[EM] Cycle Definition of BeatpathWinner

[MIKE OSSIPOFF]

A defeat is nullified if it's in a cycle that doesn't
include a weaker defeat.

A candidate wins if he doesn't have an unnullified
defeat.

[end of definition]

This is a briefer definition of BeatpathWinner.
It has as obvious & natural motivation & justification
as CSSD, but it's much briefer than either the
BeatpathWinner wording or the CSSD wording.

It's reasonable to say that a defeat is nullified if
it's in a cycle that doesn't have a weaker defeat.
If a defeat is in a cycle of equal defeats, there's
no particular reason why it should be one of those
that's honored. If a candidate has a defeat, and
the only cycle that it's in consists of all equal
defeats, it's obvious that that defeat can't be
called a reason why that candidate can't win.

IRVists and others often criticize Condorcet by saying
that it's only about electing a BeatsAll candidate,
and by portraying cycles as a problem that spoils
Condorcet's justification.

Nothing could be farther from the truth--The better
Condorcet versions are or can be defined in terms
of cycles. Cycles are at the basis of what Condorcet
is.

If the people indicate that they collectively prefer
X to Y, then Y shouldn't win, unless...what?
The only thing that could nullify that defeat and
justify letting Y win would obviously be if that
defeat is in a cycle in which there aren't weaker
defeats.

Obviously, there's no point calling that method
BeatpathWinner, in a public proposal. I don't know
what would be a good name.
Maybe Non-Iterative-Nullification (NIN). And, Josh, I'm
not saying that should necessarily be the name for
public proposals. It's just the descriptive name,
for that definition, that occurs to me.

Mike Ossipoff




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