I told Rob Richie, use "IRV", its catchy (was Re: [EM]Approval Elections & Effective Weights

Craig Carey research at ijs.co.nz
Thu Apr 12 03:26:09 PDT 2001

At 2001-04-12 03:55 +0100 Thursday, Martin Harper wrote:
 >Never in the field of human conversation have so many words been used to say
 >so little to so few...
 >To summarise: Craig has criticised Approval on the basis of his "effective
 >weight" criterion. Sadly, he can't give us any kind of defintion on what the
 >heck this criterion might be. Until we have such a definition, we can't
 >decide whether Approval passes it or fails it. Neither can we decide whether
 >it is a good method to pass.

What is the last sentence there: what is it that subscribers are not able to
decide upon?.

Mr Harper's term effective weight is in my opinion, not defined well enough
for it to be a desirable rule that can test a method. I am not sad that
Mr Harper did not specify the constraints on the FPTP balancing opposition.
Approval is rejected anyway for being outside of the topic.

Martin Harper, just above, read my article showing how Approval can allocate
a power that is 30 million times too big and hear endears his thinking to
the list by saying the dispute is temporarily resolved because I never gave
any a comment doubtless including that one. If he missed it, it is copied

If subscribers were to imagine the formula of power in radio waves : the
squared power is proportional to the integral of the square of the
amplitudes of the waves. Mr Harper has not ever said that there can't be
over 200 billion candidates. How is it that Martin Harper concluded that
you, the reader, can not see a problem with the Approval Vote method when
it is electing 1 candidate out of 40 factions and there are 650 thousand
trillion candidates attempting to win.


I am not entering into a discussion over checkbox methods. A quick check at
the dmoz.org website shows that Rob specifically did not constrain this
list to be about preferential voting methods.

This is the description (it has not changed much or at all):

   Election Methods Mailing List - Discussion of single-winner election
   reform, the relative merits of different proportional representation
   systems, and the technical underpinnings of all election methods.


So what is proportional about allowing people to have over 20 times more
power under Approval than they would if voting under FPTP?. It does not
sound like Approval Advocates are trying to offset large scale vote
splitting where rations might be 20% to 40%.


I doubt Mr Harper has a good idea of what his "effective weighting". I said
it was an idea of offsetting, i.e. constraining the point within the surface
of the multiwinner boundary between 2 election sets.

Martin used that term but believed he was writing about a testing 'rule'
that tested Approval. More detail has to be added before a rule would
result; i.e. a subspace flat corresponding to the particular rule, that
intersects the tangent flat holding the point at the win-lose surface.
I shan' write more, but it until he changes his term, I am sure the absence
of a full enough definition is a problem that is mainly located on Martin's
side. Anyway the conclusion was that of claiming to be bored or something
so subscribers could allow Martin to make more blunders in his reasoning
than would be hoped for from me.

The effective weighting depends on the subspace imposed. There is a
proper aim of avoiding imposing any IIA style requirement. So a cut is
needed to reduce the papers involved so no candidate not named on the
paper(s) is able to contribute an FPTP paper that opposes.
They may be more than one paper: with them being grouped by first

[The subspace can be just all flats parallel to the simplex-universe face
that has as vertices only those vertices named on the paper.]

Mr Harper would not need to have any 4 candidate definition. I gave a
3 candidate definition of the rule at the PaP list. From the above, is
he more interested in the test or the power number?: he seems to have not
bee thinking of the single real number I have not defined perfectly that
I call power. The test is clearly stated but it does not apply to
methods outside of the topic of preferential voting (i.e. checkbox methods,
e.g. the ASVB sub-vote Variant Block Vote voting method. I call it Approval.
I don't recommend it. Reformers everywhere are trying to remove it from
public elections, in part due to its faults.


At 2001-04-09 05:43 +1200 Monday, Craig Carey wrote:
>At 2001.04.04 17:47 +0100 Wednesday, Martin Harper wrote:
> >Approval for Tom, and others who reckon one-man-one-vote is solely 
> referring to
> >how an invisible genie moves your vote around, and is absolutely sacred - I


>Two parties, the Green and the Orange party, would have a spokesperson 
>The candidates are:
>R1, R2, R3, R4, R5, R6, R7, R8, R9, R10
>O1, O2, O3, O4, O5, O6, O7, O8, O9, O10,
>X1, X2, X3, X4, X5, X6, X7, X8, X9, X10,
>Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10
>Voting block A had 20 voters that each voted with identical papers. Each
>paper was marked in this way:
>  Subvotes list = { R1, R2, R3, R4, R5, R6, R7, R8, R9, R10 }

Where there is 1 vote for R and one vote for O, there are 10 subvotes for
the R candidates and 1 sub-vote for the O candidates. It is easy to
see that it can't compare with extant preferential STV-ish voting methods.

>Also, voting block B had 20 voters that voted as follows:
>1, 2:  Subvotes list = { O1 }
>3, 4:  Subvotes list = { O2 }
>5, 6:  Subvotes list = { O3 }
>7, 8:  Subvotes list = { O4 }
>9, 10:  Subvotes list = { O5 }
>11, 12:  Subvotes list = { O6 }
>13, 14:  Subvotes list = { O7 }
>15, 16:  Subvotes list = { O8 }
>17, 18:  Subvotes list = { O9 }
>19, 20:  Subvotes list = { O10 }
>There were very few other voters, but a very small number of them voted for 
>X and Y candidates.

