The question which seems important to me now is: does Will think that the probability of high influentialness conditional on birth rank (but before accounting for any empirical knowledge) is roughly the same as the negative exponential distribution Toby discussed in the comments on his original post?
I actually think the negative exponential gives too little weight to later people, because I’m not certain that late people can’t be influential. But if I had a person from the first 1e-89 of all people who’ve ever lived and a random person from the middle, I’d certainly say that the former was more likely to be one of the most influential people. They’d also be more likely to be one of the least influential people! Their position is just so special!
Maybe my prior would be like 30% to a uniform function, 40% to negative exponentials of various slopes, and 30% to other functions (e.g. the last person who ever lived seems more likely to be the most influential than a random person in the middle.)
Only using a single, simple function for something so complicated seems overconfident to me. And any mix of functions where one of them assigns decent probability to early people being the most influential is enough that it’s not super unlikely that early people are the most influential.
“Only using a single, simple function for something so complicated seems overconfident to me. And any mix of functions where one of them assigns decent probability to early people being the most influential is enough that it’s not super unlikely that early people are the most influential.”
I strongly agree with this. The fact that under a mix of distributions, it becomes not super unlikely that early people are the most influential, is really important and was somewhat buried in the original comments-discussion.
And then we’re also very distinctive in other ways: being on one planet, being at such a high-growth period, etc.
I agree that our earliness gives a dramatic update in favor of us being influential. I don’t have a stable view on the magnitude of that.
I’m not convinced that the negative exponential form of Toby’s distribution is the right one, but I don’t have any better suggestions
Like Lukas, I think that Toby’s distribution gives too much weight to early people, so the update I would make is less dramatic than Toby’s
Seeing as Toby’s prior is quite sensitive to choice of reference-class, I would want to choose the reference class of all observer-moments, where an observer is a conscious being. This means we’re not as early as we would say if we used the distribution of Homo sapiens, or of hominids. I haven’t thought about what exactly that means, though my intuition is that it means the update isn’t nearly as big.
So I guess the answer to your question is ‘no’: our earliness is an enormous update, but not as big as Toby would suggest.
The question which seems important to me now is: does Will think that the probability of high influentialness conditional on birth rank (but before accounting for any empirical knowledge) is roughly the same as the negative exponential distribution Toby discussed in the comments on his original post?
I actually think the negative exponential gives too little weight to later people, because I’m not certain that late people can’t be influential. But if I had a person from the first 1e-89 of all people who’ve ever lived and a random person from the middle, I’d certainly say that the former was more likely to be one of the most influential people. They’d also be more likely to be one of the least influential people! Their position is just so special!
Maybe my prior would be like 30% to a uniform function, 40% to negative exponentials of various slopes, and 30% to other functions (e.g. the last person who ever lived seems more likely to be the most influential than a random person in the middle.)
Only using a single, simple function for something so complicated seems overconfident to me. And any mix of functions where one of them assigns decent probability to early people being the most influential is enough that it’s not super unlikely that early people are the most influential.
“Only using a single, simple function for something so complicated seems overconfident to me. And any mix of functions where one of them assigns decent probability to early people being the most influential is enough that it’s not super unlikely that early people are the most influential.”
I strongly agree with this. The fact that under a mix of distributions, it becomes not super unlikely that early people are the most influential, is really important and was somewhat buried in the original comments-discussion.
And then we’re also very distinctive in other ways: being on one planet, being at such a high-growth period, etc.
Thanks, I agree that this is key. My thoughts:
I agree that our earliness gives a dramatic update in favor of us being influential. I don’t have a stable view on the magnitude of that.
I’m not convinced that the negative exponential form of Toby’s distribution is the right one, but I don’t have any better suggestions
Like Lukas, I think that Toby’s distribution gives too much weight to early people, so the update I would make is less dramatic than Toby’s
Seeing as Toby’s prior is quite sensitive to choice of reference-class, I would want to choose the reference class of all observer-moments, where an observer is a conscious being. This means we’re not as early as we would say if we used the distribution of Homo sapiens, or of hominids. I haven’t thought about what exactly that means, though my intuition is that it means the update isn’t nearly as big.
So I guess the answer to your question is ‘no’: our earliness is an enormous update, but not as big as Toby would suggest.