To me, the problem is essentially the same as the following: You are one of 10,000 people who have been taken to a prison. Nobody has explained why. Every morning, the guards randomly select 9⁄10 of the remaining prisoners and take them away, without explanation. Among the prisoners, there are two theories: one faction thinks that the people taken away are set free. The other faction thinks that they are getting executed.
It is the fourth morning. You’re still in prison. The nine other people who remained have just been taken away. Now, if the other people have been executed, then you are the only remaining observer, so if you’re a random observer, it’s not surprising that you should find yourself in prison. But if the other people have been set free, then they’re still alive, so if you’re a random observer, there is only a 1⁄10,000 chance that you are still in prison. Both of these statements are correct if you are a random (surviving) observer. But it doesn’t follow that you should conclude that the other people are getting shot, does it? (Clearly you learned nothing about that, because whether or not they get shot does not affect anything you’re able to observe.)
An excellently clear way of putting it!
bites bullet