Kevin wrote
Sprucing up Bucklin and IRV seem particularly interesting. But I doubt it is able to do anything helpful with the 49 A, 24 B, 27 C>B scenario.
I (mis)read 49 A, 24 B>C, 27 C>B
In Kevin's example B beats A beats C beats B, so there is no covered candidate to eliminate nor any beat clone set to collapse. So, as Kevin correctly divined, sprucing up does nothing for this example.
Sorry for the confusion; I'll just blame the curled up tongue!
It's an ill wind that blows no good. I hope the example of collapsing, etc. is valuable once you understand that is is based on what I read instead of what Kevin wrote.
Has anybody gone to the trouble of doing a symmetric completion on Kevin's example, followed by as much reverse cancellation as possible?
I'm not sure if that would improve things, but those steps would be necessary in order to reduce the geometry to two dimensions.
Here's what I get:
25 ACB 5 CBA 24 BAC
Candidate A wins under Bucklin, Borda, and all reputable versions of Condorcet, which is what margins would also give in the original (before the symmetric completion), but contrary to winning votes, which would give B in the original, along with Bucklin and MCA.
IRV gives A in the original, but B after the symmetric completion and reverse cancellation, just backwards from winning votes Condorcet methods and Bucklin.
So far, Spruced Up Bucklin seems to be holding up.
[Remember the symmetric completion and reverse cancellation are not part of the sprucing up property; they are only an assumption making possible two dimensional geometrical analysis of spruced up methods that already happen to satisfy the Symmetric Completion and Reverse Cancellation properties.]
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