[EM] Markus--BeatpathWinner isn't SSD

[MIKE OSSIPOFF]

I'd said:

>Yes, but to outdo a majority pairwise vote, it's necessary
>for that MPV to be in a cycle of MPVs _all of which are at
>least as strong as it is_.

You say:

In 1997, I proposed the following method (Schulze method,
Schwartz sequential dropping, cloneproof Schwartz sequential
dropping, beatpath method, beatpath winner, path voting,
path winner):

I reply:

SSD and CSSD are two different methods, which can give two different 
outcomes with the same ballot-set. So BeatpathWinner can't be both SSD and 
CSSD.

BeatpathWinner is equivalent to CSSD, but not to SSD.

I mention that for your information, so that, if you want to be correct, you 
can leave SSD out of the list of names that refer to BeatpathWinner or 
methods equivalent to it. But it isn't important, and, as I said, I mention 
it only for your information.

You continued:

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

I reply:

And that's relevant to...what?

Yes, a candidate who can't win without violating majority rule also can't 
win in BeatpathWinner. But the set of candidates who can win without 
violating majority rule is not the same set as BeatpathWinner's winner-set.

Now, comparing Beatpath GMC to majority rule:

Here's an example of how my definitioin of majority rule differs from your 
Beatpath GMC criterion:

100 voters:

AB52, BC51, CA51

Beatpath GMC doesn't say that B shouldn't win, but if B wins that's a 
violation of majority rule as I define it.

The reason why my definition of majority rule is different from your 
Beatpath GMC is that I don't consider a defeat to be nullified unless it's 
in a cycle whose other defeats are all at least as strong as it is.

By the way, that's a good way to motivate and justify BeatpathWinner, RP & 
MAM in public proposals.

Mike Ossipoff

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