On second thoughts, I think it’s worth clarifying that my claim is still true even though yours is important in its own right. On Gott’s reasoning, P(high influence | world has 2^N times the # of people who’ve already lived) is still just 2^-N (that’s 2^-(N-1) if summed over all k>=N). As you said, these tiny probabilities are balanced out by asymptotically infinite impact.
I’ll write up a separate objection to that claim but first a clarifying question: Why do you call Gott’s conditional probability a prior? Isn’t it more of a likelihood? In my model it should be combined with a prior P(number of people the world has). The resulting posterior is then the prior for further enquiries.
On second thoughts, I think it’s worth clarifying that my claim is still true even though yours is important in its own right. On Gott’s reasoning, P(high influence | world has 2^N times the # of people who’ve already lived) is still just 2^-N (that’s 2^-(N-1) if summed over all k>=N). As you said, these tiny probabilities are balanced out by asymptotically infinite impact.
I’ll write up a separate objection to that claim but first a clarifying question: Why do you call Gott’s conditional probability a prior? Isn’t it more of a likelihood? In my model it should be combined with a prior P(number of people the world has). The resulting posterior is then the prior for further enquiries.