To address your first category: When I meet new people and interact with them, I do more than gain information- I perform transitive actions that move them out of the group “people I’ve never met” that I don’t care about, and into the group of people that I do care about.
Addressing your second: I found that a very effective way to estimate my intuition would be to imagine a group of X people that I have never met (or specific strangers) on one minecart track, and a specific person that I know on the other. I care so little about small groups of strangers, compared to people that I know, that I find my intuition about billions is roughly proportional; the dominant factor in my caring about strangers is that some number of people who are strangers to me are important to people who are important to me, and therefore indirectly important to me.
To address your first category: When I meet new people and interact with them, I do more than gain information- I perform transitive actions that move them out of the group “people I’ve never met” that I don’t care about, and into the group of people that I do care about.
Addressing your second: I found that a very effective way to estimate my intuition would be to imagine a group of X people that I have never met (or specific strangers) on one minecart track, and a specific person that I know on the other. I care so little about small groups of strangers, compared to people that I know, that I find my intuition about billions is roughly proportional; the dominant factor in my caring about strangers is that some number of people who are strangers to me are important to people who are important to me, and therefore indirectly important to me.