8Joined Nov 2020


I think there's some confusion here about "Will's prior". Some people seem to think that Will's prior implies that the influentialness of an arbitrary individual is independent of the time in which they live. However, this isn't right - Will's prior instead says that, before I know when I will live, I shouldn't expect to live in a very influential time (or in later statements, that I shouldn't expect to be a particularly influential person).

~ means "is of similar magnitude" in the following.

Suppose our prior defines some probability space on which we have the following random variables: C: index of century in which I'm alive, H: a function century index -> hingeyness, Z:= H(X) and U: a function time -> human population, M: index identifying the human who is "me".

Will's prior invokes the self sampling assumption, which says that P(M) is uniform over the set of all humans (or consciousness-moments). This implies that P(C=i|U) is proportional to U(i). Then P(Z) = \sum_{C,H} P(Z|C=i,H=h)P(C=i,H=h)  = \sum_{C,H} delta_h(i)P(C=i,H=h).

This puts no restriction at all on P(C=i,H=h). Will argues, I think, that it would be unreasonable to presume that max(H) and C are strongly correlated enough to lead to E(Z)  close to E[max(H)]. 

Several people suggest - I think - that we might be able to come up with reasonable prior guesses of P(H|U); for example, if U is large for a very long time, H might be uniformly low or decreasing over time. It could also be increasing over time and because I don't really understand "influence" or "hingeyness" I have a hard time  thinking about this question.

If large U => E[H] decreases over time, then E[Z|C~0] might be close to E[max(H)], but E[Z] will continue to be small, which seems to satisfy both Buck's and Will's intuitions.

Myself, I don't know what I should think of P(Z|C~0), which seems to be the crucial probability here.