# [EM] One Man One Vote in equation form; Power and rejecting Approval

Craig Carey research at ijs.co.nz
Tue Aug 6 07:30:39 PDT 2002

At 02\08\05 20:41 -0700 Monday, Richard Moore wrote:
>Craig Carey wrote:
> > At 2002\08\01 22:32 -0700 Thursday, Richard Moore wrote:
> > >
...
> > Members can browse to my long reply which is now at this webpage:
> >
> > http://groups.yahoo.com/group/politicians-and-polytopes/message/184
>
...
>To the issue of how to run a two-candidate election without resorting
>to a pairwise method, while retaining fairness, he posted a reply
>about using SNTV in a 2-winner election. Always picking two winners
>out of a field of two candidates is a cop-out. Maybe Craig wants to
>

Mr Moore has possibly slid the meaning of the word "election" from that
of being consistent with a single mathematical point in some space
defined as it was defined, over to something "run".

This is what I wrote.

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At 02\08\03 01:17 +1200 Saturday, Craig Carey wrote:
...
>At 02\08\01 22:32 -0700 Thursday, Richard Moore wrote:
>>Craig, you didn't respond to my simple question about a two-candidate
>>election. I guess you're smart enough to realize that a correct answer
>
>Mr Moore asserts a wrong principle and adds to the mistake by trying
>to say that no one else can avoid his personal mistake or finding
>some importance in preferential comparing:
>
>>inconvenient. Rejecting pairwise comparison would compromise the
>>ability to pick a winner in a two-candidate election using a
>>non-arbitrary and non-dictatorial method.
>
>That is completely false and embedding SNTV into a new method during
>its derivation can solve the 4 paper 2 winner election problem. It
>is hard to imagine how Mr Moore could have missed that, yet the
>text says "Rejecting pairwise comparison would compromise the
>>ability to pick a winner". Mr Moore can attempt to save the text
>by filling in the details about non-dictatorial methods.
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Mr Moore was trying to mix anj enduring worthless and untrue idea
in with the question. That is the background to how I did not say
that 0 winner and 1 winner SNTV/FPTP would be embedded in the
non-biased method that would be derived from the axioms.

It is bothersome to have som many totally untrue ideas that will
bring only ignorance wherever they extend, intertwined with the
about "non-dictatorial" methods somehow implying that pairwise
comparing is known to be more significant?. I suppose that Mr Moore
wants to have others believe that the number of winners is
constrained, but the text did not say that explictly. How are we
supposed to see that as being implied (eh?).

>I listed three problems with his P4 criterion. To the first problem,
>that FPTP ballot powers vary with power structures, he replied that
>there are no electorates in mathematical equations. That flippant
>answer was simply an evasion of the issue that was raised.
>

I don't have a definition of "power structure of the electorate".
would readily assume I ought not ask. I request the final or
imperfect algebraic (quantifier logic, presumably) definition of the
"power structure of an electorate". The aim of Mr Moore did look
like it was to reject my "P4" quantifier logic definition.
While we wait for Mr Moore to reply, I remind the members that this
Election Methods List has, since 2000, tried to argue that lying
about whether a 'not actually held' definition is held, is a very
important thing at this mailing list.

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>
>>1. P4 uses FPTP ballots as a unit of "power". But FPTP ballots have a
>>power that varies with the power structure of the electorate. That
>
>There are no electorates in mathematical equations. If you refer to
>some equations you have not made available, then be free to make them
>accessible.
-----------------------------------------------------------------------

>Craig ignored the second of the three, about the huge disparity
>between power=1.0 ballots and power=0.0 ballots within the constraints
>of P4. One could define a method that says "Count the ballots as in
>FPTP, except that any ballots cast for candidate X are given 0
>weight". It would pass P4.
>

It would pass P4 if no possible ratios of all possible kinds of
papers, would never result in the election of a given candidate.
All that does is strain the link between the human rights definition
of equal suffrage and my P4. It does not appear to have a practical
consequence.

>Since he did not try to answer that one, presumably he is conceding
>the point.
>

Another axiom ("PP") 'aims' to raise the power of the papers.
Mr Moore did not comment on that. There was no argument in that
text that led to the conclusion saying that P4 is wrong/useless.

>To the third issue, about how one definition that increases the power
>as the number of marked preferences increases conflicts with another
>definition that decreases the power, Craig confined his response to
>the special case of a zero-preference ballot vs. a single-preference
>ballot. Is that the only region that needs to be considered? For N

This is easily explained. Mr Moore wrote two ideas and they
contradicted because one of the ideas appears to be a mistake.
I can't really write a lot about that. Mr Moore can have another look
at the two simply asserted contradicting statements and correct the
mistake. But instead he identified a constraint that was inside of
my proof that he was in the wrong, and wrote that "Craig confined his
response to the special case ...". Instead it seems to me that Mr Moore
got it wrong when writing "There were two contrary definitions".

