Suggestion by Tideman: “Bottom Two Elimination Runoff”
Tideman suggests a Condorcet-compliant version of IRV, where the bottom two least (top)-preferred candidates undergo a majoritarian preference runoff, with the loser being eliminated and the process repeating. This complies with the Smith criterion as well, I’m not sure what other criteria it satisfies (ex: I doubt it is monotonic, although it does seem to have more resistance to producing non-monotonic results than IRV--could it be monotonic?) but I thought it was an interesting concept. I think with exact ties, quasi/weak-Condorcet winners can still be eliminated which is potentially problematic, but I like the idea of this method because it can be used to shrink large candidate pools to any desired size in a simple and consistent way.
Here is an example with three candidates and a comparison with the results of other methods:
In this case, there is no Condorcet winner. This new method by Tideman, his older method Ranked Pairs, IRV, Dodgson and Young voting all agree with the ranking A>B>C.
A and B are both Bucklin winners, so depending on how a single-winner is chosen it could give A>B>C or B>A>C. Black voting (AKA Condorcet/Borda) on the other hand ranks B>A>C.
An argument against the ranking B>A>C is that if C were removed, A would beat B, meaning that using Black voting has made C a spoiler for A. In any case it isn't actually clear which ranking is preferable, the ambiguity is related to the independence of irrelevant alternatives criterion.
Generally speaking, he endorses any kind of Condorcet method; for a while he and another world-class economist had together written some essays proposing what is essentially Copeland//Borda (now rebranded by EVC as Ranked Robin)
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@cfrank Not long ago I posted this, I assume we are talking about the same thing? I usually call it BTR. Tldr: I like it.