# [EM] Fw: IBCM, Tideman, Schulze

Markus Schulze schulze at sol.physik.tu-berlin.de
Sat Jun 3 07:34:15 PDT 2000

```Dear Steve,

you wrote (2 Jun 2000):
> Also, MTM has a brief description: "Elect the leader of the
> ranking which minimizes thwarted majorities."  That seems much
> simpler than any other excellent method's brief description
> because it doesn't refer to cycles or beatpaths.  It refers to
> more familiar terms.  The definition of "thwarted" majority is
> quite intuitive: If more voters ranked x over y than vice versa
> but x doesn't finish over y, we say that the majority who ranked
> x over y is thwarted.
>
> ...
>
> MTM is quite elegant and appears easiest to explain.

I want you to remember that also the Schulze method minimizes the
maximum thwarted majority. The maximum thwarted majority of the
Tideman ranking is always identical to the maximum thwarted
majority of the Schulze ranking (although I don't propose that
the Schulze method should be used to calculate a ranking).

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.

******

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).

By the way, when Schulze, path voting, SD and SSD are more
intuitive than IBCM and DCD for the members of this mailing
list then I don't see any reason why this shouldn't be true
for "members of the general public."

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

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From: "Steve Eppley" <SEppley at alumni.caltech.edu>
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Subject: How to calculate a social ranking (was Re: [EM] Fw: IBCM, Tideman, Schulze)
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Markus S wrote:
> 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.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

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Mike O wrote:
> Markus S wrote:
> >I want you to remember that the Ossipoff Subcycle Method (= your
> >favourite method until August 1998) actually violates the Pareto
> >criterion.
>
> What's the Ossipoff Subcycle Method? If you mean what I used
> to call the "subcycle rule", it was a way to avoid subcycle
> fratricide. It was never my favorite proposal.
-snip-

This isn't the first time Markus has made the illogical
inference that if someone mentions a merit of a method it means
that method is his/her favorite.  He wrote in February that at
one time the Well-Timed Withdrawal methods (a.k.a. Just-In-Time
Withdrawal) were my favorite.

> I said that Pareto is useless because it is failed by so few
> methods.
-snip-

I disagree with Mike.  It is useful to distinguish methods which
satisfy Pareto from methods which fail Pareto.  Furthermore, if
we publicly proposed a method which fails Pareto, it will likely
be heavily criticized for that failure since Pareto is a widely
accepted criterion.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

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Subject: Re: [EM] Fw: IBCM, Tideman, Schulze
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Markus S wrote:
-snip-
> 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.

> 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.

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.  :-)

> By the way, when Schulze, path voting, SD and SSD are more
> intuitive than IBCM and DCD for the members of this mailing
> list then I don't see any reason why this shouldn't be true
> for "members of the general public."

I'm unaware of any poll in EM about which is more intuitive.  I
believe Mike Ossipoff and I consider IBCM (DCD) more intuitive
than Schulze.

Furthermore, there is a glaring reason why the general public
might differ from the subscribers of EM:  EM subscribers are not
a representative sample of the general public because EM
subscribers have, by self-selection, immersed themselves in
social choice theory.

It's probably moot, however, since no one is advocating IBCM or
DCD, due to its non-monotonicity.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

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Markus S wrote:
> Dear Steve, you wrote (2 Jun 2000):
-snip-
> Therefore, my main arguments against the IBCM method and
> in favour of the Schulze method are:
>
> (1) The IBCM method violates monotonicity.
> (2) The IBCM method violates beat path GMC.
> (3) The IBCM winner usually depends on more elements of the
>     pairwise matrix than the Schulze winner.

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.)

I accept (1) as a good argument, because monotonicity is
accepted widely and by me.

(2) is not an rational argument unless a clear justification for
Beatpath GMC is provided.

(3) is false.  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.

> You wrote (2 Jun 2000):
> > Each reader must judge the relative importance of criteria.
>
> But then you have to accept that I consider these criteria
> important.

Of course.  But it would be nice to know *why* Markus thinks
Beatpath GMC is important.

It would also be nice to know why he has retreated from his
prior position that when there is a stronger criterion (i.e.,
"Stronger Beatpath") which doesn't cost compliance with some
other desirable criterion, he prefers the stronger one.

