Wrong information at Green-Armytage webpage (Re: [EM] Re: majority rule criteria--alternative nomenclature

[Craig Carey]

This webpage by Mr James Green-Armytage contains mistakes:

http://fc.antioch.edu/~jarmyta@antioch-college.edu/voting_methods/cwp_criteria.htm
   | [Title:] Criteria passed and failed by Cardinal-Weighted Pairwise
   | [By:]  James Green-Armytage

Mainly I show here that Mr Green-Armytage's trick of copying while
leaning produce really bad results when that same person copies
untrue ideas that are later protected with spotty dissembling coverups,
etc.

Here is the text of Mr G-A's Pareto rule from the webpage:

| 4. Pareto: If at least one voter ranks candidate A over candidate B,
| and zero voters rank candidate B over candidate A, then candidate B
| should certainly not win.

Mr Green-Armytage (G-A) fails to define what "A over ... B" means.

Let's suppose that Mr G-A defines "over" in a way that causes a match
with the 1*(AB) ballot paper of this 2 candidate election:

   1 * (AB)

Then Mr G-A's Pareto will find that a candidate B must lose this
irrespective of how many winners are before-hand declared to be the
correct number.

So how does he do it: make a mistake that election method designer could
but which is presumably just normal at the Election Methods List ?.

------

The webpage of Mr Green-Amytage seems to have a purpose of copying
claims from the 2003 Voting Matters 17 article of Mr Schulze.

Here is some text showing a footnote of Mr G-A's webpage:

| [1] Markus Schulze, “A New Monotonic and Clone-Independent
|  Single-Winner Election Method,” Voting Matters, issue 17, page 9-19,
|  October 2003

---

Mr G-A makes a hoax claim that the method is monotonic.

Without explanation Mr G-A produces a seeming proof of monotonicity.

It can't be a true proof since Mr Schulze takes every opportunity to
conceal from me while at the Election Methods List, his terms "strictly
prefer", that is in the PDF article of October 2003.

-----

Here is the definition of Monotonicity of Mr G-A:

| 5. Monotonicity: If candidate A wins with certainty according to a set
| of ballots, and some of the ballots are subsequently changed only in
| that A is ranked and/or rated higher on those ballots, then A should
| still win with certainty.

Compare that with the wordign of Mr Schulze's Voting Matters 17 article:


} 5.2 Monotonicity
}
} Monotonicity says that when some voters rank candidate A higher without
} changing the order in which they rank the other candidates relatively
} to each other then the probability that candidate A is elected must not
} decrease.
}
} The Schulze method meets monotonicity.

Clearly that is too wrong to be acceptable since:

(1) Both use the word "higher" to mean 'lower'.

(2) Mr G-A got rid of Mr Schulze's mistake of using the word "probability".

(3) Both authors claim that an undefined preferential voting method is
  passed by their rule of monotonicity. That would be hard to believe.

(4) Both make the mistake of forgetting to exclude negative weights.

  E.g. This can cause candidate A to change from a winner into a loser:

     -1*(BA) --> -1*(AB)

  A mistake at the start of a deduction can affect the inferred answer.

-----


Mr G-A used these words to attempt to prove that an undefined method is
 monotonic:

| If A’s rating and/or ranking is increased, it can only increase the
| strength of pairwise comparisons which A wins, and decrease the strength
| of pairwise comparisons which A loses. This cannot lead to an increase
| in any beatpath from any B to A, because a pairwise comparison in which
| A wins (the only comparisons that have potentially increased) will not
| be included in any beatpath from B to A. It also cannot lead to a
| decrease in any beatpath from A to B, because a pairwise comparison in
| which A loses (the only comparisons that have potentially decreased)
| will not be included in any beatpath from A to B. Hence, if A had a
| beatpath win against, B, A will still have a beatpath win over B.


The region where A wins is simply a polytope (unless faces are curved).

[The polytopes still exist even when an EML subscriber develops a
purpose of never using the word "polytope" in their e-mail messages.]

A claim of monotonicity is made about an undefined method. As is usual
for devotees of Heitzig's pairwise comparing beliefs, the summation idea
is left undefined.

So how can Mr G-A prove that some thing so undefined is passed by the
rule ?.

Possibly Mr G-A was shifting 100% of all of the non-monotonic faces into
the space that is the slices/cuts between the cases.

How is it possible for Mr G-A to not spot such an obvious mistake?:
possibly the student does not read what I write, but instead learnt from
men who unfailingly censor out the word polytope. Maybe those who censor
do not use solvers. It could be how the REDUCE software costs USD$99.
However the American students AND the German men, never actually say
that cost is a problem. I guess that thinking right is more difficult
than paying USD$99.

-----


So Mr G-A is showing poor results after appearing to be a student of the
(false) writings of people who can be barely comprehensible.

----

Even to this day Mr Schulze, has kept secret the categories and weights
of the "strictly prefer" sum. Mr G-A also did the same on the webpage.

Possibly Mr G-A can help us all out and do this:

(1) Starting with Mr Schulze's conclusions (hoax claims of how the
method passes), Mr G-A can infer what the "x over y" weightings and
categories are. Are there 5 categories or 12 ?. Mr Schulze certainly
kept the categories undisclosed, and Mr G-A's webpage does the same.


------


At 2005-01-13 10:44 -0500 Thursday, RLSuter at aol.com wrote:
>James,
>
>I wish you would read and think more carefully before
>you respond.
>

I show that such advice is plausible, with my text above.

...
>You wrote:
>
>>Moreover, any process for making collective decisions,
>>including plurality voting and even some random selection
>>processes, could be considered a majority process if
>>it were chosen by a majority of voters and they agreed
>>beforehand to accept the outcome of the process.
>
>     That's a stretch.
>
>My response:
>
>It's a stretch only if you have not given it any serious
>thought to it. You clearly have not. Why should citizens
>not be permitted to vote on voting methods themselves?

>If a 2/3 majority were to decide to go with plurality and
>agree to accept the winner, who is to say they should not
>be allowed to do so, provided opponents of plurality are
>permitted to debate the issue prior to the vote, and
>provided the issue is revisited from time to time so
>that citizens have a chance to change their minds in
>the future?
>
>
...


PS. The 50% majority quota is not an ideal.

Suppose this 3 candidate election has exactly 1 winner:

       52% (A)
       51% (B)
       -3% (C)

A 50% quota will find 2 winners, which makes that rule/test be
inconsistent with a "Right number of winners" axiom. I assume that it is
too petty to keep rules away from negative numbers. Also there is the
untested promising rule saying that swapping winenrs and losers and
negating votes, leaves the method unchanged.


Craig Carey, Auckland, New Zealand
Preferential voting:
   http://groups.yahoo.com/group/politicians-and-polytopes/