Hm, yeah. I see your point.Showsni wrote:Which is kind of my point; you end up with an obviously wrong answer because I'm not a proper random selection from the distribution. But then, doesn't the Doomsday thingy have exactly the same problem? We're using the number of total humans up to this date as our datum, which means we're using the humans alive today as our "random" choice. But this isn't a random selection from all the humans who will ever live, so it has the same error as thinking I might live to 520.
I guess like most controversial probability problems, it comes down to how exactly you're making your choice and what exactly you mean when you state probabilities.
On 5% of all the days of George Washington's life, it's true that he was less than 5% of the way through his life. For 5% of all humans, past present and future, it's true that they are among the first 5% ever to be born. On 5% of the days of George Washington's life, he would have been correct to believe that he'd live to be at least 20 times his current age. For 5% of all humans ever, it would be correct to believe that the total number of humans ever will be at least 20 times the number born before them. I think the difficulty lies in the fact that we can't help but have additional information in both cases. Washington at 50 obviously could be far more than 95% confident that he wouldn't live past 1000, and the last sterile vestiges of a post-nuclear-war humanity could be far more than 95% confident of being among the last humans ever born.
In the parlance of the German tank problem, this additional information should bias the estimator we use in the frequentist approach, and it should suggest something other than a uniform distribution for the Bayesian approach.