It seems that your understanding of the Doomsday argument is not entirely correct—at least your village example doesn’t really capture the essence of the argument.
Here is a different analogy: Let’s imagine a marathon with an unknown number of participants. For the sake of argument, let’s assume it could be a small local event or a massive international competition with billions of runners. You’re trying to estimate the size of this marathon, and to assist you, the organizer picks a random runner and tells you how many participants are trailing behind them.
For example, if you’re told that there are only 10 runners behind the selected participant, it would be reasonable to conclude that this is likely not a marathon of billions. In such a large event, the odds of picking a runner with only 10 people behind them would be incredibly low. This logic also applies to the Doomsday Argument, whether you’re an outside observer or one of the ‘participants’. The key piece of information here is that you only know the number of individuals ‘behind’ you, which can be used to infer how likely it is that the total number of total ‘participants’ is more than X.
In the doomsday argument, we are the random runner. If the runner with only 10 people behind him assumed his position was randomly selected, and tried to estimate the total number of runners, he would be very wrong. We could very well be that runner near the back of the race; we weren’t randomly selected to be at the back, we just are, and the fact that there are ten people behind us doesn’t give us meaningful information about the total number of runners.
Humans alive today not being a random sample can be a valid objection against the Doomsday argument but not for the reasons that you are mentioning.
You seem to be suggesting something along the lines of “Given that I am at the beginning, I cannot possibly be somewhere else. Everyone who finds themselves in the position of the first humans has a 100% chance of being in that position”. However, for the Doomsday argument, your relative ranking among all humans is not the given variable but the unknown variable. Just because your ranking is fixed (you could not possibly be in any other position), does not mean that it is known and that we cannot make probabilistic statements about it.
It seems that your understanding of the Doomsday argument is not entirely correct—at least your village example doesn’t really capture the essence of the argument.
Here is a different analogy: Let’s imagine a marathon with an unknown number of participants. For the sake of argument, let’s assume it could be a small local event or a massive international competition with billions of runners. You’re trying to estimate the size of this marathon, and to assist you, the organizer picks a random runner and tells you how many participants are trailing behind them.
For example, if you’re told that there are only 10 runners behind the selected participant, it would be reasonable to conclude that this is likely not a marathon of billions. In such a large event, the odds of picking a runner with only 10 people behind them would be incredibly low. This logic also applies to the Doomsday Argument, whether you’re an outside observer or one of the ‘participants’. The key piece of information here is that you only know the number of individuals ‘behind’ you, which can be used to infer how likely it is that the total number of total ‘participants’ is more than X.
In the doomsday argument, we are the random runner. If the runner with only 10 people behind him assumed his position was randomly selected, and tried to estimate the total number of runners, he would be very wrong. We could very well be that runner near the back of the race; we weren’t randomly selected to be at the back, we just are, and the fact that there are ten people behind us doesn’t give us meaningful information about the total number of runners.
Humans alive today not being a random sample can be a valid objection against the Doomsday argument but not for the reasons that you are mentioning.
You seem to be suggesting something along the lines of “Given that I am at the beginning, I cannot possibly be somewhere else. Everyone who finds themselves in the position of the first humans has a 100% chance of being in that position”. However, for the Doomsday argument, your relative ranking among all humans is not the given variable but the unknown variable. Just because your ranking is fixed (you could not possibly be in any other position), does not mean that it is known and that we cannot make probabilistic statements about it.