[EM] Fw: IBCM, Tideman, Schulze

[Markus Schulze]

Dear Steve,

you wrote (3 Jun 2000):
> I snipped the part where Markus pretended to have discovered 
> IBCM's non-monotonicity.  (Similar to how he has repeatedly 
> pretended during the past few weeks to have discovered that 
> Mike's 1998 Tideman GMC example was impossible, when I was the 
> one who pointed out that it was impossible.)

You pretend that I claim that I have discovered that IBCM
violates monotonicity. Could you please tell me where I make
that claim?

You pretend that I claim that I have discovered that Mike's
1998 Tideman GMC example was impossible. Actually, you wrote in
your 13 May 2000 mail that Mike's example was impossible. But
Mike replied (13 May 2000) that such an example _is_ possible.
Therefore I have sent a new proof of the impossibility of such
an example in my 19 May 2000 mail.

******

You wrote (3 Jun 2000):
> Markus wrote (3 Jun 2000):
> > You wrote (2 Jun 2000):
> > > Markus noted, shortly after, that I didn't specify who I had in
> > > mind (to suggest I was lying?).  Markus pointed out Blake and
> > > Mike as examples of people who understand Schulze's method,
> > > clearly missing the point that our concern is about members of
> > > the general public who don't study voting methods but would be
> > > asked to decide whether to change their voting method.
> > 
> > I want you to remember that you used the same phrase in your
> > 26 Feb 2000 mail ("Neither did Markus identify the participants
> > in this maillist who believe that Schulze meets an important
> > criterion not met by Tideman."). Therefore there is no
> > justification for you to believe that I suggest that you
> > were lying (except for the case that you wanted to suggest
> > in your 26 Feb 2000 mail that I was lying).
>
> Except that there is a big difference between the two events.  
> Markus has omitted the context of my comment.  I wrote:
>
> >   Markus neglected to define "top set."  Nor did he identify
> >   the participants in this maillist who believe that Schulze
> >   meets an important criterion not met by Tideman.  If Markus
> >   was counting me among them, he shouldn't.  And based on
> >   private email correspondence with Mike Ossipoff over the
> >   last few months, it's clear to me that Mike also does not
> >   believe Schulze is better than Tideman in any important way,
> >   and Mike no longer considers GMC or Beatpath GMC to be
> >   important.
>
> So in my case, there was ample reason to believe that Markus had 
> erred when he claimed support by others.  I was pointing out 
> that it was likely Markus was counting people whose minds had 
> changed.  Clearly that is not a suggestion that he was lying, 
> but a suggestion that his information was not up-to-date.

You made your claim just after Norman had explained at great
length that he "personally considers GMC to be a very important
criterion" (8 Feb 2000). When you read his 8 Feb 2000 mail (and
his 27 May 2000 mail) then you will observe that he is always
talking about beat path GMC.

******

You wrote (3 Jun 2000):
> Markus also nastily replied that I should have let Mike speak 
> for himself about GMC and Beatpath GMC. (To which I disagree: 
> there's no guarantee that Mike would notice the discussion or 
> have time to respond).  So apparently, when it comes to 
> mentioning the names of others, you're damned by Markus if you 
> do and damned if you don't.  :-)

The problem is that you always refer to Mike although Mike
disagrees with you in so many points.

******

You wrote (3 Jun 2000):
> Markus wrote (3 Jun 2000):
> > If more than one majority has to be thwarted then "Elect the
> > leader of the ranking which minimizes thwarted majorities."
> > rather sounds like the Kemeny-Young method than like the
> > Tideman method.
> > 
> > If you really want to describe the Tideman method properly then
> > you have to use a significantly longer description.
>
> Not so.  Tideman pointed out in his 1987 article on clones, 
> where he defined his method, that it
>
>    "... is akin to applying the minimax rule to orderings
>    rather than to candidates."
>
> (Then Tideman went on to explain that he technically means 
> minileximax rather than minimax, when there are minimax ties.)
>
> MTM is not Tideman.  Tideman's minileximax used margins, whereas 
> MTM's minileximax uses majorities.
>
>    "Thwarted majorities":  If more voters ranked x over y than
>    vice versa, but the social ranking does not rank x over y,
>    then the social ranking "thwarts" the majority who ranked
>    x over y.
>
> Thus, it is accurate to say that MTM elects the leader of the 
> ranking which minimizes thwarted majorities.

But then you have to say: "Elect the leader of the ranking of the
minilexmax thwarted majority." and to explain what the minilexmax
thwarted majority is.

When you only say "Elect the leader of the ranking which minimizes
thwarted majorities." then it is not clear how the total violation
is measured when more than one majority has to be thwarted.

******

You wrote (3 Jun 2000):
> Markus wrote (3 Jun 2000):
> > Dear Steve, you wrote (2 Jun 2000):
> -snip-
> > >    Define the "1st place finisher" as the given method's winner.
> > >    Define the "Nth place finisher" as the alternative which
> > >    would be chosen by the given method if preferences for the
> > >    1st thru (N-1)th place finishers were neglected.
> -snip-
> > I want you to remember that you haven't yet explained how the
> > IBCM method is used to calculate a ranking of the candidates.
> > If your answer is "I don't use the IBCM method to calculate a
> > ranking." then your argumentation becomes quite meaningless
> > because this answer would demonstrate that you agree with me
> > that the task of an election method is to find a winner and not
> > a ranking.
> -snip-
>
> The algorithm I provided above shows how such a ranking can be 
> calculated for any single-winner method.  Including IBCM.  
> Therefore Markus' conditional suggestion that my argument was 
> meaningless is irrelevant.

But if you use that algorithm then the IBCM method violates the
Subsequence Invariance Criterion too.

******

The biggest problem of your argumentation is the fact that when
you try to show a problem of the Schulze method you compare it
sometimes with the IBCM method and sometimes with the Tideman
method. It is clear that if you want to show that the Schulze
method is inferior then you always have to compare it with the
same method.

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de