APR (18): Steve's 18th
dialogue with Toby (Steve)
Date: Wed, 25 Feb 2015 22:27:24 +0000
From: tdp201b <at> yahoo.co.uk
To: stevebosworth <at> hotmail.com; election-methods <at> lists.electorama.com
Subject: Re: APR (17): Steve's 17th dialogue with Toby (Steve)
To Toby and everyone:
Thank you for being willing
further to explain your current understandings. I think they have allowed our
dialogue to make progress, i.e. to avoid “circles”. After combining some of your recent words with
your earlier sentences, I think I may have finally grasped what you mean by
“full proportionality”, i.e. what you want an electoral system to offer. Consequently, the core of my responses today
are in my first posts (located between the two +++++++++++ lines below).
Perhaps you will discover
that you only need to respond to this post because you may see the remaining
posts below the second ++++++++++line as only repeating or elaborating upon the
elements in this post.
I’ve also tagged our
previous posts with XT: and XS:, and our newest posts with T: and S:
I look forward to your
1S: When re-reading your
various sentences listed below, perhaps now I understand what you see as “full
proportionality”. Correct me if I am
mistaken, your ideal electoral system would provide each citizen with exactly
equal voting power in the Commons, i.e. the total voting power that each
citizen would have through the votes of the MPs who represent her would be
equal to the total voting power of each other citizen. For you, this calculation for each citizen would
include all the votes or parts of votes in the Commons of the MP or MPs who
have a similar scale of values to her own.
You like score voting because the scores given to any number of
candidates by each citizen determine the degree to which she sees the scale of
vales of each of the candidates she has scored as according with her own. Consequently,
a voting citizen’s total voting power in the Commons is calculated by adding
together the contribution her scores have made to every MP she has helped to
elect. Each such contribution marks the
extent to which each citizen believes that she will be represented by each MP
she has help to elect. At the same time,
however, you already accept that score voting cannot completely offer this
“full“ proportionality. In fact, I will argue later that this full
proportionality is neither possible nor desirable.
However, the above
calculations would at least offer a measurement of the extent to which the
total voting power of each voting citizen in the Commons approximates or
deviates from the mean. You believe that
the result of an election is better to the extent that the deviations it
produces from the mean are as small as possible. You also accept that some citizens’ scores
may fail to help elect any MP and so they would have no voting power in the
Commons. This failure might even
continue as a result of this citizen’s top scored but eliminated candidate
being delegated by her to passing on another copy of his pre-declared scores to
other candidates on her behalf. This
contrasts with APR’s guarantee that each voting citizen’s vote will be added to
the weighted vote in the Commons of her most trusted MP.
Your criticism of APR is
1) With APR,
only one of the rankings of candidates by each citizen can count when electing
the official MP for each citizen, i.e. all her other rankings have no effect
upon which other candidates will be eliminated or elected, i.e. APR has no
electoral use for these other rankings.
This is in contrast to the possibility of many of the scores given by a
score voter to many candidates can sometime help to elect more than one MP who
will represent her.
addition to APR’s guaranteeing that one favoured official MP will be elected
for each citizen (say, Citizen Smith), APR allows other citizens to elect a number
of other MPs, each MP officially to represent each of them. When, by chance, a number of these other MPs
share the scale of values held by Citizen Smith, she will effectively but
unofficially represented also by the combined weighted vote of this number of
MPs. She will be represented by many
more weighted votes in the Commons than some other citizens. You object to this chance inequality because
it reduces the so-called “full
proportionality” that you want.. (Please see paragraphs 20, 21, 22, 39, 40, 41,
69-72, 81 and 82 below.)
However, the truth is that
every one-person-one-vote electoral system must and should allow for this kind
of inequality to be recognized. It is the purpose of elections to discover
and give more political power to larger groups of like minded citizens. Each person’s power is appropriately increased
the more she can cooperate with others.
Each weighed vote within a majority coalition has more power than each
weighted vote held by MPs not a member of this coalition can actually make laws
and elect the state’s chief executive in a parliamentary system. When necessary, the majority rules the
minority. This is democracy. What do you
2XT: … Full proportionality
is achieved if every voter has representation of c/v. …
3T: We're going round in circles here. As has
been made clear, APR does not guarantee full proportionality in any meaningful
4S: Please explain what you mean here by “full
proportionality in a meaningful sense”.
