[EM] Review of Reversing preference lists paper by Mr Barney, Mr D. G. Saari

[Craig Carey]

>[EM] "Consequences of Reversing Preferences" 
>Markus Schulze markus.schulze at alumni.tu-berlin.de 
>Tue Dec 2 06:13:05 2003 
>
>Dear Steve,
>
>I have just read your paper:
>http://hypatia.ss.uci.edu/imbs/tr/Final1.pdf
>
>I am very disappointed that you mention neither
>Tideman's ranked pairs method nor my beatpath
>method in your paper. The ordinary reader will
>get to the conclusion that all election methods
>that satisfy reversal symmetry have some serious
>drawbacks.
>
>Markus Schulze

The paper is jointly authored by Mr D G Saari (who quit preferential
voting, it was said) and one Mr Steve Barney. I recall he was at this
list and I wrote adversely and no response occured. The PDF creating
program can be handy for those special where every reader would
assume that the statements are too valueless to be fit for a write-up.

Perhaps Mr Saari has not properly read the co-authored paper yet.
I suppose that much of the text with the triangle diagrams is
Mr Saari's.

Mr Riker, who suggested that methods should be monotonic, gets a
very minor mention:

| Among the widely used election methods are what William Riker [1982]
| calls positional methods. Riker, who was a pioneer in using
| mathematics to address problems from political science, coined the
| word “positional”

Two other persons can be identified as participating in the
production of the PDF document, since page 1 says:

| Our thanks to Hannu Nurmi, Tom Ratliff, and two referees for their
| comments on an earlier version.


Now there is 4 names to bear in mind rather than two, and this paper
gets through the final checks.

Here is some text that is seemingly false for using only 2
significant digits when truthfulness would require nothing less than
an infinite number of significant digits.

| Theorem 7.
|
| For three candidates,the following probability statements hold for
| any probability distribution of voter profiles where, as the number
| of voters grows, the distribution is asymptotically independent with
| a common variance, and the mean has an equal number of voters of
| each type.
| 
| 1. A necessary and sufficient condition for a profile's of outcomes
| of all positional method outcomes to be reversed when the profile is
| reversed is for p's plurality and antiplurality outcomes to agree.
| The likelihood of such a behavior is 0.31.
|
| 2. A necessary and sufficient condition for a reversal effect to
| occur for the plurality outcome is that a profile's antiplurality
| outcome reverses the plurality outcome. This behavior occurs with
| probability 0.06.
|
| 3. A necessary and sufficient condition for a plurality (or
| antiplurality) top-reversal, or a two-winner reversal effect is for
| the profile to allow five different election rankings as the
| positional methods change (and the plurality outcome to be a strict
| ranking). This occurs with probability 0.19

When the text says that the likelihood of the behaviour is 0.31, we
know that the statement has got to be perfectly untrue since the
author is either covering up the use of a computer or else has
converted an infinite number of significant digits down to two.

Also the method that was tested on the computer (if any) is not
described in the section claiming to be a theorem. I would not say
that 'Theorem 7' is actually a theorem.

Actually there is no proof for that theorem. Surely Mr Saari and
reviewers Hannu Nurmi and Tom Ratliff saw that. Maybe the reviewers
can give advice but it might get disregarded.

Anyway, parts of the documents are apparently untrue.
When I look at the text I sense that it is fluid goo of falsehoods.
I do hope that Steve Barney will let us know who wrote it.

I am not aware of why probabilities were being computed. This is
not a review based on a proper reading of the document, not that
any is appropriate.


----

Mr Saari has thinking aberration that results in lengthy articles.

How is a preference beyond the 10,000-th going to affect the
winner ?. To brin the bottom preferences up to the top is no
hardly likely to be more important that some study of randomizing
preferences but not the top 1000.

Despite being 19 pages long its last lines contain a question and
speculation:

| But as s -> 1/2, a procedure becomes less susceptible to the
| Reversal components. Is there a connection? Probably, but it has not
| been established.

"Reversal components" is some idea that is best ignored.

The author(s) have the same worthless idea at the start of the paper:

| ... he [the chairperson] expected the voters to vote in the opposite
| way.As such,when tallying the ballots, he treated a first and last
| listed candidate, respectively, as the voter's last and first choice.1
|  Imagine the outcry if after retallying the ballots the chair reported
| that the election ranking remained unchanged; ...

There author wrote "Imagine the outcry" but at the start and at the end,
completely fails to say of the rule should be completely ignored. The
author is using the salesman trick of saying that others would agree.
The author seems to be unaware that good methods are not threatened
by fail results when tested with wrong rules.

The public is not so strung-out as to think that
  *  when some winners are known, and when
  *  preference lists that contain over 60 million named candidates
     are written back to front,
  *  and also when there is only 7 ballots (stored on an IDE hard disk of
     co-author Barney);
then there is an important relationship between who wins the first and
who wins the 2nd. I.e. the public would not believe that.

Maybe Steve Barney could post in the rule since the long paper failed
to focus on its central topic.

If the idea is worthless for over 99.9999983% of all elections, then
why would anybody spend time on producing diagrams in triangles ?.

Readers can briefly consider what reversing preferences in large
elections, and then be very confident that there is not any good
rule there in that topic, at all. The disappoints since it fails
to arrive at the wholly obvious conclusion, which is that there is
no political polytope testing rule based on reversing preferences.

