@toby-pereira I agree with this. Something in that spirit I am considering is that the power allocations can still be traced back to ballots. For example, if the seated representatives and powers were {A:45, B:35, C:20}, in principle, those single seats could be subdivided into multiple seats of roughly equal power, depending on the candidate pool (i.e. how many candidates are available).
Possibly, a sub-election could be run to determine the representatives within the A:45 group, etc. Maybe they could be given 4 seats, the B:35 group 3 seats, and C:20 2 seats. That could refine representation, some candidates might pick up multiple seats. It’s probably getting messy and complicated, it essentially becomes a hierarchical partitioning of ballots. I’m not sure what to make of the prospect of that.
I do see what you mean. An individual voter may actually prefer a particular coalition of candidates, rather than just want to get their top guy in. I wonder if non-strict rankings and distributed power would mitigate this issue, or for instance, if the A:45 group's sub-election guaranteed a seat for A, and ran the election on the remaining candidates, that might align with the spirit of preference for whole coalitions.
You definitely are more familiar with this space than I am, so I wager some of my objections may be non-issues when one considers alternative PR methods. But it seems to me that in this case, pushing for coalitions that respect single individual preferences for whole coalitions can lean toward reduced diversity and reduced minority representation. Is that inaccurate? Or is that a common tradeoff issue in PR systems?
“Would the weighting purely count towards their voting power in the elected body, or does it have other effects such as more time to speak?”
Yeah, it does beg some questions.
EDIT: After multiple adjustments made to guard against clone dependence and tactical voting, there is a non-monotonicity issue in my version, where a minority faction can gain strictly preferred representation in the form of a seated candidate by merely withholding approval for that candidate. I have a concrete example of this, and may try to see how to address it. It may be due to something unnecessary.