[EM] Rejecting the Schulze preferential voting method: a time for reform

Craig Carey research at ijs.co.nz
Thu Dec 18 09:42:02 PST 2003

I see that Marcus/Markus Schulze posted in 2 lines. While we wait
for the rest of the clipped communication (not conversation) I
post up some ideas. As ever, guessing is second to a catechistic
approach (with mind-changing over the answers allowed).


Mr Schulze did not reply to the issues which was that his method was
in the trash can and he had:
 1. got it to be biased in that same way that occurs for a method that
    always picks the 1st candidate on the list of candidates no matter
    what the votes are. I assume Mr Schulze agrees but he as usual he
    comment in response to every issue painting him up and not knowing
    how to design a preferential voting method.
 2. The presence of absence of the last preference affects who wins.

Both those ideas can indicate that the whole article was a junk and
trash. Mr Schulze wrote as if he could possibly begin to sense the
problem. With the idea that Mr Shulze can't understand everything that
much better theorists can precisely informa him of, I was going to
write a computer program to prove that his computer algorithm is

That follows his leaking following being moderated for censoring out
all information about the purpose for being so in the wrong which
the STV mailing list was certainly not getting adequately informed

Mr Schulze has got a bias and I believe htat he has a purpose of
providing untrue information. The topic of how Mr Schulze can not
reply to 100% of the e-mails implying he start doing research into
nothing but his own trashy Schulze methods does not seem that
interesting. Why are core ideas of Condorcet so suboptimal since
proportionality and fairness are crushed/mangled together ?.

After these 5 years the ulitmate best Mr Schulze has been able to
do in the area of defending the garbage ideal, is to keep up the
pretense of never being able to identify the topic. That seems to be
the uniting ideal of Condorcet: even if Dr Dolittle's animals could
all understand why the lie of Condorcet pairwise comparing being
good is something so suboptimal that the method can't be said to be
optimal, the Condorcet believer would be suggesting he is following
the public idea that pairwise comparing is important. External is
idealized STV where both fairness and proportionally are both
perfectly defined and achieved except as best possible in the

Also Mr Schulze seems to get a few lines out every month to public
lists and constantly nothing at all to private e-mail. Teh big
aim in public mailing lists seems to be to drop names. When he
has a problem with transparency of purpose he slips into a dumb
mailing list - this one, where persons who know nothing and do
no useful research, congregate wishing that some religious man
unable to decide nothing is something and visa versa, would lead
them out.

In the grand sweep of Mr Schulzes exposition, he designed the
algorithm in the paper so the input is never votes. The preprocessing
stage that proves that the method is stupid, got censored out. It
is the case that reasoning indicates that Schulze's method should
be rejected instead of tested. 

Let's consider the algorithm itself. Here I quote from the VM 17
PDF file:

:     Suppose that d[X,Y] is the number of voters who
:     strictly prefer candidate X to candidate Y. Then the
:     Smith set is the smallest non-empty set of candidates
:     with d[A,B] > d[B,A] for each candidate B outside this
:     set.

The English text of Schulze probably seems to imply this

* Let there be only 3 candidates. Let the ballot papers be these:

2 (CA)
5 (CAB)
1 (CBA)

What is Mr Schulze's d[A,B] ?.

We could look at the computer algorithm source code but it takes
the "d" matrix as an input. The vote counting algorithm can't actually
accept votes.

The d[A,B] value would be:

 (Interpretation 1) the number 7, or
 (Interpretation 2) the number 5, or
 (Interpretation 3) the number 6, or
 (Interpretation 4) the number 4, or

I suppose Interpretations 3 and 4 can be rejected.

So dim are the followers of Condorcet that ruling out interpretations
using a correct reading of the text, could create a dispute.

For 5 years Schulze has be glued onto the falsehood and it seems
that in that time, evolution and pure thinking has brought to him
(a) a desire to censor out the perfectly wrong idea that pairwise
   comparing is not to be rejected
(b) for the STV community, he trashes their perfectly inconsistent
   views by presenting himself as needing exactly 2 words to
   "strictly prefer", Also the idea of summing is added with the
   relentlessly useless wording "the number of voters". If there are
   no voters, or the counts are non-integral or P2 is failed and the
   probing at negative numbers does not occur, that it would be
   false to conclude that the method is monotonic.

Here is the title of the paper:

  "A New Monotonic and Clone-Independent Single-Winner Election Method"

The publishing agency is the McDougall Trust.

Mr Shulze's credibility as theoriticians is incompatible with the
private e-mail messages from me to him on 3 October 2003 and 23
October 2003. At that time I was hampered by the ambiguous trashy
wording he relied upon.

