What's wrong with the Doomsday argument? https://en.m.wikipedia.org/wiki/Doomsday_argument
Suppose each new human born has the knowledge of the total number of humans born so far. So in their life, each human multiplies that number by 20 to get the upper bound for the total number of humans.
Assuming humans will eventually go extinct, 95% of the humans will calculate the upper bound correctly using the 'multiply by 20' rule.
But still, does that really imply that the number that I calculate right now would be correct with 95% accuracy?
What if we repeat this experiment to check if my calculation really works 95% of the time?
For each experiment, God randomly chooses a natural number N (as the total number of humans to be born). Assuming there is only one point in time when I can be born (which seems like a valid assumption), in each experiment, I'm always born as the $n$th human. So the upper bound I calculate is always $20n$.
Now it's easy to see that my calculation will be correct in 0% of these experiments, instead of 95.
So what is the correct probability? 0% or 95%?
 A: For each possible world, 95% of all humans in that world will get the correct answer. But it isn't the "same" 95% in every world. Because there are infinite potential humans to choose from.  You're assuming a consistent identity across all worlds, instead of picking at random from the infinite born and unborn potential humans. Imagine this scenario:
1) In world 1 there's 20 humans, and then they go extinct. These 20 would get the correct answer. 
2) In world 2 there's 20 humans, after which there's another 400 humans, after which they go extinct. Only the last 400 would get correct answer.  
3) In world 3 there's 20 humans, after which there's another 400 humans, after which there's another 8000 humans, after which they go extinct. Here only the last 8000 would get correct answers. etc.
Assuming consistent identity across worlds, any individual human has 0% chance to get the correct answer. But 95% of any of the humans that exist in any given world will get the correct answer. 
Here's the trick: you can't know exactly what that 95% will be unless you know already when the humans will go extinct. Are the humans that existed until now 95% of all humans that will ever exist, or are they just 0.0001%? We have no prior way of knowing. 
If a doomsday cult is right, then a greater percentage of humans is right than if it were wrong. Because if it were wrong, more humans would be born, and the percent of doomsday humans would have become smaller. The total amount of humans isn't a prior defined quantity. Even if you get this right, and you're 95% of all humans that have existed, you're still 0% of the potential humans that might have existed.   
A: I think the problem is that 60B (current population) is not a randomly selected number out of the set {1,2,3,4.....N}, where N is the total number of humans ever going to exist.
Assuming we know nothing about $N$, and each natural number value of $N$ is equally likely, the law of total probability says that there's a 0% chance that 60B is at least 5% of $N$
$$P(60B\geq 0.05N)=\lim_{N\rightarrow \infty} \sum_{n=60B}^{1200B} \frac{1}{N} P(60B\geq 0.05N | N=n) $$
$$=\lim_{N\rightarrow \infty} \sum_{n=60B}^{1200B} \frac{1}{N}=0$$ 
If $60B$ had been randomly selected out of the set {1,2,3....N}, then we'd have gained some information about $N$ (larger values of $N$ would've been less likely), and hence the above calculation wouldn't apply in that case.
