[EM] Chris BC reply

[Chris Benham]

Michael Ossipoff wrote:

>
> 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 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.
>
> Chris says:
>
> This "Beatpath Criterion" is more or less just Schulze(Winning Votes) 
> dressed up as a criterion.

> I reply now:
>
> BC is a criterion, more than it’s “Schulze’s method dressed-up as a 
> criterion“. That’s because, if “Schulze’s method” were a criterion, it 
> would be met only by one method. A narrow criterion indeed. BC, on the 
> other hand, is met by a set of methods (including, but certainly not 
> limited to, “Schulze’s method”).

There is group of pairwise methods that use "winning votes" to measure 
"defeat strength" that as I understand it always give
the same winner unless there are more than three candidates in a top 
cycle. That situation would be very very rare and almost
certainly would never happen in a public political election, so for 
practical intents and purposes the differences between them
are insignificant and they are one method.

The most prominent member of this group is Schulze (aka Beatpath), but 
others are the Winning Votes versions of Ranked Pairs,
River, and Smith//MinMax. Correct me if I'm wrong, but isn't this all 
that you are referring to by "a set of methods"?

> BC is for my own use. I don’t offer it as a criterion.

Well, its labelled as a criterion and posted on your webpage.

> That’s why Benham caught me off-guard when he told me that BC, which 
> I’d been using, isn’t useful. 

I meant that I don't think it is generally useful for the task of 
evaluating voting methods, for discerning or discovering
which is/are the best. Because if someone thinks that it is a big black 
mark for a method if it doesn't meet all four of
WDSC, SDSC,SFC, GSFC then their mind is mostly made up.

Chris Benham