Above and previously I have understood that it is secured for you only
when each citizen’s voting power in the Commons is the same. I still do not understand that even though
APR satisfies this test completely, it still does not satisfy you. Perhaps this is why we may have gone “around
in circles”. Please explain.
5T: … APR only guarantees
that each voter will be assigned a candidate.
6S: Every APR voter is not “assigned to” an MP
but directly or indirectly chooses her most trusted MP. Even if this MP was her lowest preference
candidate, he still is the best MP for her because all her higher preference
candidates were eliminated. They were
eliminated because not enough other citizens ranked them. He is her “best possible” MP, given the unavoidable
constraints provided by the current distribution of preferences held by the
voting population. It is this “practical
best MP” that APR offers to each citizen.
Unlike APR, score voting cannot guarantee this benefit.
No electoral system
(including APR or score voting) could or should guarantee that each citizen’s
top ranked (or top scored) candidate will be elected.
6XS: >Please explain the
extra benefits you see in score voting which makes you prefer it to APR, i.e.
even when APR:
>1) avoids violating the
principle of one-person-one-vote,
7T: Addressed above. The score voting system does not violate one person one
vote any more than APR. Under both systems, some voters will be better
represented than others, but this disparity is more likely to happen under APR
because of the fact that it allows chance extra representation that isn't
8S: Rather than saying it
“isn’t measured”, I think it would be better to say that an APR voter’s
rankings below the one that is added to the weighted vote of her favoured
official MP do not affect the election or elimination of any other
candidate. However, it would be possible
for researches, after the election, to analyse all the rankings given by any
citizen in order to calculate the extent to which she is also represented
unofficially by other MPs, i.e. candidates that were also given one of these
lower rankings by this citizen. In this
way, her “chance extra representation could be measured”. In this way, these other ranking would not be
ignored, even though they would still not affect which candidates are
elected. What do you think?
9XS: >2) uses voting and counting methods which are much simpler for
ordinary people to understand, and
10T: Ranking is not simpler than scoring,
12T: … even if the actual
counting process is still a bit simpler under APR.
13S: Please also see post 49S:
14XS: >3) enables each citizen to
guarantee that their one vote will be added to the weighted vote of her most
favoured MP (or the MP most favoured by the eliminate candidate she most
15T: It might be their 300th favourite
candidate. This might be unlikely, but the same applies for someone's vote not
counting in score voting as long as they score enough candidates, or delegate
to their favourite candidate.
16S: Please also see post 20S:
17T: I want to summarise the key points here:
First of all, we seem to be going round in circles somewhat. Some of the points
I have made several times and go on being missed by you. I think this
conversation is beginning to reach the point where it may have run its course.
But to clarify two things:
1. You seem to think that APR is perfectly proportional because every voter has
added an equal amount of power into the Commons. However, some voters are able
to add weight to more preferred candidates than others. …
18S: Correct me if I am mistaken: you mean that while each APR voter only can
add 1 vote to her official MP’s weighted vote, she may only have the option of
giving this 1 vote to her least favoured but still favoured candidate. I agree that this remains a possibility for
citizens using APR. An APR voter can
only add her vote to a candidate who has also been ranked by enough other
citizens so he can be elected, i.e. in the end she is only “able to add weight
to” a candidate who is also “preferred” by “more” citizens (i.e. enough to
On the other hand, your
words might suggest that an APR voter is able to add her vote to the weighed
vote of more than one MP? This is not
19T: … Some voters would
not get any of their top few elected and would only be adding weight to
candidates they don't really like. …
20S: No, an APR voter rationally would only rank
candidates she likes. If none of these
candidates is elected, her top choice but failed candidate would automatically
give her one vote to the weighted vote of the MP highest on his pre-declared
preference list. If she did not like the
candidates on his list, she could tick the relevant box on her ballot to
cancels this way of passing on her vote to an MP. Still, if she did not like his list, why
would she have ranked him first?
