Thanks for the close read and the thoughtful comments!
Open:
1. Loss function, future-oriented: interesting questions; I have thoughts on them; I left them out the first time through but may add them later.
2. gerrymandering; “infinite”; proposal I don’t fully grasp: Also interesting but I think beside the points I want to make here.
3. Dimensions.
“The choice of dimensions seems like a bigger deal than the number.” I’m implicitly assuming that they’re chosen by principal component analysis or something similar. Of course that’s not robust to scaling or other monotone transforms, but I think it’s close enough to being well-defined to handwave away for my purposes.
But if I’m wrong, and the variation in political opinions/interests that are politically salient in an ideal world is much higher, then the very “republican idea” of representative democracy is problematic.
“whether things interact with each other to greatly affect outcomes”: good point. I’ll see if I can incorporate it without being too wordy.
4. Weighted legislatures: yes, that’s a whole topic I could write an entire section on. For now, can’t afford to get that sidetracked, sorry.
“Variance seems like it might be a red herring, given a focus on outcomes/exemplariness.”
Um. It’s possible I’m not being clear what I mean by “variance”. I don’t mean variance of ideologies of legislators; I mean variance (meta-variance?) of distributions. That is to say, a 1-dimensional procedure for picking 2 legislators would have higher variance if it sometimes picked {5,5} and sometimes picked {4,6}, than if it reliably picked {0,10}.
I think there may something to your critique here aside from that possible misunderstanding, though. I have some thoughts but I’m not sure how I should or will deal with this issue. Probably, I should respond to that in a separate comment.
5.
“Weird methods:” Maybe I should explain how my existing proposal for rating voting methods would handle that? Because I have thought about it, and it is a tricky case. But I think I’ll save that for later; for now, I want to stick with simpler cases.
...
to be continued; probably in a separate comment or comments, for better notification.
Thanks for the close read and the thoughtful comments!
Open:
1. Loss function, future-oriented: interesting questions; I have thoughts on them; I left them out the first time through but may add them later.
2. gerrymandering; “infinite”; proposal I don’t fully grasp: Also interesting but I think beside the points I want to make here.
3. Dimensions.
“The choice of dimensions seems like a bigger deal than the number.” I’m implicitly assuming that they’re chosen by principal component analysis or something similar. Of course that’s not robust to scaling or other monotone transforms, but I think it’s close enough to being well-defined to handwave away for my purposes.
“whether things interact with each other to greatly affect outcomes”: good point. I’ll see if I can incorporate it without being too wordy.
4. Weighted legislatures: yes, that’s a whole topic I could write an entire section on. For now, can’t afford to get that sidetracked, sorry.
“Variance seems like it might be a red herring, given a focus on outcomes/exemplariness.”
Um. It’s possible I’m not being clear what I mean by “variance”. I don’t mean variance of ideologies of legislators; I mean variance (meta-variance?) of distributions. That is to say, a 1-dimensional procedure for picking 2 legislators would have higher variance if it sometimes picked {5,5} and sometimes picked {4,6}, than if it reliably picked {0,10}.
I think there may something to your critique here aside from that possible misunderstanding, though. I have some thoughts but I’m not sure how I should or will deal with this issue. Probably, I should respond to that in a separate comment.
5.
“Weird methods:” Maybe I should explain how my existing proposal for rating voting methods would handle that? Because I have thought about it, and it is a tricky case. But I think I’ll save that for later; for now, I want to stick with simpler cases.
...
to be continued; probably in a separate comment or comments, for better notification.