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Pasting from Mike's web page :<br>
<blockquote type="cite">
<h2>Beatpath Criterion (BC): </h2>
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.
<p>BC: </p>
<p>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). </p>
<p>*** </p>
<p>BC is met only by SD, SSD, RP, and a few closely related methods. </p>
<p>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. </p>
</blockquote>
<br>
<br>
Michael Ossipoff wrote:<br>
<blockquote type="cite"> 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.
</blockquote>
<br>
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<br>
<br>
(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<br>
<br>
(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.<br>
<br>
<br>
Chris Benham<br>
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