Here is the text.

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>>3. There were two contrary definitions given, one in which "power" is
>>the number of FPTP ballots a ballot can be replaced by (to get same or
>>better results), and another in which it is the number of FPTP ballots
>>a ballot cancels. As the number of check marks on an approval ballot
>>increases, the first definition has "power" increasing while the
>>second has "power" decreasing. It makes no sense for the quantity to
>>be increasing and decreasing at the same time.
>>
>
>That says: "the second has "power" decreasing", and that is wrong.
>For example, the paper with 0 preferences has no power, But a
>1 sub-vote Approval paper can offset a similar paper exactly and it
>does not have a negative power.
>
>
>>This gives Craig another chance to respond, but I expect he will opt
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I don't see that this is true:

"while the second has "power" decreasing"

Mr Moore wrote:

"Craig confined his response to the special case of a
zero-preference ballot vs. a single-preference ballot."

Actually I was showing that "the second" has power 'increasing;.
A paper with 1 preference has more power than a spoiled vote.
Yet Mr Moore wrote obviously saying that an Approval ballot paper
with No checkbox marked, has more power that an Approval
paper with a single check box mark.

This there is a mistake in the text of Mr Moore and no argument
for the existence of a problem with the P4 definition (that is in
the last message at the Politicians And Polytopes mailing list).

>definition that decreases the power, Craig confined his response to
>the special case of a zero-preference ballot vs. a single-preference
>ballot. Is that the only region that needs to be considered? For N

Spectacular: after such an obvious blunder that I described, and
without the tiniest hint of Mr Moore backing out of the blunder,
there is another question for. Quite possibly the motive is to
suggest that I will not answer it.

>candidates, a 1-preference approval ballot can cancel N-1
>(non-aligned) FPTP ballots; a 2-preference approval ballot can cancel
>N-2; etc. Craig stated that the 1-preference ballot offsets a single
>"similar paper" rather than N-1. Maybe Craig has a different idea of
>what "cancel" or "offset" means, and would like to share it. At any
>rate, I could suggest a simple correction to fix problem 3, but it
>would leave the problem of the unreliable FPTP "power" standard in place.
>

Why not actually look at the P4 equation?.

What "unreliable .. power" problem?.

I have not clearly said that the equation ought test a checkbox
method as faulty as Approval. I don't research outside of
preferential voting, partly since the mathematics inside of the topic
is much more interesting. The best this mailing list gets on Approval
is a few scattered false comments saying that voters want "utility"
numbers. Even manipulating an Approval election is a dull topic:
it seems to be merely a problem that can be solved with a computer.

>In short, I have seen no reason given why anyone should care whether a
>method passes P4 or not.
>

Unless the problems in elections with 2 or more winners are actually
ruled out then they will turn up in the solutions.

I am sure that a rule defining equal suffrage is needed for the
solution of the 2 winner 4 candidate problem. Eliminating the
Approval checkbox method is entirely possible, e.g. without any
reasoning being used.

Did anybody notice that Mr Hager of Illinois was a bit ambiguous over
the merits of pairwise comparing too, i.e. one whether there is a
little bit of something to uphold in it, or whether there is nothing
there.

I ask Mr Moore to tell me and the readers, how he managed to
not correct these errors he made, but cut out constraints from
my disproofs using examples, and then tried to say that I had not
answered his questions. I seem to recall that a while back when
Lanphier was writing about the difficulty of getting a system
where members could secretly vote, that Mr Moore tried to argue
that I ought not use a Socratic questioning technique under a
purpose of nailing members here as lying. In short: I must not
expect members to answer questions. Quite a bit of what I am

I recently read Mr Ossipoff saying that rules are subjective.
That is a complete error and rules should be tested which will
protect a theorist from getting on the wrong side of whether a
plausible rule is one that should actually be used or not.

------------------

Mr Schulze [who had to quit the Election Methods List, perhaps the
members were not intereted in voting], has a paper in Wichmann's
'Voting Matters' mini-journal on STV.

That is in the technical documents area of this website:

http://www.electoral-reform.org.uk/

Craig Carey

http://groups.yahoo.com/group/politicians-and-polytopes/
http://groups.yahoo.com/group/single-transferable-vote
IFPP axioms: http://www.ijs.co.nz/ifpp.htm

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