@toby-pereira yes definitely. I started trying to actually prove participation last evening, and it got much hairier than I would have liked... lots of branching edge-case conditions. I think an actual proof (or counterexample) of participation for this system would require some nice insights, and/or a larger scale planning and brute-force organized accounting of every relevant case.
For example, I’m quite certain the new participant V can never change the top sorted candidate to somebody they prefer less. So it would have to be an upset via the B2R survivor, who would have to become the new winner, and be preferred less than the old winner by V. But that situation gets complicated in terms of the sorting and the rank tie-breaking authority.