Alternatively, any APR voter could instead adopt the following strategy
probably to guarantee that her vote will continue to support her scale of
values in the Commons: she could rank
one or more very popular candidates last (ones that are safely predicted to be
elected), e.g. the leader of the party she most favours.
Also, you may recall that
APR’s primary enables each voter to help guarantee that there will be
attractive candidate available for her to rank in the later general election,
i.e. by ranking the applicant voluntary organizations with which she identifies
so she can channel her vote in the general election through one of the
candidates seeking to represent the “association” which she sees as promoting
the scale of values closest to her own.
In contrast to score
voting, not only would APR guarantee that each citizen’s vote can count for one
in the Commons, this primary and associational feature of APR seems to make it
almost certain that each voter will also be represented by an official MP she
21T: … This is no better than
some votes not affecting the result, which might [also] happen in score voting.
But you simply define it to be fully proportional and think that that somehow
settles the matter. But [APR] voters do not have equality despite your claims.
2. APR ignores representation from MPs that aren't a voter's official
representative, unlike the score system I have described. Because of this, the
actual representation that voters receive under APR has a much higher chance
element than in the score voting system. This is objectively true
22S: The “chance element”
here in both APR and score voting is determined by the number of other citizens
(unknown in advance) who happen to rank or score the candidates in a similar
way when compared to the rankings or scorings of any one citizen we might
choose to study. The difference is that
APR’s counting of these rankings guarantees that each citizens will continue
officially to count only for one in the Commons, while a score voter can only
be assured that the scores she has given to candidates will help to elect only
those candidates (i.e. perhaps none or many) who have also received enough
scores by chance from enough other citizens.
This means that she might
not help any candidate to be elected and thus her vote will not continue to
count at all in the Commons. At the same
time, if her scores for candidates do help to elect one or more MPs, her
continued total official voting power in the Commons will be more or less than
equivalent to one vote. It is in this respect that score voting violate the
principle of one-person-one-vote.
Admittedly, unlike the
counting of scores, the counting of the rankings that an APR citizen has
recorded on her ballot do nothing to help that citizen to be ideologically
represented in the Commons by any MPs in addition to her own official one. Any such extra but unofficial representation
would only result by chance, i.e. by enough other citizens happening to rank
ideologically similar candidates to make them their own official MPs (and her
In contrast to APR, score
voting enables a citizen to try to help all the candidates she likes to be
elected. However, her success or failure
in this regard is left entirely to chance, i.e. it depends on enough other
citizens scoring the candidates in a similar way. However, APR still has the advantage over
score voting in guaranteeing that each citizen will have a continued voting
power of one within the weighted vote of her official MP. Score voting can only grant each citizen
either no voting power at all or unequal official voting power in the
Commons. Do you agree with this
23XS: >You say that score voting uses more
information but what extra benefit does this use provide?
24T: It offers proportionality on a more
sophisticated level, given that it takes into account the representation each
voter gets from all elected candidates. …
25S: Please explain what additional benefit is
supplied by this “sophistication”. If
there is no additional benefit, “more sophistication” only means needless
26T: To be clear, where you said "APR has the
advantage that it would guarantee any such multiple representation
27S: More exactly, I would only claim that APR
1) to elect
all those favoured candidates who are ranked by sufficient numbers of citizens,
2) that to
the extent that the number of a group of citizens share the same scale of
values and is large enough to elect many MPs, all the weighted votes of all
these MPs will unofficially represent all these citizens (i.e. except each of
these citizens will have only one of these MPs as her official representative).
was false but applies more accurately to the score system I have described.
29S: Again, I need you to
explain the reasoning process by which you arrived at this conclusion.
30T: First of all, you
weren't clear about some of my explanations. For example, the score conversion
of the approval method. Basically because the system works using approval
votes, the scores are converted into approvals. Let's say the max score is 10.
