[EM] Re: BeatpathWinner is SSD

[MIKE OSSIPOFF]

Markus--

You said:

BeatpathWinner _is_ SSD _is_ CSSD in so far as all of them
share this property:

   If p(z)[A,B] > p(z)[B,A], then candidate B must be
   elected with zero probability.

If you don't agree with this then please post an example
where this is not true.

I reply:

If sharing a property makes methods the same, then BeatpathWinner is 
Approval, because both methods meet WDSC.

Maybe you're  now defining BeatpathWinner as a class of methods, in which 
case BeatpathWinner, as defined by you, is not a method. But in that case, 
we can say that SSD is BeatpathWinner, but not that BeatpathWinner is SSD. 
That's for the same reasons that it's correct to say that schnauzers are 
dogs, but it isn't correct to say that dogs are schnauzers.

So  no:  No matter whether you define BeatpathWinner as a method or a class 
of methods, BeatpathWinner is not SSD.

By the way, it's always been understood here that BeatpathWinner is a 
method, not a class of methods, except that some people speak of a 
BeatpathWinner(margins) and a BeatpathWinner(wv).

Here's an example in which BeatpathWinner (when defined as a method)  and 
SSD choose differently:

AB102, BC101, CA100   A,B,& C are all pairwise tied with D.

SSD elects D, because SSD says:

1, If there is/are any unbeaten candidate(s), they win and the count ends.

2. Otherwise, determine which candidates are in the Schwartz set, based only 
on undropped defeats.

3. Drop the weakest defeat among the members of that set. Go to 1.

[end of SSD definition]

BeatpathWinner and CSSD elect D and A.

BeatpathWinner chooses D and A  because neither has any candidate with a 
beatpath win against them.

CSSD always chooses the same as BeatpathWinner. CSSD's rule is:

1. Determine which candidates are in the Schwartz set, based only on 
undropped defeats.

2. If there are no defeats among the members of that set then they win, and 
the count ends.

3. Otherwise, drop the weakest defeat among the members of that set. Go to 
1.

[end of CSSD definition]

Mike Ossipoff

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