[EM] Re: Schulze's method is BeatpathWinner

[MIKE OSSIPOFF]

I'd said:

>In an example such as that, BeatpathWinner and SSD
>give different results. There isn't come version
>of BeatpathWinner that is SSD.

But in your example you argue that BeatpathWinner
is indifferent between A and D while SSD chooses D.
Therefore, your example doesn't demonstrate that
"SSD isn't a special case of BeatpathWinner".

I reply:

SSD isn't a special case of BeatpathWinner because BeatpathWinner doesn't 
have a version that is SSD. Unless you count Margins, there's one 
BeatpathWinner and there's one SSD. There aren't any BeatpathWinners other 
than the one that I demonstrated to not be SSD.

It isn't just that BeatpathWinner is indifferent between A and D, as if 
BeatpathWinner had trouble choosing between them. It's a simple matter of 
BeatpathWinner choosing {A,lD} as its winner-set.
BeatpathWinner's winner-set is {A,B}, and SSD's winnner-set is {D}.

Same ballot-set. Different winner-sets. Different methods.

And, as I said, BeatpathWinner is one method, and SSD is one method, and 
they are different methods.

You continued:

To demonstrate that "SSD isn't a special case of
BeatpathWinner" you would have to post an example
where SSD chooses a candidate who isn't a potential
BeatpathWinner winner.

I reply:

No, not really. It's necessary only to show an example in which, with the 
same ballot-set, BeatpathWinner and SSD have different winner-sets.

A is a winner in BeatpathWinner, but not in SSD.

By the way, now that you're defining Schulze's method as a broad class of 
methods that includes SSD and MajorityBeatpathWinner, you can no longer say 
"Schulze's method" when you mean BeatpathWinner.

Mike Ossipoff

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