I’m quite sure now, I came to the same conclusion independently of GPT after getting a hint from it, which itself I had already almost guessed.
A woman having the top 10% of any characteristic is almost the same as rolling a 10 sided die and coming up with a 1 (this was the actual problem I presented GPT with, and when it answered it did so in what looked like a hybrid of code and text so I’m quite sure it is computing this somehow).
What was clearly wrong with the first math was that if I roll just three die, there would already be1*10^3 or1/1000 chance of ...
Ah dang sorry, was not aware of this. Brute force re-taught myself how to do this quick 10^5 / (5-2)! = 100,000 / 6 = 1/16,666. You are right, that was off by more than a factor of ten! Thanks for the tip.
Edit: agghh I hate combinatorials. This seemed way off to me, I thought the original seemed correct. GPT had originally explained the math but I didn’t understand the notation, after working on the problem again for a while I had it explain it’s method to me in easier to understand language and I’m actually pretty sure it was correct.
Ah, thanks for the clarification, this is very helpful. I made a few updates including changing the title of the piece and adding a note about this in the assumptions. Here is the assumption and footnote I added, which I think explains my views on this:
Whenever I say "lives saved" this is shorthand for “future lives saved from nonexistence.” This is not the same as saving existing lives, which may cause profound emotional pain for people left behind, and some may consider more tragic than future people never being born.[6]
Here is footnote 6, created for br...
As to your second objection, I think that for many people the question of whether murdering people in order to save other people is a good idea is a separate moral question from which altruistic actions we should take to have the most positive impact. I am certainly not advocating murdering billions of people.
But whether saving present people or (in expectation) saving many more unborn future people is a better use of altruistic resources seems to be largely a matter of temperament. I have heard a few discussions of this and they never seem to make much se...
Interesting objections!
I mentioned a few times that some and perhaps most x-risk work may have negative value ex post. I go into detail how work may likely be negative in footnote 13.
It seems somewhat unreasonable to me, however, to be virtually 100% confident that x-risk work is as likely to have zero or negative value ex ante as it is to have positive value.
I tried to include the extreme difficulty of influencing the future by giving work relatively low efficacy, i.e. in the moderate case 100,000 (hopefully extremely competent) people working on x-risk f...
Hm, logically this makes sense, but I don’t think most agents in the world are fully rational, hence the continuing problems with potential threats of nuclear war despite mutually assured destruction and extremely negative sum outcomes for everyone. I think this could be made much more dangerous by much more powerful technologies. If there is a strong offense bias and even a single sufficiently powerful agent willing to kill others, and another agent willing to strike back despite being unable to defend themselves by doing so, this could result in everyone...
Yes, that’s the main place I’m still uncertain, the ten combinations of three 1’s have to be statistically independent which I’m having trouble visualizing; if you rolled six die, the chance that either three pre-selected specific die would be 1’s or the other three die would all be 1’s could just be added together.
But since you have five die, and you are asking whether three of them will be 1’s, or another overlapping set will be 1’s, you have to somehow get these to be statistically independent. Part of that is actually what I left out (that GPT told me,... (read more)