Re: Least-bad Single-winner Ranking Method?
Among Condorcet methods, I'm most happy with Approval Sorted Margins. It's simple and resolves in a sensible way.
I used to maintain that page a lot but haven't had time recently.
Lately I like to think of the method as Preference Approval Sorted Margins. I feel like it's less confusing for voters if any ranking above Reject is interpreted as some level of acceptance for that candidate winning, but that there is a higher preference for certain candidates.
Let's say you have 6 tiers of approval. The top 3 tiers, A, B, and C, are preferred. Tiers D and E are approved (tolerable / acceptable). Tier F is disapproved/Reject. Rank can be inferred from rating.
This gives the same degree of expression as 4 levels of ranking with a preference cutoff. In general, any ranking with M levels with a preference cutoff is equivalent to 2M - 2 levels with top (M-1) ranks preferred, next (M-2) ranks approved, bottom rejected.
Voters are instructed to give a rating of A, B, or C to their preferred candidate, ratings D or E to candidates they can tolerate, and F to those they reject completely.
Count pairwise preferences and total preference, and total approval.
Seed an initial ranking by sorting in descending order of total preference, breaking ties with descending order of total approval. There's some room for argument on further tie-breakers, but that should do for now.
Then search the entire seeded ranking for the pair that is out of order pairwise, with minimum preference margin (breaking ties with minimum approval margin, etc.). Swap that pair. Then repeat until the sequence is in pairwise order.
This process is symmetric and biased toward higher preference. It is intuitive to voters. It is Condorcet compliant, Smith efficient, and clone resistant. It is not completely burial resistant, but it is more resistant to chicken dilemma and burial than other methods (if an "ally" is a strategic threat, put them in the approved but not preferred slot).
As described in the Electowiki page, this method is optimal in that it disrupts the overall preference rating as minimally as possible.