Each voter is effectively turned into 10 mini-voters. All 10 approved
candidates are given a score of 10, 9 of them will approve candidates and giving
a score of 9 [each] and so on. So if a voter gives a score of 6 out of 10 to a
candidate, then 60% of the mini-voters will approve the candidate and 40%
32T: APR makes no such
guarantees that multiple representation will be proportional. In fact, I
demonstrated [illustrated] it with my example in the last e-mail. I will
present it again. Scores out of 10:
Voter 1: A=10, B=10, C=10
Voter 2: A=10, B=10, C=0
The score system would elect A and B. We can easily see that this is the best
33S: Yes, in this case,
score voting gives each of these two voters equal voting power in the Commons
from 2 MPs who have received their highest scores. However, score voting cannot guarantee such
equal representation to each and every citizen.
34T: Under APR, [from the above scores]
the same two voters might rank the candidates as follows]:
Voter 1: C>A>B [or C>B>A, or B>A>C, or B>C>A, or A>C>B,
Voter 2: A>B
A and C are elected, giving voter 1 better representation because he has extra
unofficial representation from A. To be clear, it is objectively incorrect to
claim that APR gives more proportional "multiple" representation. …
35S: Yes, in this example, voter 1 has one
official rep and one unofficial rep.
This sometime happens in any electoral system and there is nothing wrong
with this. Also, please see post 1S:
36S: In this case, you again seem to have a
definition of “proportional” other than the one you seemed to have in mind on
some other occasions. On those occasions, perfect proportionality seemed in
practice to be present only when there is no difference between each person’s
actual total voting power and the per capita mean voting power in an election.
For your above use, please define what you mean by “proportional”. Please also see post 1S:
37 T: … APR has no way of
counting and checking multiple representation and has no mechanism to ensure
that it is in any way proportional. The amount of representation voters get in
APR is more down to chance than it is in the score voting system.
38S: I need you to spell out your reasons for
coming to your conclusion in the last above sentence. Please also see post 1S:
39S: 2) Also, in contrast to APR, scale voting
would encourage groups of like minded voters to coordinate their individual
scores of the candidates they favour so as to make it more probable that all these
favoured candidates will be elected. Admittedly, score voting does not
guarantee such results but to the extent that this strategy is successful, the
total voting power of each of these citizens would be greater than that of
individual voting citizens who are similarly members of smaller groups, or who
are not members of any such like minded group. Perhaps these latter voters
would know fewer candidates that they would want to score and thus each of
these citizen’s total share in the voting power in the Commons would be smaller
than that held by the individuals in the larger groups, i.e. score voting would
allow such strategic groups to gain more power per person than other
individuals would have with regard to all their official MPs. In this regard, unlike
APR, score voting would allow violations of the principle of one-person-one-official-vote.
It could do this by allowing some voters to produce greater deviations of their
voting power from the mean (i.e. each member of a big group having a voting
power greater than the mean, and thus leave other citizens, per person, to
share even less voting power than the mean. This seems contrary to what you say
Please explain if you think I am mistaken about this.
40T: If you are saying what I think you
are, then you are mistaken. If a group of like-minded voters get together in
this way, then they will still only be able to elect the number of candidates
that matches their proportion of the electorate. …
41S: Not necessarily. Please compare the following two cases:
member of a group constituting 40% of the electorate gives a 10 to candidate K,
but K is elected by having received only half of these 10s.
member of a different group constituting 20% of the electorate give a 10 to
candidate Q and these scores alone elect Q.
As a result, the 40% of the
electorate in 1) has only the same voting power in the Commons as the 20% in 2)
have. Alternatively expressed, each voter
in 1) has half the voting power in the Commons when compared with the voting
power of each citizen in 2). This shows
that score voting cannot guarantee that “the number of candidates [elected] …
matches their proportion of the electorate”.
42XS: Still, if I do
understand you correctly, you have not yet attempted exactly to define and
explain the extra benefit you see as provided by score voting as contrasted
with APR, i.e. the benefit you see as making it worth
>1) denying equality to each citizen, …
43T: I wouldn't be denying equality. Of course, APR allows for inequality with
"non-official" representation to a far greater extent than my score
44S: Again, I need you to explain the reasoning
process by which you have come to this view.
45T: … I hope you
understand this now. Also, some voters have their favourite candidate elected
and some don't. This is another inequality of APR.
