[EM] Schulze's method isn't BeatpathWinner

[MIKE OSSIPOFF]

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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