Dear gentlemen, I’ve been playing with idea of the Serious Candidate Set (set of candidates who would, in the context of a ranked ballot, win an approval count if they were to serve as universal approval cutoffs, SCS below) a bit more and, having done some improvements on my earlier thinking (h/t Chris Benham and Kristofer Munsterhjelm), I think I have chanced upon a half-decent method, a Condorcet-Approval hybrid. Alas, a complex count which is, at the very least, non-monotonic, non-additive and fails Later-no-Harm. The count applies to ranked ballots where equal ranking and truncation are allowed. STEP 1, if any remaining candidate has a majority of first preferences, elect them. Otherwise, STEP 2, remove the last preference from any ballot that ranks all remaining candidates. Then, STEP 3, compute the SCS. If the SCS includes only one candidate, elect them. Otherwise, STEP 4, remove all candidates not in the SCS from all ballots. If at least one candidate is thus removed, return to STEP 1. Otherwise (and this would occur in a minority of cases), STEP 5, [put a backup resolution method here, I go with Iterated Bucklin because of course I do]. I believe the first 4 steps (which should produce a resolution and won’t require step 5 most of the time, even when there isn’t a CW) are an alternative algorithm suited to electing the Condorcet Winner if there is one. Not a particularly efficient algorithm of course, but one that will elect a winner even if there is no CW. Unlike algos like Nanson/Baldwin though, these first steps may, at times, enter a cycle with no resolution requiring a backstop method. This may seem like an “elect the CW if there is one, otherwise elect the IB winner” method, but it isn’t, since there’s quite a few scenarios where this method elects a Smith Set winner different to the one the IB algorithm does. Regards, Etjon