Chris quotes me:
Pasting from Mike's web page :
Beatpath Criterion (BC):
BC is only applied to rank methods. Its purpose is as a test for compliance
with SFC, GSFC, WDSC, & SDSC. Any rank method that meets BC meets those 4
criteria.
BC:
No one should win who has a pairwise defeat that isn't the weakest defeat in
some cycle. (The strength of B's defeat by A is the number of people voting
A over B).
***
BC is met only by SD, SSD, RP, and a few closely related methods.
BC generalizes & underlies the 4 majority-based defensive strategy criteria
(WDSC, SDSC, SFC, & GSFC). Any rank method that meets BC also meets those 5
criteria.
Michael Ossipoff wrote:
So I prefer my own preference-based wordings of my defensive strategy
criteria. However, I myself have used a votes-only, rank-methods-only test
for compliance with my criteria: Steve Epplelys Beatpath Criterion. Any
rank method that meets BC meets all four majority defensive strategy
criteria (SFC, GSFC,. WDSC, & SDSC). You could say that no nonrank method
meets BC, or you could say that its only applied to rank methods. But its
a convenient way to test for compliance with all the majority defensive
strategy criteria. BCs wording doesnt make it obvious why it should be
met, and so I prefer my criteria, as criteria. I use BC as a test.
Chris says:
This "Beatpath Criterion" is more or less just Schulze(Winning Votes)
I reply now:
How about a bit more less than more <smiley>
Maybe Chris knows what he means by more or less. You could say that
anything is more or less anything, though it might be more on the less
side.
If you dressed-up BeatpathWinner as a criterion, various wv methods that
meet BC wouldnt meet BeatpathWinner.
Chris continues:
dressed up as a criterion.
I reply now:
No, not dressed up as a criterion. BC is a criterion. No one has proposed it
as a method. It is different from BeatpathWinner. As is often the case with
criteria and methods, a number of methods meet BC, but only one method is
BeatpathWinner. BC is not BeatpathWinner, and BC is a criterion.
Chris continues:
I don't think this is very useful
I reply now:
That depends on what you want to use it for, stupid.
I stated what I use it for. I said that I use it for demonstrating
compliance with all four of the majority defensive strategy criteria. Its
very useful for that. I never said that it was useful for anything else,
stupid.
Chris continues:
because
(a) anybody who insists that a voting method meets this (i.e. the 4 criteria
it tests for) has (98%) ended their search for the best voting method, and
I reply now:
Hey, Einstein, what if someone wants me to show them that, say,
BeatpathWinner meets the four majority defensive strategy criteria.? There
are properties that I claim desirable. Can you find it in your heart to
forgive me if I want a way to demonstrate which methods comply?
Chris continues:
(b) some people like one or some but not all of the 4 criteria, so it is
much better to be able to test for them individually.
I reply now:
People have asked me to demonstrate that certain methods meet all four of
the majority defensive strategy criteria.
Mike Ossipoff
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