaccines were long-term safe and thus this one is long-term safe is equivalent to assuming a prior of the form P[X]=1/(X (1-X)), which is hard to justify (and diverges at 0 and 1).

Basically, the problem is that we are entering the territory where the risk from the disease is comparable to a rational estimate of the risk of what we don't know, and it's hard to come to any kind of cogent conclusion.

But anybody who claims that all past vaccines were long-term safe and thus this one is long-term safe clearly does not understand basic probability.

Since the disease is highly age-stratified and dependent on risk factors, the same goes for the vaccines. For elderly, it's a complete no-brainer. For me, in my forties, it's overwhelmingly false and I got vaccinated as bloody fast as I could. And for anyone in a risk group, it's false as well.

But for healthy kids and teenagers? It's a wash for them personally, but if they're hanging around people in risk groups, there's a clear benefit of them getting vaccinated.

> the vaccine has been proven to be safe

There are several vaccines, and some of them have issues. The AstraZeneca one is pretty much not in use any longer in the west because of the blood clotting issue, and there are reports now that teenage boys might suffer myocarditis from the Pfizer vaccine. Incredibly rare, but the risk is not zero.

You are generally correct that the cure is not worse than the disease, for an overwhelming majority of people, but the truth is more complicated, and without long-term safety data for these vaccines, I completely understand that some people are hesitant.

At the core of the anti-vaxx bullshit is a tiny kernel of truth, and I think it's better to address that than to completely suppress everything they say, because that's just gonna make people on the fence extremely suspicious and tip them over the wrong way.

Another interesting factor at play here is that some people prefer for negative outcomes to come from inaction than action. It's like the trolley problem (https://en.wikipedia.org/wiki/Trolley_problem) when people try to evaluate morality.

In this case, they would rather not take an action (get vaccinated) if there's a chance of harm and would prefer inaction (don't get vaccinated) despite the higher statistical risk of bad outcomes.

How many kids and teenagers aren't usually around groups of 40 year olds? Are there cities which are only populated with 12 year olds? Apartment complexes exclusively for those under 18?

Kids living with their grandparents should definitely get vaccinated.