46S: This possibility exists in all electoral
systems as far as I know. Do you
47XS: …2) using much more complicated mathematics that few citizens would
48T: It is more complicated. But there's a couple of points to make regarding
this. Firstly, it's unclear exactly how one would decide how complicated is too
49S: Any additional
complication is too much unless it gives voters an important additional
benefit. As yet, I have not understood
how score voting gives any extra benefit.
Please try to explain more.
At the same time, APR only
requires people to understand how to add whole numbers. Score voting also requires people to
understand subtraction, decimals, and why some numbers need to be squared, i.e.
all this, in addition to understanding why their vote will probably not count
equally when compared to the voting power of each other citizen.
50T: APR is also fairly complicated. Secondly,
I've said before that this score method is only a working model anyway.
Thirdly, I only introduced it into this discussion to show up flaws in APR. The
point is that those flaws still exist even if you want to separately argue for
keeping APR on the grounds of greater simplicity or other flaws in the score
51S: Please list the “flaws” you still believe
52XS: >3) denying to each citizen the
capacity to guarantee that her vote will count fully within the weighted vote
of the MP she most trusts (or the MP most trusted by her most favoured but
53T: I am guaranteeing that someone's vote [scores] will count towards finding
the most proportional result given that everyone's votes are counted equally. …
54S: Please explain the reasoning process by which
you arrived at this conclusion. Firstly,
your “someone’s” still means that some (not all) citizens’ votes will help some
candidates to be elected, and those that do, will be unequal in the amount of
voting power each gives to those elected.
If so, “everyone's votes are counted equally” could only mean that all
votes are counted according to the same rules.
Is this correct?
55T: …Under APR, someone's
favourite candidate might not be elected (as you acknowledge) but even if this
is the case the MP most trusted by their most favoured but eliminated candidate
might be way down their list, so not really a suitable representative for the
56S: Also, please see post 20S:
57XS: So you accept that
with score voting some citizens’ votes will be entirely wasted (i.e. not help
to elect any candidate), and those that do help will usually count somewhat
unequally. If so, is this not a needless violation of the principle of
58T: It's possible that some votes will
be wasted in this sense. If a voter gives positive scores to some candidates,
it's possible that none of these will be elected. …
60T: … But obviously
someone could give a score to all candidates, in which case their vote would
61S: Yes, but surely a score voter would only
score the candidates she likes. If she
scored all of them in the same way it would be the same as not voting at all.
62XS: In any case, above you seem
already to “accept that with score voting, some citizens’ votes will be
entirely wasted (i.e. not help to elect any candidate), and those that do help
will usually count somewhat unequally. If so, in contrast to APR, you accept
that score voting violates the principle of “one-person-one-vote”?”
63T: Addressed above.
64S: Yes but also please see post 1S:
65*XT: … On weighted votes generally, I think we have largely made our points
about that and I don't really want to bring out all my arguments again because
I think we'd end up going round in circles, but it's all there in the archives.
But if you want to bring up something specific I have said, feel free to do so.
66S: Please list any remaining objections you
might have regarding weighted votes.
This would help me search the archives.
67T: Just to add to this, it was you who
steered the argument away from this. We last really discussed the weighted vote
issue back in about December, and you didn't respond to my last points on it.
68S: I do not recall steering this argument away
but perhaps your above list will help me find this December exchange.
69XT: But I will make some
points about APR's ranking v score now. When I've mentioned the measure of
disproportionality in the score result, a few times you've pointed out that
indeed any result would (realistically) have disproportionality, whereas you
have argued that APR does not have this disproportionality. But this is not a
reasonable comparison because they are not being compared by the same measure.
70XS: Let’s again compare
them by the same measure then. As I understand it, you want to measure the
results of score voting by calculating the average per capita deviation from
the mean of the voting power of all individual voters. As a result, you
discovered that it is likely that some voters would have no voting power, while
the rest would have varying degrees of voting power. You think the best result would
be when this average deviation is as small as possible. By contrast, when we
apply the same test to APR, we find both that there would be no such deviations
and each citizen could guarantee that her vote will have exactly a power of 1
within the total number of citizens voting. Therefore, while score voting would
probably provide unequal voting power for citizens, APR provides this equality.
How do you justify this inequality?
