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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