> You wrote (2 Jun 2000):
> > Norman wrote (27 May 2000):
> > > I have confirmed the result of Steve Eppley's simulation
> > > comparing the pairwise winners of Schulze, Tideman, and IBCM,
> > > which he announced to the list on February 23, 2000:
> > >
> > > >  The same software which shows that Tideman's winner tends to
> > > >  beat the Schulze winner when the two methods disagree also shows
> > > >  that the IBCM winner tends to beat the Tideman winner pairwise
> > > >  when IBCM and Tideman disagree, and the IBCM winner tends to
> > > >  beat the Schulze winner pairwise when IBCM and Schulze disagree.
> >
> > Furthermore, IBCM and MTM both have what appears to be a
> > much larger than IBCM's edge over MTM.
> >
> > MTM") I have posted some raw data, calculated by my simulation
> > software, which supports the contention that MTM dominates
>
>
> In your simulations, you implicitly presume that the voters vote
> independently. But we all agree that the voters usually don't vote
> independently.
-snip-

That sounds like a rehashed version of Markus's prior complaint
that the simulation generates voters' rankings randomly, yet
voters do not vote randomly.  I already replied to that.

> And Norman concludes correctly that then we have to prefer the
> Copeland method.

I pointed out that Norm's comment about Copeland, like Markus'
comment, is a misinterpretation of the purpose of the head-to-
comparison serves as a tie-breaker when more important criteria
are indecisive.  Perhaps Markus should give Norm time to reply
before assuming Norm won't conclude that my clarification is
sensible.

-snip-
> You wrote (2 Jun 2000):
> > If RandomVoterHierarchy is the tie-breaker, aren't IBCM and
> > MTM completely independent from clones, in whatever "strong"
> > formulation Norm referred to?
>
> Of course, you can use RandomBallot.

Markus appears to agree with me that Norm erred when he
criticized Tideman as being worse than Schulze on independence
of clones.

> But then your claim that "IBCM and MTM are more decisive than
> Schulze or Path Voting" (26 Feb 2000) becomes false.

IBCM is more decisive than Schulze or path voting.  Markus might
want people to mistakenly believe it's not, but it is.  For
instance, consider the scenario "AB52,BC51,CA51" where IBCM
chooses C and Schulze chooses C&A.  Of course, IBCM's edge in
decisiveness would only matter in small committees, not in large
public elections.

I erred when I wrote that MTM is more decisive.  The cause of
the error is that my software implemented a variation of MTM
which is faster and more decisive, but which is probably not
completely independent of clones.

The algorithm in that variation is:  When two or more of the
equally largest "unlocked & unskipped" majorities would,
individually but not collectively, not cycle with larger
"locked" majorities, check the largest "non-skipped" defeat of
the pairwinners of those majorities and lock the majority whose
pairwinner's largest non-skipped defeat is smallest.

There may be some better way to handle that case which retains
complete independence of clones (assuming that algorithm loses
complete independence of clones), but that seems to me to be a
low priority research item.  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].  I believe these are both completely independent of
clones.  Is either monotonic?

> You wrote (2 Jun 2000):
> > Markus tweaked Tideman's definition of clones and demonstrated
> > independence of "tweaked" clones of the Schulze method.  But
> > that tweak was not a strengthening of the independence
> > criterion.  It was a weakening.
>
> That isn't true. Tideman only discusses situations where every
> voter makes a complete ranking and where the winner is decisive.
> I generalized the Independence from Clones Criterion to
> situations where voters don't necessarily make complete
> rankings and where the election method could contain random
> tie breakers. Therefore, my definition of the Independence from
> Clones Criterion is stronger than Tideman's original definition.

I was referring to whatever clone criterion Norm said Tideman
didn't completely satisfy.  Norm didn't clearly state what
criterion he meant, and the only one which comes to mind is the
one having the minor technical problem when the voters are all
indifferent between a non-clone and one or more of the clones.
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.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

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Bart Ingles <bartman at netgate.net> wrote:
> Steve Eppley wrote:
> > The following data, calculated by software written to simulate
> > many voting methods, supports my contention that MTM dominates
> > prefer one's winners more than the other's winners.
> >
> > Norm Petry posted some of his own data a few days ago, but I
> > believe his data is erroneous. (See my reply to Norm in a
> > message being posted separately.)  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).)
>
> Could the difference have to do with the way random ballots are
> generated?  Randomly generated rank orders, and rankings based on
> randomly generated voter positions on one or more axes, *should* produce
> different election results.

I don't see how that can make a difference.  Regardless of how
the pairwise table is generated, Schulze, MTM, BCM, and PC(wv)
choose the same when given any 3-candidate pairwise table.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

```