[EM] Schulze's method is BeatpathWinner

[Markus Schulze]

Dear Mike,

you wrote (1 April 2005):
> SSD isn't a special case of BeatpathWinner. SSD
> and BeatpathWinner are two dilfferent methods that
> can give two different outcomes wilth the same
> ballot-set, as in the example that I posted yesterday.
> In an example such as that, BeatpathWinner and SSD
> give different results. There isn't come version
> of BeatpathWinner that is SSD.

I wrote (1 April 2005):
> 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".
> 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. But this is not possible
> because also SSD has this property (which makes
> SSD a tie-breaking strategy for the Schulze method):
>
>    If p(z)[A,B] > p(z)[B,A], then candidate B must
>    be elected with zero probability.

You wrote (2 April 2005):
> 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,D} as its winner-set.
> BeatpathWinner's winner-set is {A,D}, 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.

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. 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.

Therefore, your argumentation is incorrect. To prove
that "SSD isn't a special case of BeatpathWinner",
you would have to post an example where the winner-set
of SSD isn't a (not necessarily strict) subset of the
winner-set of BeatpathWinner.

*********

You wrote (2 April 2005):
> 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". 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.

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.

Markus Schulze