In my view, a proper use here is to compare two hypothesis: there are 2000 buses and 20 000 buses. Finding that the actual number is 1546 is an update in the direction of smaller number of buses.
I think you right that 1546 has the biggest probability compared to other probabilities for any other exact number, that is something like 1:1546. But it doesn’t means that it is likely, as it is still very small number.
In Doomsday argument we are interested in comparing not exact dates but periods, as in that case we get significant probabilities for each period and comparing them has meaning.
In my view, a proper use here is to compare two hypothesis: there are 2000 buses and 20 000 buses. Finding that the actual number is 1546 is an update in the direction of smaller number of buses.
It would also update you towards 1600 over 2000.
I think you right that 1546 has the biggest probability compared to other probabilities for any other exact number, that is something like 1:1546. But it doesn’t means that it is likely, as it is still very small number.
In Doomsday argument we are interested in comparing not exact dates but periods, as in that case we get significant probabilities for each period and comparing them has meaning.
Agreed, I just wanted to clarify that the assumption it’s double as long seems baseless to me. The point is it’s usually shortly after.
‘double’ follows either from Gott’s equation or from Laplace’s rule.