Frankly, if I try to imagine living in a world in which I am as confident that that many people exist as I am that 7 billion people exist today, I'm not sure I wouldn't kill off billions for a cookie.
I mean, if I try to imagine living in a world where only 10,000 people exist, I conclude that I would be significantly more motivated to extend the lives of an arbitrary person (e.g., by preventing them from starving) than I am now. (Leaving aside any trauma related to the dieback itself.)
If a mere six orders of magnitude difference in population can reduce my motivation to extend an arbitrary life to that extent, it seems likely that another twenty or thirty orders of magnitude would reduce me to utter apathy when it comes to an arbitrary life. Add another ten orders of magnitude and utter apathy when it comes to a billion arbitrary lives seems plausible.
What if it's billions who they've never met, and are never going to meet?
I presumed this.
If it's billions of friends instead, I no longer have any confidence in any statement about my preferences, because any system capable of having billions of friends is sufficiently different from me that I can't meaningfully predict it.
If it's billions of people including a friend of mine, I suspect that my friend is worth about as much as they are in the 7billion-person world, + (billions-1) people who I'm apathetic about. I suspect I either get really confused at this point, or compartmentalize fiercely.
Add another ten orders of magnitude and utter apathy when it comes to a billion arbitrary lives seems plausible.
A billion is nine orders of magnitude. As a very rough estimate, then, adding an order of magnitude to the number of lives in existence divides the motivation to extend an arbitrary stranger's life by an order of magnitude. And the same for any other multiplier.
That is, if G is chosen such that f(x)-f(x-1)=G, then f(Mx)-f(Mx-1)=G/M for any given x and any multiplier M. If I then define my hedons such that f(0)=0 and f(1)=1...
...then I get that...
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