Quoting from the 23 October document that comments narrowly on the
algorithm, I quote the method of the PDF VM 17 article:

| Markus Schulze, A New Monotonic and Clone-Independent
| Single-Winner Election Method, VOTING MATTERS, issue 17,
| September 2003
| Input: d[i,j] with i <> j is the number of voters who strictly
|                         prefer candidate i to candidate j.
| Output:  "w[i] = true" means that candidate i is a potential
|                         winner.
|          "w[i] = false" means that candidate i is not a
|                         potential winner.
| -- STEP 1
| for i := 1 to N do
|    for j := 1 to N do
|       if (i <> j) then p[i,j] := d[i,j] - d[j,i]; end if;
|    end loop;
| end loop;
| -- STEP 2
| for i := 1 to N do
|    for j := 1 to N do
|       if (i <> j) then
|          for k := 1 to N do
|             if (i <> k) then
|                if (j <> k) then
|                   s := min { p[j,i], p[i,k] };
|                   if (p[j,k] < s) then p[j,k] := s; end if;
|                end if;
|             end if;
|          end loop;
|       end if;
|    end loop;
| end loop;
| -- STEP 3
| for i := 1 to N do
|    w[i] := true ;
|    for j := 1 to N do
|       if (i <> j) then
|          if (p[j,i] > p[i,j]) then
|             w[i] := false ;
|          end if;
|       end if;
|    end loop;
| end loop;
| --------------

It is obvious from that Mr Schulze did not write any test at all that
attempts to clarify the words "strictly prefer".

Why Mr Schulze could not come to some clear conclusion in 1986 on how
to present with the fullest possible clarity the incompetently
pitiable deliberate error that subsequently guarantees that the
algorithm would be unfair, is baffling.

Here is the example again:

2 (CA)
5 (CAB)
1 (CBA)

The d[A,B] value:
 (Interpretation 1) the number 7, or
 (Interpretation 2) the number 5.

There are 2 cases (if not more)

(Case or Interpretation 1) The 2 is added to the 5.

  The article said "strictly prefer" instead of "prefer",  and I cant
  think of a purpose for that except to rule out this case.

  This case is so far acceptable but the whole method will not be.

(Case or Interpretation 2)
  In this case, the paper (CA) does not count towards candidate A.

Mr Schulze would be in the wrong IF ever saying that it is *obvious* that
these two cases have candidate 'A' being preferred by the same amount
against/over candidate 'B', when there are 5 or more candidates and
not 4 or less:

  (a) (C D A)
  (b) (C D A B)

Even in 1998 Mr Schulze's neutrality view appears to be a mistake.
Instead the illogic of having multivalued winners can be used.
The big argument here is that today Mr Schulze seems to reject
the neutrality rule since he could believe it would trash the [awful]
Schulze algorithm. The ideal course is to criticize Mr Schulze for
believing in the importance of the rule and again in 2003 for not
using it.

------------- example:

Suppose that the candidates are listed and the method makes the
first one listed, be the winner. So the method is faulty since it
fully ignores the ballot paper counts.

* External names: A, B
* Internal names: 1, 2
* External ballot papers:
    1 (A)
    9 (B) 
* Winner = candidate #1 = A

Re-letter externally and keep the algorithm unchanged:

* External names: B, A
* Internal names: 1, 2
* External ballot papers:
    1 (A)
    9 (B) 
* Winner = candidate #1 = B

The algorithm is returning the right number of winners, but it is
returning a multi-valued set of winners.

The definition of "multivalued". An exmaple: Log(1) is multivalued and
its values include: 0, 2*pi*i, 4*pi*i, etc.

Can Mr Shulze say what axioms lead to multivalued winner sets ?.

Why does he need a rule to stop neutrality violations and I do not.
If he disagrees and says that the rule is important it it does not
matter if it is redundant, then why was he maintaining such secrecy
on the topic of whether or not his method appearing in issue 17 of
Voting Matters fails ?. This is an argument is ambiguous, and unlike
the possible ambiguity of the Mr Schulze's "strictly prefer", the
persons creating the ambiguity is constructing the argument for all
the cases.

The Shulze algorithm has basic simple errors appearing in the very
first lines of the algorithm (Step 1). 

In Mr Schulzes world, he has got the typical Condorcet aim of
under-wording the theory of what actually happens when this paper

   1*(....A....B...)  Unnamed = ....

is altered into this paper:

   1*(....A....)  Unnamed = ....B....

Obviously what a *competent* government preferential voting method
expert will expect, is that there is no rule saying (somehow) that
A's standing with respect to B, is remains constant when that change
is done. Such a requirement would harm some other good principle.
If the theory is nearly optimal then it would be largely proportionality.

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