[EM] Chris's letter revisited

[Chris Benham]

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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