I'd said (referring to BeatpathWinner & SSD):
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 say:
Example: The Borda method chooses that candidate whose Borda score is maximal. Suppose person X suggests that when there is more than one candidate with maximum Borda score then the winner should be that candidate with maximum Borda score who has of all candidates with maximum Borda score the largest number of first preferences.
I reply:
Fine. Your person X is proposing a different method, one which, with the same ballot-set, will give a different winner-set than Borda will.
Borda is a method. With your example, if you ask someone what Borda will choose, that person will say, "Borda, with those ballots, will choose {A,B,C}, or whatever the several-candidate winner-set is.
If Borda, as you want to imply, Borda were a class of methods, instead of a method, the person would have to reply, "No one can say what Borda would choose in your example, unless you specify which Borda you're referring to. Your qurestion is unanswerable, because you haven't specified the method to be used."
You continue:
Suppose person X posts an example where the Borda method is indifferent between candidate A and candidate D while his proposal chooses only candidate D. Then this example doesn't demonstrate that his proposal isn't a special case of the Borda method.
I reply:
Borda's definition is what demonstrates that Mr. X's method isn't a special case of Borda. Borda is a single method, and Borda doesn't have a special case that consists of choosing, as the final winner, the Borda-points winner with the most 1st choice votes.
And Mr. X's method is different from Borda, because, with the same ballot-set, Mr. X's method gives a different winner-set.
I'd said:
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.
The term "Schulze method" is used since 1998. The very first time that the term "Schwartz sequential dropping" (SSD) was being used was on 18 Feb 2000 in a mail by you. Already in this mail, you wrote that "SSD is equivalent to Schulze's method".
I reply:
Did I say that without qualification, or did I say that they are equivalent when there are no pairwise ties? If I said it without qualification, then I spoke incorrectly. I, unlike you, am willing to admit having said something that was incorrect.
But even if I said that, at the time when you say that I said it, that doesn't make it true. SSD is not equivalent to BeatpathWinner, because, when there are pairwise ties, as in the example that I posted a few days ago, SSD and BeatpathWinner can give different results.
By the way, I suggest that SSD is more proposable than BeatpathWinner, because BeatpathWinner is less intuitive, and because justifying BeatpathWinner requires mention of cycles. SSD, like PC, has the great advantage of not mentioning cycles. In public elections, where it's safe to assume that there will be (at least nearly) no pairwise ties, SSD is effectively equivalent to BeatpathWinner.
You continue:
Therefore, the fact that SSD is not a completely new method, but only a tie-breaking strategy for the Schulze method isn't something new. It is known from the very beginning.
I reply:
Saying that SSD and the Schulze method are equivalent when there are no pairwise ties isn't the same as saying that SSD is a tiebreaking strategy for Schulze's method. Incorrectly saying that SSD is unqualifiedly equivalent to Schulze's method isn't the same as saying that they're equivalent. And even if it were, that woudn't matter, since the statement isn't true anyway.
If I said that Schulze and SSD are equivalent when there are no pairwise ties, I said that based on the assumption that Schulze's method is a method, rather than a broad class of methods that includes SSD and MajorityBeatpathWinner, among other things.
SSD is a single method, and so if Schuzle's method is a braod class of methods that includes MajorityBeatpathWinner, then obviously SSD is not equivalent to Schulze's method, even when there are no pairwise ties.
If Schulze's method had that broad definition at the time when I made that statement about equivalence, then I was incorrect (again, I admit having spoken incorrectly when it's true, which is one way in which you're different from me). But maybe that broader definition of Schulze's method as a broad class of methods is something new. I don't know, and it doesn't matter.
You continue:
The very first time that the term "BeatpathWinner" was being used was on 9 May 2000 in a mail by you. In this mail, you wrote: "I refer to the method that's been known as 'Schulze's method', and which I'll sometimes call 'Beatpath Winner'." Therefore, the fact that BeatpathWinner is not a completely new method, but only a new name for the Schulze method isn't something new. It is known from the very beginning.
I reply:
Yes, I said that believing that Schulze's method is a single method. Maybe it was at that time, in which case my statement then was correct. Or maybe, even then, you meant for "Schulze's method" to mean a broad class of methods that includes MajorityBeatpathWinner, etc. In that latter case, obviously my statement that BeatpathWinner is a name for Schulze's method was incorrect.
Again, it doesn't matter which is of those two possible cases is the correct one.
Mike Ossipoff
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