Instant Pairwise Runoff and similar Condorcet methods seem like they would produce good results, though I'm averse to unsummable methods for practical reasons.

Instant Pairwise Runoff and similar Condorcet methods seem like they would produce good results, though I'm averse to unsummable methods for practical reasons. But I think there's more nuance than saying a ranking method better captures voter preference than Approval because there's numbers. An ordinal method loses information about the distance between ranks. A voter could strongly prefer two candidates and then despise the rest of the pack pretty equally, and much of that distinction is lost in ranking. And the overall end result, even if it doesn't end up electing a despised candidate, is making a despised candidate look like they're the third most popular. That information helps shape who's involved in future elections.