@gregw BTR/score (or BTR/approval) is an excellent system, although it is not stable ex ante under majority preference—only a maximal lottery is. Maximal lotteries also satisfy participation and Condorcet (they can do that because they are inherently non-deterministic in the case of Condorcet cycles—those properties are incompatible for deterministic methods).

BTR was invented by Nicolaus Tideman. He is still around, I don’t know how accessible he is but he is certainly involved in voting theory. Sorting/tie-breaking by score or approval in BTR is an obvious extension.

For primaries, a specified multi-winner method is needed, which could be a “natural” extension of a single-winner method. Peeling winners of BTR off recursively is one option, although it would be more stable to prioritize candidates in the Smith/bipartisan set (the naive recursion can lead to results that violate multi-winner Smith compliance). A PR/multi-winner method would probably be theoretically preferable, maybe some others more versed in multi-winner methods can comment on options for simplicity.

Something on my mind, for any Condorcet method, even a maximal lottery, being intrinsically stable under majority preference after a winner is chosen is simply impossible with Condorcet cycles. My thinking lately is, this implies that stability requires a supplementary mechanism that compensates dissatisfied majorities in the event of Condorcet cycles, specifically to the extent that majority grievances are sufficiently reduced. However, I don’t know what that mechanism ought to be or how it ought to be enforced, and serious consideration of that enters the interface between technical voting theory, real politics, and law. I mused about that here: https://www.votingtheory.org/forum/topic/591/maximal-lotteries/8

Just food for thought. I’m glad your reform efforts are picking up steam!

P.S.: While I do like Condorcet methods, my opinion is that realistic and highly impactful reforms would be easiest to implement by pushing for approval voting. We discussed that point here as well and it seems to have broad agreement, but obviously that’s just my personal interpretation and some disagree for their own reasons: https://www.votingtheory.org/forum/topic/495/approval-voting-as-a-workable-compromise/20?_=1768708850097

Ultimate approval would still require a multi-winner primary system.