[EM] APR (11): Steve's 11th dialogue with Toby (Steve)

Tue Dec 30 04:11:28 PST 2014

APR (11): Steve's 11th
dialogue with Toby (Steve)

Date: Mon, 29 Dec 2014 23:25:02 +0000

From: tdp201b at yahoo.co.uk

To: stevebosworth at hotmail.com; election-methods at lists.electorama.com

Subject: Re: APR (10): Steve's 10th dialogue with Toby (Steve)

 Hi Toby (and
everyone)

Here's my
latest reply. My new replies are tagged with SS:.)

 Steve 
-----------------------------------

T: Well, even under APR, someone's favourite candidate might not be elected.

1S: Correct.
However, each APR citizen’s vote can be guarantee to be added to the weighted
vote in the Commons of the MP most trusted by him, by his most trusted but
eliminated candidate, or by his very popular MP. Is your preferred system or
any other system that you know about able equally to guarantee this?

T:  It wouldn't make the same guarantees,
but an approval/score system makes different guarantees - someone's rating of
every elected candidate can be considered when calculating the how proportional
that slate of candidates is.

SS:  Correct but this not a guarantee that each
elector will be represented.  None of the
candidates he scored or approved may have been elected.

T: It would be
impossible to equalise it completely. But the system I referred you to is an
example of a system that uses the difference in representation as the measure
it tries to minimise, so it's likely to minimise it better than APR.? 

2S: The problem
with your suggestion is that by minimising these differences in this way, you
could elect an assembly that represents each citizen equally badly, and some
not at all. Therefore, APR has the advantage of guaranteeing that each citizen
will be represented as well as possible by at least one MP.

T:   It would only not represent someone
at all if they only gave a score/approval to very few candidates and none of
these were elected. This can happen in APR too.

SS: No. Remember
that if all of the candidates ranked by an APR elector are eliminated, his “default”
will be given to the first choice MP of the elector’s first choice but
eliminated candidate.

> S: Yes,
but if every system allows such deals sometimes to happen by chance, then it?s
not a reason to favour one system over another.

T: Again, some
systems allow it to a greater extent than others. It's not all or nothing.

3S: Are you
saying that APR would allow it to a greater extent than your preferred system?
If so, please explain how you have arrived at this conclusion. In any case, why
would this continue to be seen as a valid criticism if APR also has the
advantage stated above in 2S:?

T: I would say that a proportional approval/score system could well mean that
it is less likely that some people would get extra representation by mere
chance because it takes into account your rating of every candidate, not just
the one that's deemed to be yours. Therefore it wouldn't have the problem I
highlighted in the example (quoted from a previous e-mail below).

SS:  I do not see how we can say that any system
will have either more or less “extra” presentation when it happens purely by
chance in any system.  Chance means
unpredictable.

T: But to
change it slightly, we might be forced into a strict preference, so I rank
C>B>A, even though they are the same to me. You rank A>B>D. I get C
and you get A. APR doesn't know that I would be equally happy with A.

4S: Correct,
APR would not know this but it has guaranteed “happiness” for us both.? If a
system can guarantee this, why is it so important to you that you have a system
that would know this, even when it could not guarantee that each citizen will
be represented by their favourite or equally favourite MP?

T: Happiness
isn't guaranteed by having your favourite representative elected. …

5S: Of course,
nothing can absolutely guarantee “happiness”. However, democratic elections are
justified partly by the assumption that citizens should equally have the
opportunity to elect a representative they trust, and that this will probably
make them happier than if they could not do this.

S: In any case,
does your preferred system not care whether citizens are satisfied with their
representatives or not?

T:  Of course this matters, but I'd
measure my happiness by looking at how well I feel my views are represented by
parliament overall, not just by whether my favourite politician got in.

SS:  If I am correct that approval/ score voting
cannot guarantee that you will have even one MP that you like, neither can it
guarantee (or even make it more probable) that your “views are represented by
parliament overall”.

T: … Someone's representative
is just one part of a parliament that votes on legislation. In the example I
gave, one person would have better representation than the other, so would
likely end up with more of their favoured legislation getting passed. 

