[EM] Approval Vote: The unfairness of being dead .. to Schulze

Craig Carey research at ijs.co.nz
Wed May 31 03:47:10 PDT 2000

Here is an example from a letter drafted for Mr Catchpole but which I
plan to not send:

 >Voters average hair length = x
 >Voters votes equals vector v
 >Winners = W(x,v) = W(v)

The problem for the scrutineers is this: explain again how voters'
hair length made it permissible to have a particularly weak test
for some bad method (the same one being advocated)?. However some
members of the list never seem to figure it out, so tailored to the
needs of the list, here is test for detecting probably incompetence
in the mathematics of preferential voting theory:

Test X1: if the word "voter" or idea of a voter is used. then replace
   it with the idea of one or more papers, and if the text no longer has
   the same meaning and a good meaning, the author fails test X1.
   In all other instances, no statement is made.

Of three I checked recently, David, Mike, and at least in private
communications and less clearly, Markus Schulz, write in a way that
fails test X1. I presume it shows up a disregard for the mathematical
theory of functions. Arguments that test X1 is "unfair" might yet be
made. Voters can grow their hair to any length they want ... David?.

At 10:24 31.05.00 +0200, Markus Schulze wrote:
 >Dear Craig,
 >you wrote (31 May 2000):
 >> I just sent a message to my list commenting on Blake Cretney's webpage
 >> on rules. He defined the Majority Criteria as saying a candidate
 >> should get above 50%. That is false, and this example confirms that:
 >> Election system V =
 >>      1: A
 >> Number of winners = 0
 >> People now have strong mathematical justification for ignore
 >> messages from Mr Schulze.
 >You'll have to rephrase this, because I have absolutely no idea what
 >you mean.
The sentence "People..." is unrelated with the zero winner example.

I was referring to the argument on this page, and nothing but this:

Fall and Decline of Condorcet Theory:

I wrote off Condorcet theory on some assumptions listed and on the
assumption that when Condorcet gives a winner then that is the winner
chosen. It is not unexpected but might help lift the sensation of
oppression existing amongst those that do not like Condorcet but
couldn't remove it.

I do not know if the Schulze method is by Markus Schulze of the list.
Any info?.

 >The Majority Criterion says that if more than half of the voters
 >strictly prefer candidate A to every other candidate then candidate
 >A must be elected. Where does your example show any problems of the
 >Majority Criterion?

What it does Mr Schulze, is prove that the Majority Criterion rejects
the best preferential voting methods, and all or most of other methods.

 >Also I don't understand your phrase: "People now have strong mathematical
 >justification for ignore messages from Mr Schulze." What do my messages
 >have to do with Blake Cretney's webpage?

That was unrelated here too. I was referring again the message 23 of the
P&P list.

 >>    http://www.egroups.com/message/politicians-and-polytopes/23?&start=1
 >>             No need to reply, Markus. I know you no longer reply to my
 >>             personal e-mail [due to the detail and length of the
 >>             criticism]
 >You'll have to rephrase this, because I have absolutely no idea what
 >you mean.

The detail and length part is wrong apparently.

I was hoping for support in a dispute with Mike over minimum standards
for exactness and rigorousness in the laying in of linkages of
reasoning. An aim I hold is to clarify the linkage between wrong
conclusions and wrong premises. Still I suppose that is better than
reminding people of wrong rules or methods.

 >By the way, I did reply to your personal mails. Didn't I?

Warning: dud idea:
Maybe you missed nothing. I wrote saying that the participation axiom
used a flat perpendicular to a flat through the point (election) and
the flat between all the considered candidate's first preference
vertices. That much is fact. I then suggested another similarly
constructed constraint for the normal of the win-lose surface be the
translated flat of the participation axiom constraint on normals for
when the point (election) was at the centre of the simplex (or maybe
other midpoints). That gives a 2nd flat.
There is still that participation axioms 1st flat's undesirable
tilting according to the position of the point (like disc anchor on
a cord pulling from a vertex constraining normals to win surfaces to
be on the (A*) side of the perpendicular 'disc'.

It sounds to me too weak to even bother with, except that someone
interested in tightening participation axiom bounds around STV might
be interested. I would simply reject for the far more preferable P1,
but STV fails that.

 >You wrote (31 May 2000):
 >> Mr Shulze wrote that having a method based on axioms is a test that
 >> passes any method.
 >I wrote that for almost every election method it is possible to
 >define seemingly reasonable criteria such that this election method
 >is the unique election method that meets these criteria.

I don't see that as a powerful result.
You wrote a message saying that to have a method axiom based would
pass any method. Axiom based methods have a better chance perhaps,
of being explained to the public and not have the public say that
that is crap.

 >In a private mail, you asked me which criteria could be used to
 >make Alternative Voting "axiom based." And I answered that the
 >Majority Criterion, the Positive Involvement Criterion, and the
 >Independence from Clones Criterion exclude almost every other
 >election method.

Those are not maximally tight bounds and the three do not define
the AV method (which you agree with). There are others: truncation
resistance (which can replace Positive Involvement), & my P4 which
is used to derive the new whatever it was criteria.

 >In a reply, you wrote that "the majority criterion is not a desirable
 >rule." You wrote that the Positive Involvement Criterion is a "misplaced
 >idea." And you wrote that the Independence from Clones Criterion has no
 >"appearance of importance" and that it is "a rule I can ignore."

Following a discovery that the EM List had some interest in the Majority
Criterion, I derived it from my axioms. It was difficult to not get a
multiwinner result. A derivation of the multiwinner version is at:

The public(?) version is undesirable since wrong.

Here is the new Multiwinner Majority Rule (might as well drop the use
  of the word "criterion"):

If there are NW winners, then a candidate wins if it has over
   1/(NW+1) of the first preference votes.

When the number of winners is 0, my formula says nothing if the
candidate does not get over 1 of the vote. That happens always.
Who would devise a rule that had 0.5 in it when that is
mathematically wrong unless a constraint is in there. Votes can be
negative but not the number of winners since that is the size of a
set (the set of winners). So none need say that nw, the number
of winners satisfies (nw >= 0).

So this upheld rule fails to be true for 1 candidate elections. I infer
from that that it has not been tested.

I have not rejected the "Independence from Clones Criterion".
I am extremely pessimistic about it ending up being free from the
problem of small example showing it dumb (which seems to be what
usually happens). I read what you defined and I did not understand that
fully (and from there, I did not reject it in truth. Eventually I may
reconsider it).

 >In so far as your unique argument to reject these criteria was that
 >you don't like them and in so far as you didn't give any mathematical
 >reasoning, there was no basis for me to reply to you.
I look forward to answering few questions too. I shall not study up
on your messages because I believe that they will be on the far side
of the dispute over the acceptability of (AB{C+)-(C{B+).

The Positive Involvement (of Donald Saari you wrote) is weak and I am
sure it will be difficult to get on with in algebraic manipulations.
It is a weak rule suggesting that somewhere out there there was a bad
method that Donald once considered.


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