[EM] APR (12): Steve's 12th dialogue with Toby (Steve)

[steve bosworth]

Date: Tue, 30 Dec 2014
13:19:06 +0000

From: tdp201b at yahoo.co.uk

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

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

 Toby (and everyone).

 My most recent responses are tagged by "SSS:" 

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.



T: But that's not a defining difference between APR and approval/score. We
could just as easily set up an approval/score system where your approvals/scores
are put into the hands of your favourite candidate if yours are all eliminated.

 

SSS: True, but please explain how your highest
scored but eliminated candidate is going to pass on your one vote to an elected
rep. Are you in favour of this addition to a score system?



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: Different systems can have different amounts of predictability.

 

SSS: Please explain how you might objectively
predict that more chance extra votes would be given to APR reps than to
approval/score reps. I do not yet see that this is possible.



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: Approval/score can give better levels of proportionality by using more
information, so it doesn't make it more probable that any given individual will
have their views better represented in parliament, but I would argue that it
reduces the chances of people being over or under-represented making it fairer
overall.



SSS: As it stands, this seems only to be your own vague and subjective opinion.
I keep asking you to define what you mean by "proportionality"
mathematically in an objective way but you have not yet done so. Why?

 

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: Indeed. There is no removable chance nature. But there is this unremovable
chance nature intrinsic to APR that is less present in systems of proportional
score/approval.

 

SSS: As I see it, it is impossible for you to
show that it is less present in score/approval systems than in APR without you
first mathematically defining "proportional" (or "overall
proportionality", i.e. the goal that seems to be most important to you
with regard to electoral systems).

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



T: As I said in the previous post an MP's representation (and yes this is the
amount of weight they have) is split among voters who support that candidate to
some degree. It's split equally in approval voting or proportional to the score
received from each voter in score voting. From this, each voter then has a
numerical score for the amount of representation they have. The total amount of
representation is always the same (provided the elected candidate has had non-zero
support), and proportionality is measured by the voters' total squared difference
from the mean amount of representation.

 

SSS: Correct me if I have misunderstood you:
Assuming that each MP has one vote in the Commons in your voting system, this
means each MP's "total amount of representation [voting power] is always
the same". At the same time, each approving elector for an MP would have
an equal share of this power. Alternatively, each scoring elector would have a
proportion of this power equal to the score he gave to this MP.

 

However, I do not yet understand your
phrases:  "provided the elected
candidate has had non-zero support";  "proportionality is measured by the
voters' total squared difference from the mean amount of representation".
I need these phrases to be explained. 
Please explain this calculation using examples both for approval/score
and APR.

 

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).

 

SSS: 
Surely, "One good bird in the hand is better than two less good
birds in the bush”.  

 

Yes, your score voting system (not your approval
voting system), like APR, might require your highest scored but eliminated
candidate to pass on your score to an MP on his “list of favourite candidates”.  If so, the system would seem to do all that is possible to guarantee the voting satisfaction of each citizen.  However, do you see this is also like APR in
guaranteeing that no part of any citizen’s full vote will be wasted?  If so, explain how your score voting could
achieve this.  Would this now be an
essential part of your preferred system?



Toby

 

 

 

 		 	   		  
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