6S: Yes. Why is
this a problem for you? You seem to be forgetting that they could have this
“better representation” using most any electoral system only because more of
their fellow citizens have a scale of values similar to their own. APR’s
weighted votes represent each scale of values proportionately (each citizen’s
vote continues to have the same official weight in the Commons), i.e. exactly
what a democratic election should offer. Do you not agree with this? If not,
why not?

T:  I think you've missed the point here.
Obviously if more people have a particular view than my view, then they would
get more representation between them. But my example was not about that. It was
about some people getting more representation by the chance nature of APR not
looking at how well people are represented by MPs other than their own. APR
ignores all information below the "transfer line".

SS:  There is no removable “chance nature” in
APR.  APR ignores the “information below
the transfer line" because the APR citizen has given greater importance to
the information above the transfer line.

T: That is why
a balance of voters' preferences across all MPs is desirable rather than simply
having their favourite elected.

SS: Please give
me your mathematical definition of “balance”. In any case, please explain why
the points made above by 2S:, 3S: & 4S: should remove your preference for
this balance.

T:  I suppose by "balance" I
just mean overall proportionality and I'd refer you back to the definition
implied by the approval system I mentioned earlier (but see bottom for a bit
more detail).

SS:  “Overall proportionality” is still too vague
to be helpful.  Can you not give it a
mathematical definition?

T: Ranked
systems in general don't know, whereas score systems give details about [equal]
intensity of preference, and approval systems at least give voters the chance
to say that they approve or not of a candidate.

SS: Again, why
is this more important to you than being guaranteed representation by your most
trusted MP?

T: I think overall proportionality is important, and I think a definition of
proportionality that can look at people's ratings of all elected politicians is
better because it uses more information.

SS:  It seems to me that you must define “overall
proportionality” in order to explain the use to which this ill defined “more
information” could be put.

……………………

SS: Your
preferred system does allow each citizen to record her score or approval given
to as many candidates as she might wish but it does not guarantee that she will
be represented even by a candidate she approves, let alone one she scores
highest. Do you accept that this is true? If this is true, please explain why
you or anyone else would prefer a system that would not offer APR’s guarantee
to be represented by the MP you judge to be best?

T:  It is true that someone won't
necessarily get their favourite elected. But for example, if I scored one
candidate 10/10 and two others 9/10 each, I'd rather get the two 9s than the
one 10 (assuming for now that each MP has equal weight).

SS: A good bird
in the hand is surely better than two not so good birds in the bush.  Your preferred system does not guarantee that
even one of your 9/10 candidates will be elected.  Is this not true?  If so, why would you prefer that system?

……………………..

SS: I still
would like to receive your mathematical definition of an ideally
“balanced/proportional result”. In practice, would your preferred system
guarantee this result? Do you think this will both explain and justify why you
want to reject the seemingly unique guarantee offered by APR? 

SS: Finally,
given that you accept “that it would be computationally insane” to use Forest Simmons’
method to “worked out the ideal proportions”, such a method would seem to be
entirely irrelevant for practical purpose in our discussion assessing different
systems for electing many winners by many voters. Do you agree?

T: To put it simply, if a candidate is elected with a certain amount of power,…

SS: Does “a
certain amount of power” for you mean something other than “a weighted vote”?

T:  …… that MP's representation would be split
among the voters that have voted for them - equally in approval voting, but
proportional to the scores in score voting. Perfect proportionality is achieved
if every voter ends up with equal representation. ….

SS: APR
guarantees this “equal representation”, your preferred system does not.  Do you accept this as true?

T:  Otherwise it's measured on the total of the
squared differences.

….ideal proportionality it would be computationally insane, but if you elect
candiates sequentially, it would be quite doable and probably very close to the
ideal result.

T:  And this is probably the most
important point saved until last - I think I have given some valid criticisms
of ranked PR systems. It might be that other systems end up with more problems
of their own, so would be worse overall, but that doesn't negate the
criticisms. Whichever system is the "best" is never going to be
perfect. I didn't actually intend this to get into a big discussion of score v
rank, but just merely to point out that APR does ignore certain information,
information that I would argue a perfect all-knowing system would use.

SS:  Again, I think you need to give a
mathematical definition of “overall proportionality” in order also to define
what you mean by a “perfect all-knowing system”.  I hope you can do this.

Toby

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