>the R candidates tend to win because their voters
>have roughly ten times the power than they ought have. If ten is too
>small, and slighly bigger example could get the power excess beyond a
>factor of 30 million.

>At 2001.04.02 22:03 +0000 Monday, Anthony Simmons wrote:


> >It's a natural human tendency to accept what we have
> >heard unchallenged all of our lives, but it seems to
> >me that this business about "one vote per voter" is a
> >flat earth theory.
> >

This is apparently untrue. What is the argument making the
people relevant. There is none. There is also no trace of an
argument making the final ("flat earth") theory relevant.

It is not clear what Mr Harper has heard. All that I have
read indicates to me that Mr Harper is not all all clear on
whether "one vote per voter" is able to be decomposed into
2 strict rules and one aim.

> >equivalent to the usual way Plurality is done, but
> >one of the equivalents satisfies "one vote per voter"
> >and the other doesn't.  Therefore "one vote per
> >voter" is not, as they say, even well-defined.  In
> >other words, it's a phantom.
>Really?. It can be defined without a lot of difficulty, for
>3 candidates. It is worthwhile to do so, since the proper

Power clipping (there is a definition in message 110 below) was
assumed by me to be something that Martin Harper would see is
a major component of the idea of 'one vote per vote'. I don't
think that that should be assumed.

>comments are much disbelieved by me because I derived an
>expression for (1) [which seems to be mainly what Mr Harper
>was writing about], with these equations:
>'Limitation of Power'


This is the private message I got, that I referred to. It has the
0.5 value that I asked Martin Harper to provide the function of.
Mr Catchpole and I have argued over testing somehow producing numbers
that allegedly were part of a test of a preferential voting method
but the numbers seemed to have very little to do with the method.

The following is a fiction of numbers. I invite Martin Harper to
prove that the value of every number that is the value of a "P"
function is correct. There appears to be a use of a bad notation
since P is not a function of the function that defines the method.

I tell Mr Harper that I am not asking for a weak failed attempt
to dismiss me with artificial and transparently purposes skepticism,
instead I am asking for the exact definition of the formulae that
lead logically to the numbers that were e-mailed to me and which
appear below. In short, truth, and no explanation about any lies.

At 2001-04-09 15:53 +0100 Monday, Martin Harper wrote:
 >Craig Carey wrote:

>Anyway, here's an example to see how the concept works in practice, for 
>those who
>aren't keen on maths without examples. Skip otherwise.
>100 voters have the following utilities, and represent the 'A' faction:
>1.0 A
>0.1 B
>0.0 C
>zero or one voters (equiprobably) have the following utilities, and 
>represent the
>'B' faction:
>1.0 B
>0.0 A,C
>100 voters have the following utilities, and represent the 'C' faction.
>1.0 C
>0.1 B
>0.0 A
>If we are a new member of the A faction, we get the values shown for our only
>possibly sincere vote:
>Initial:   P(A) = 0, P(B) = 0.5, P(C) = 0, P(A,C) = 0.5, U = 0.3
>After:    P(A) = 0.5, P(B) = 0, P(C) = 0, P(A,B) = 0.5, U' = 0.775
>So our effective weight is 0.475
>A new member of the C faction has the same weight.
>If we are a new member of the B faction, we get the values shown for our only
>possible sincere vote:
>Initial:   P(A) = 0, P(B) = 0.5, P(C) = 0, P(A,C) = 0.5, U = 0.5
>After: P(A) = 0, P(B) = 1, P(C) = 0, U=1
>So our effective weight is 0.5
>Hence, the Condorcet effective weights are 0.475 and 0.5.
>Presume that at least 60% of the A and C factions bullet vote.
>If we are a new member of the A faction, we get the values shown for an AB 
>and an A vote (the two sincere votes available)
>Initial:   P(A) = 0, P(B) = 0, P(C) = 0, P(A,C) = 1.0, U = 0.5
>AB:     P(A) = 1, P(B) = 0, P(C) = 0, U' = 1.0
>A:      P(A) = 1, P(B) = 0, P(C) = 0, U' = 1.0
>So our effective weight is 0.5

I ask for the derivation of the value 0.5, the equation U=0.5,
and a good analysis showing how the 60% figure affects both thos
values and the conclusion which is that the "weight" is 0.5.

Obviously Mr Harper might have believed he was arguing for the
"Approval" thing.

>A new member of the C faction has the same weight.
>If we are a new member of the B faction, we get the values shown for our only
>possible sincere vote (bullet vote for B):
>Initial:   P(A) = 0, P(B) = 0, P(C) = 0, P(A,C) = 1.0, U = 0.5
>After:   P(A) = 0, P(B) = 0, P(C) = 0, P(A,C) = 1.0, U = 0.5
>So our effective weight is zero.
>Hence the Approval effective weights are 0.5 and 0

How does Martin Harper stop rows of ladies having more power than they
rightly deserving of getting?. It would be a real problem except that
the method appears to not be a real method, i.e. one that a government
or state uses in large public elections and keeps using.

What is that "if we are a new member of the B faction ... our sincere
vote". Can you post to me or the list the sincerity formula(e) or the
definition of sincerity?. Is it a probabilisitic quantity with a sometimes
non zero variance?.

Martin Harper: if you can;t provide P then please concede that the
derivation above is a fabric of lies.

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