I just don't understand the Doomsday argument at all. As Wikipedia tells it, you say that "I'm 95% likely to not be one of the first 5% people to be born", and then because of that multiply the number of people born so far by 20 and claim a 95% probability of that being the upper bound on total humans born with 95% certainty.
I just don't understand how this is supposed to work.
- The 100th person ever born could make the exact same calculation and find that with 95% confidence that humanity will go extinct after 1900 more people are born.
- Every single person has a unique $n$, therefore everyone who makes this calculation will find different results.
- If you draw the first $n$ elements from a set of size $N$, all that tells you is that $N$ is at least $n$. How could it possibly tell you how many more are left in $N$, regardless of what you do with the numbers?
- Isn't it just equivalent to saying that lifetimes of intelligent species (in terms of # individuals born) follow a simple power law distribution? How can we claim such a distribution, when we've only ever observed one such species, and even that not to conclusion?
Unless I'm missing something, the conclusions fail some pretty basic sanity checks, so the argument must be wrong. But where is the problem?
Wikipedia also has a non-mathematical analogy, which seems to me equally insane: It reminds me of people who say you have 50% chance of succeeding any challenge ("either you succeed or you fail"). I would say that if you know absolutely nothing a priori, estimating the probability to be 0.5 is no better than estimating it as 0.1 or any other number.