If you have a vote split in a 6-winner election between two parties of:
the proportionally better answer seems to be 3 A 3 B but this contradicts majority rule, which would seem to require 4 A 2 B, since otherwise the A’s and B’s will tie when voting contentiously in the legislature and the majority of voters won’t have full control (though they’ll have veto power). A similar analogy could probably be made with cardinal ballots if one party gave greater social utility overall.
If the tiebreaker suggested above is used (and for cardinal methods, it might make sense to say that one side must not only give greater overall utility, but receive a majority of support i.e. majority of points possible, which I suspect can be thought of as receiving majority preference after applying the KP transform), then the majority will have full control even under the proportionally better result.
Maybe when computing majority preference, votes for irrelevant candidates shouldn’t be figured in. On the other hand, those votes may be protest voters who wanted to make it harder for anyone to get a majority.