@toby-pereira yes monotonicity fails, but I think pairwise probability margins are apparently monotonic.

I think maximal lotteries are interesting too, and I wonder if it makes sense to compensate the dissatisfied majorities with electoral credit to spend in subsequent election(s).

For example, say the maximal lottery (or maybe any other Condorcet method) elects A when there is no Condorcet winner. Let beat(X) be the set of candidates that beat X in a head-to-head majority.

Then for each B in beat(A), it seems like the majority preferring B to A should be compensated in some way. My thinking is that in aggregate, that majority should be compensated by something like the smallest extra weight they would have needed to secure B as the (Condorcet) winner against each C in beat(B). This might get complicated, and there may already be literature on this kind of thing.