71T: No, because APR's proportionality
is based on the fact that everyone has equal "official"
representation. It says nothing of their true level of representation - i.e.
how represented they feel by their official representative or indeed by anyone
else. APR is likely to have more inequality than score, because it uses less of
the information and leaves more to chance.
72S: Given the above, perhaps it is your desire
that each citizen have an equal number of votes of MPs in the Commons that
agree with each citizen’s own scale of value.
Perhaps this is your idea of “full proportionality”. If so, this would prevent larger groups of
citizens from having more voting power than smaller groups in the Commons. I do
not think this what you want? Also, please see post 1S:
76XT: … APR's measure is purely on wasted votes. As long as every voter is able
to be assigned a candidate …
77S: Also, please see post 1S:
78T: … that they have
ranked (somewhere on their list), then no votes are wasted and APR has achieved
perfect proportionality. All very well and good. Except that in the case where
all voters give a full ranking of all candidates, every single result would end
up as fully proportional under APR's measure. …
79XS: Not exactly. I think
we already agreed that both systems should allow each voter
>1) to rank or score as
many or as few of the candidates in the country as they might wish, and
>2) allow her to require
her top ranked (or top scored) but eliminated candidate to pass on her APR vote
to the rep most favoured in that candidate’s pre-declared ranked list of other
candidates ( or to pass on one score vote worth of this eliminated candidate’s
pre-declared scores to other candidates).
>This means that without
needing to “give a full ranking of all candidates”, an APR voter could
guarantee that her whole vote would at least be added to the weighted vote of
an indirectly favoured MP. However, it
does not guarantee that any scores that are similarly passed on will help
electing any MP.
80XS: Now you seem to be
meaning something different by “perfectly proportional”. Previously you meant,
each voter having a voting power in the commons that does not at all deviate
from the mean. Now “perfect” seems to require that each citizen be represented
by her top ranked candidate? In this sense, I grant that APR does not guarantee
this. It only allows a citizen to guarantee that her vote will be added to the
weighted vote of the MP (not candidate) she most trusts (or to the MP most
trusted either by her top ranked but eliminated candidate, or trusted by the MP
she has help to elect but who received more than 10% of the weighted votes in
81T: I'm using your meaning, not mine.
It seems that you think as long as each voter has the same amount of official
representation, then the result is fully proportional regardless of how
represented they feel by their MP or how much extra representation they get
from MPs other than their own.
82S: Yes, as proportional
as it should be: each citizen guaranteed
to have one official MP that she favours, and perhaps other unofficial but
liked MPs in proportion to the numbers of her fellow citizens that share her
scale of values… Also, please see post
83XT: … If, in a score voting election, voter 1's 10/10 candidate is elected
and voter 2 just gets their 8/10 candidate elected, then the mechanism would
measure some disproportionality. However, if this happened in APR it might be
that voter 1 would have their top rank elected and voter 2 their second rank.
One might still see some disproportionality in this, but APR ignores this. ..
84S: Yes. Also, please see
85XS: Rather than calling
this “disproportionality”, I think it would be more apt to say that such a
result is not “perfect” in the above new sense, i.e. because “voter 2” is not
as pleased with his MP as is “voter 1”. However, this is not the fault of APR
but a correct result of the fact that more fellow citizen ranked voter 1’s top
ranked candidate than voter 2’s top ranked candidate. At the same time, APR
guaranteed that each voter’s vote was added to the weighted vote of the MP (not
necessarily the candidate) that each most trusts.
86T: Call it what you want but it's
still deviation from the ideal result. …
87S: I assume that neither
of us are primarily focussed on a concept of the “ideal” or the “perfect” when
it is impossible in practice. Again, no
system could or should guarantee that each citizen will have their top choice
candidate as their MP.
88T: … In an "ideal
world" using APR logic, there would be no 10% limit for each MP's
weighting and no limit on the number of MPs elected. …
89S: You might suggest a limit other than 10% but
I think we might also agree that a limit should be applied to remove the
possibility that any one MP could be in a position to dictate to the Commons.
90T: … A perfect result
would be for every voter to add the same amount as each other to their
deviation, and APR would deviate.
91S: In the context, I do not understand the above. Why have you used the word “deviation” in
relation to APR. Please explain.