[EM] Replying to Markus

[Markus Schulze]

Dear Mike,

you wrote (17 Apr 2001):
> Markus wrote (17 Apr 2001):
> > It isn't clear what you mean with "BeatpathWinner. Due to the
> > usual way, in which new terms are created out of old terms in this
> > mailing list, the "BeatpathWinner" seems to be the winner of the
> > Beatpath Criterion Method.
>
> No, BeatpathWinner is the name of a method, not a candidate.
> Steve and I both began using the term "BeatpathWinner" here around
> the same time, to refer to what we then believed you to mean by
> "Schulze's method".

Nope! Steve Eppley never used the term "BeatpathWinner" in this
context. He always used the term "Schulze method." Therefore it
seems that you have mixed up the Schulze method and the Beatpath
Criterion Method and that some time you began to use these terms
synonymously. Please read Steve Eppley's mails in the archive!

He wrote (2 Jun 2000):
> As Markus noted last year, given 3 candidates, Schulze and
> PC(wv) choose the same.  Yet we can see that Norm's 3-candidate
> column ranks PC(wv), MTM, and IBCM below Schulze.
>
> [snip]
>
> Schulze, MTM, and PC(wv) must tie in the 3-candidate stat.
>
> [snip]
>
> So in the 3-candidate comparison, the stat when comparing any two
> of {IBCM, MTM, Schulze, PC(wv)} is 0-to-0.  If I also counted
> indecisive scenarios (which would be rare in large public elections
> but not in committees) I believe IBCM would show an edge over Schulze
> in the 3-candidate case, due to scenarios where Schulze chooses two
> and IBCM chooses the pairwinner of Schulze's two. (For example,
> the scenario "BC52,CA51,AB51" where Schulze chooses A&B and IBCM
> chooses A.  When the Schulze tie is broken, it may choose B,
> which would count fractionally for IBCM head-to-head.) So I stand
> by my conclusions: IBCM & MTM dominate Schulze on the head-to-head
> comparison.
>
> [snip]
>
> Another criterion which distinguishes between MTM and Schulze is
> the Subsequence Invariance criterion I posted in February.
>
> [snip]
>
> Markus tweaked Tideman's definition of clones and demonstrated
> independence of "tweaked" clones of the Schulze method.
>
> [snip]
>
> I planned to post a message about this after the Tideman vs.
> Schulze debate is wrapped up.
>
> [snip]
>
> Norm is one of the people I had in mind when I wrote a
> couple of weeks ago that some people in EM have written they
> think it may be too hard to explain Schulze's method.
>
> [snip]
>
> This leaves MTM, Schulze, and perhaps SSD.
>
> [snip]
>
> SSD's definition doesn't seem nearly as simple as other methods,
> since it refers to the (dynamically recalculated) Schwartz set.
> Given that plus its iteration, people may find SSD hard to
> understand, maybe even harder than Schulze, and if that's true
> then SSD offers nothing Schulze doesn't offer.
>
> [snip]
>
> The following data, calculated by software written to simulate
> many voting methods, supports my contention that MTM dominates
> Schulze in the head-to-head comparison of whether voters would
> prefer one's winners more than the other's winners.
>
> [snip]
>
> In particular, Norm's data showed Schulze best when there are
> 3 alternatives, but my reckoning is that, when there are 3
> alternatives, the Schulze winner never beats the MTM winner or
> the IBCM winner or the PC(wv) winner. (As Markus noted a year
> ago, when there are 3 alternatives, the Schulze method chooses
> the same as PC(wv).)
>
> [snip]
>
> 1. With 3 (or fewer) alternatives, Schulze and MTM behave the
> same, in accordance with theory.
>
> 2. With 4 or more alternatives, MTM dominates Schulze, and the
> more alternatives there are, the greater is MTM's dominance of
> the "W1-W2" stat.
>
> 3. The secondary stat "V1-V2" (the number of voters preferring
> the MTM winner more than the Schulze winner minus the number of
> voters preferring the Schulze winner more than the MTM winner,
> averaged over the scenarios where the two methods are decisive
> and disagree) also favors MTM.
>
> Note: Each reader must judge the relative importance of
> criteria.  The head-to-head comparison can serve to distinguish
> between methods which are not distinguished by any of the
> criteria the reader considers more important than the head-to-
> head comparison.
>
>    Method 1 = MTM (majoritarian Tideman)
>    Method 2 = Schulze

He wrote (3 Jun 2000):
> I believe Mike Ossipoff and I consider IBCM (DCD) more intuitive
> than Schulze.
>
> [snip]
>
> It should be reworded as saying that the IBCM winner depends
> *more often* on more elements of the pairwise matrix than does
> the Schulze winner.  Since this can be considered a feature of
> IBCM (and MTM) and a bug for Schulze, one can use (3) as an
> argument in favor of IBCM (and MTM) and against the Schulze
> method.
>
> [snip]
>
> Markus appears to agree with me that Norm erred when he
> criticized Tideman as being worse than Schulze on
> independence of clones.
>
> [snip]
>
> IBCM is more decisive than Schulze or path voting.
>
> [snip]
>
> The issue of Schulze vs. MTM does not depend on an argument that
> MTM is more decisive than Schulze.  So let's continue to compare
> the Schulze and MTM which are both completely independent of
> clones. Another way to enhance decisiveness is to repeat a
> method: [MTM] & [Schulze].
>
> [snip]
>
> That technical problem was solved by weakening the criterion,
> and that solves it for Tideman (and MTM and BCM and IBCM) as
> well as for Schulze.
>
> [snip]
>
> Regardless of how the pairwise table is generated, Schulze,
> MTM, BCM, and PC(wv) choose the same when given any 3-candidate
> pairwise table.
>
> [snip]
>
> In a message I posted earlier today, I retracted a claim made
> a few months ago that MTM is more decisive than Schulze.
>
> [snip]
>
> Schulze chooses A & B & C.
>
> [snip]
>
> So MTM appears to be more decisive than Schulze, without
> compromising its complete independence of clones.

In so far as Steve Eppley never promoted the Schulze method,
there is also no real reason why he should have introduced
a new term for this method.

Markus Schulze