Take the Doomsday Argument(DA) as an example. It proposes the uninformed prior of one’s own birth rank among all human beings ought to be uniformly distributed from the 1st to the last. So learning our actual birth rank (we are around the 100 billionth) should shift our belief about the future toward earlier extinction. E.g. I am more likely to be the 100 billionth person if there are only 200 Billion humans overall rather than 200 Trillion. So the fact I’m the 100 billionth means the former is more likely.
This is not how DA goes. It goes like this: if we are just as likely to be any particular observer, then the probability of being born at any particular time period is proportional to how many observers are alive at that time period. So, on the most outside-ish view (i.e., not taking into account what we know about the world, what we can predict about how the future is going to unfold etc), we should assign the most probability mass to those distributions of observers over history, where the time we were born had the most observers, which means that in the future there’s going to be fewer observers than right now, probably because of extinction or something.
Also, if you assume the number of people alive throughout history is “fixed” at 200 billion “you” are just as likely to be the first person as the 100 billionth and 200 billionth. If you predict to be the 100 billionth, you can at best minimize the prediction error/deviation score.
This is not how DA goes. It goes like this: if we are just as likely to be any particular observer, then the probability of being born at any particular time period is proportional to how many observers are alive at that time period. So, on the most outside-ish view (i.e., not taking into account what we know about the world, what we can predict about how the future is going to unfold etc), we should assign the most probability mass to those distributions of observers over history, where the time we were born had the most observers, which means that in the future there’s going to be fewer observers than right now, probably because of extinction or something.
Also, if you assume the number of people alive throughout history is “fixed” at 200 billion “you” are just as likely to be the first person as the 100 billionth and 200 billionth. If you predict to be the 100 billionth, you can at best minimize the prediction error/deviation score.