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 Epplely's 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 it's only
applied to rank methods. But it's a convenient way to test for
compliance with all the majority defensive strategy criteria. BC's
wording doesn't make it obvious why it should be met, and so I prefer
my criteria, as criteria. I use BC as a test.
This "Beatpath Criterion" is more or less just Schulze(Winning Votes)
dressed up as a criterion. I don't think this is very useful 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
(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.
Chris Benham
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