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

[Toby Pereira]

Steve (and everyone). My newest comments are untagged as usual.

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.
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.
  
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.
Different systems can have different amounts of predictability.

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”.
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.

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.
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.
  SS:  “Overall proportionality” is still too vague to be helpful.  Can you not give it a mathematical definition?
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 is elected candidate has had non-zero support), and proportionality is measured by the voters' total squared diference from the mean amount of representation.
  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?
APR also makes no such guarantees. As you said, if all your favourite candidates are eliminated then your vote can be transferred using your favourite candidate's list (not that there's any guarantee you'll like any of these candidates), but this can be implemented in an approval/score system as well.
  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?
I don't accept that because, as I have argued, representation comes from more than just your official candidate.  
Toby 
 
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