
Bad math. If the vaccine works 0% of the time or 100% of the time, this meme is right. If it works some of the time, which is the way most things work in medicine, this meme is wrong.
Lets say that the chance of the vaccine working on a person is x.
If I meet you, I’m vaccinated, and you’re not, the chance I’m safe is x.
If I meet you, I’m vaccinated and you’re vaccinated, the chance I’m unsafe is the chance that my vaccine didn’t work (1-x) and yours didn’t work (1-x), or (1-x)^2. The chance that at least one of them worked is therefore 1-(1-x)^2.
The advantage for me in having you vaccinated is therefore
1-(1-x)^2-x = 1-(1-2x+x^2)-x = 1-1+2x-x^2-x = x-x^2.
If x=0 or x=1 then this advantage is indeed zero. But if x=0.5 (the vaccine works on half the people) the advantage is 0.5-0.5^2 = 0.25. If x=0.9 (the vaccine works on 90% of the people) the advantage is 0.9-0.81 = 0.09. Etc.
Note: I am NOT arguing that we should require vaccines. I am merely arguing that this meme is bad logic.








