Rank methods, Participation, Consistency

[MIKE OSSIPOFF]

Richard wrote:

Can you name a specific ranked method that's monotonic, that fails the
other two? I've heard claims that Condorcet is monotonic, but I wonder if
it's true. If so, *which* Condorcet completion methods are monotonic? Are
there proofs for these methods being monotonic?

I reply:

I can't name a method that fails Participation & Consistency and
has been proven Monotonic. It seems to me that Ranked Pairs is widely
assumed to be Monotonic, but I don't know if that's proved. The fact
that Tideman liked RP suggests that he knew it was Monotonic, but
I don't know. Has Markus shown that BeatpathWinner (Schulze's method)
is Monotonic?

PC (Minmax) can be stated in a non-iterative way, and I once believed
that that meant it's monotonic. But I seem to have heard that Dodgson
is nonmonotonic, even though it isn't iterative.

It's been shown on EM that at least one Condorcet version, which
I'd called "Sequential Dropping" (not SSD) is nonmonotonic. SD
repeatedly drops the weakest defeat that's in a cycle, till there's
an undefeated alternative.

Of course, as I think you suggested, not much can be said about
this till Monotonicity has a definite definition.

Mike Ossipoff


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