It looked like Dr Saari was the last mathematician in USA that had
some special interest in preferential voting. If the paper is
published then it unquestionably will be seen that Dr Saari can't
identify the mistake of years earlier, where it was suggested
that reversing preferences was worth mentioning to some online
journalists. That could leave USA with 0 top experts.
The well known duality principle is presumably what Dr Saari would
have written on had the article been more politically useful.
I.e. that requirement that the same method results when winners
are swapped with losers, and the votes are negated.

I have read some of Mr Steve Barney's writings at the Election Methods
List, and in the past he didn't write back to me, and did run low
accuracy computer simulations using random numbers that tested minor
methods with totally worthless rules. That is precisely what a lot of
the PDF article was doing.

In the more political arena of STV variants, it can be assumed that
they don't mind if a perfectly unfair, unjust, or anti-political
method is failing the STV method.

The paper has diagrams in it too, and that is abnormal. In the
preferential voting, and the article is not really simple, the
dimension is high diagrams are replaced with algebra. The author of
of a competent article is more likely to spend time writing
new symbolic algebra software that can simplify polytope expressions.

The paper is not just exploring a wretched obviously wrong rule,
and then permitting only 3 candidates, but it seems to prohibit the
9 papers lacking a 3rd preference. Or at least, what else could this
mean?:

| Skepticism might be the kindest reaction to greet an announcement
| that the election ranking for a profile -- a listing which specifies
| the number of voters whose preferences are given by each (complete,
| transitive) ranking of the candidates is the same for the profile
| where each voter's preference ordering is reversed.

I suppose the word transitive applies to the symbols on the paper.
E.g., for this ballot paper "A B C",
it can be said that A is to the left of B, and B is to the left of C.

It is quite bad: 20 pages that fails to come to any conclusion about
a rule that is obviously worthless, and without good explanation
two more restrictions are piled onto that:
 * there is only 1 winner
 * and apparently all 3 preferences need to be written.

The authors of the papers are perhaps under the pairwise tradition
of tolerating corruptness in their method and vote-negating with
secret diversions of votes to the wrong candidates. The text of the
PDF file does not contain the words 'monotonic' and 'monotonicity'.

The paper uses Dr Saari's rotated-Aries symbol to indicate some
relation. That idea seems to have no place fair multiwinner
preferential voting theory.

The article does not contain the word "fair". I can't recall a
moment ever when an interest in being fair to others coexisted
with an interest in pairwise comparing.


Dr Saari should not have made the mistake about back-to-front
preferences in the first place. I could have used much text to
persuade Dr Saari but he is uncontactable as if beyond the reach
of telephone lines.

It was never the case that pairwise comparing is worth a tin of
fish to the designer of STV-like high quality preferential voting
methods that would be used in government elections.

Donald Saari should re-read the introduction since it is pathetic:

|  Imagine the outcry if after retallying the ballots the chair reported
| that the election ranking remained unchanged; ...

That looks like an argument that the CVD would use: "start to
proper influences from the clues that other mainlanders are now
plainly signalling to us". I guess that Steve Barney wrote
that. That is the same Steve that made one decision to not
reply to me. The expert in using wrong tests and coming in with
[printouts] lists of numbers.

Readers will expect a high probability of no outcry at all when
informed that a wretched wrong rule from a world of people who
make mistakes that members of the public can't themselves make,
fails some preferential voting method. A key detail is that the
rule fails the method that that public desires above all other
methods, a fairest method. Where are the error bounds?.

Looking at the wording more closely, it is in the Soc Choice
style, for the text "Imagine the outcry" is permitting no
outcry whatsoever.

The big issue here is that Donald Saari made a complete mistake
at the time of the last foray into back-to-front preference lists,
and if the silence is snapped with the publication of the paper
of Don and Steve, then it takes United States top expert, perhaps,
maybe 4 years or more to figure out errors that takes me seconds
to identify.

I see the reversal ideas dying when a very large number of
preferences, and possibly Mr Saari and Barney wave still time
until the final version of their paper is out, and then the new
issue of the number of candidates being restricted to only 3
has appeareed.

Many of us are not able to drop to the depths of irrationality
that seems to accompany a belief in transitivity of something
or other that is not a symbol on a list. For that idea,
Mr Donald G Saari uses the rotated Aries symbol.  Every paper
containing that symbol is set against the humana right of
equal suffrage, i.e. rules restricting the changes in winners
when papers are changed infinitesimally.
Reversing preferences has to be done infinitesimally or else on
that finding alone, the paper can discarded (easily without
being unfair too).

I got a comment from Mr Thomas Cool who said that Donald Saari
did not reply to him. Mr Saari's last response to this list
was troubling for it said he was just going to complete investigating
the topic of some super-linear (completely un-political) 3 candidate
methods. I am not sure about the 3 candidate part.
It could have been better if Donald Saari had of considered
methods good enough to actually use. So long as results are
plotted, thoroughness is fairly useless since the way of
presenting results becomes unusable as the problems get larger.

Dear Steve: which people needed that paper ?. Just the critics?,
or were you writing for a wider audience?.

Here ends the review of the two men who could mention the name
"Riker", and the idea of Mr Saari's trnsitivity, but who had no
space for the "fair" and "monotonic". A wrong rule can get
get into a disagreement with, at worst, all correct rules.

I can list the correct axioms in private.

I see that Mr Marcus Schulze got his comments very badly
designed. Mr Schulze wrote as if he failed to detect the worthlessness
of the paper of Mr Donald Saari and Mr Steve Barney.

I guess it is fixable for that was not a final release, but in
the Condorcet fanatic's world, things are basically not improving
all of the time.











Craig Carey <research at ijs.co.nz>    Auckland, New Zealand
Freedom of Information America: http://listserv.syr.edu/archives/foi-l.html
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