You are right that having a fuzzy starting point for when we started drawing from the urn causes problems for Laplace’s Law of Succession, making it less appropriate without modification. However, note that in terms of people who have ever lived, there isn’t that much variation as populations were so low for so long, compared to now.
I see your point re ‘arbitrary superlatives’, but am not sure it goes through technically. If I could choose a prior over the relative timescale of beginning to the final year of humanity, I would intuitively have peaks at both ends. But denominated in years, we don’t know where the final year is and have a distribution over this that smears that second peak out over a long time. This often leaves us just with the initial peak and a monotonic decline (though not necessarily of the functional form of LLS). That said, this interacts with your first point, as the beginning of humanity is also vague, smearing that peak out somewhat too.
You are right that having a fuzzy starting point for when we started drawing from the urn causes problems for Laplace’s Law of Succession, making it less appropriate without modification. However, note that in terms of people who have ever lived, there isn’t that much variation as populations were so low for so long, compared to now.
I see your point re ‘arbitrary superlatives’, but am not sure it goes through technically. If I could choose a prior over the relative timescale of beginning to the final year of humanity, I would intuitively have peaks at both ends. But denominated in years, we don’t know where the final year is and have a distribution over this that smears that second peak out over a long time. This often leaves us just with the initial peak and a monotonic decline (though not necessarily of the functional form of LLS). That said, this interacts with your first point, as the beginning of humanity is also vague, smearing that peak out somewhat too.