[EM] Subject: APR (13): Steve's 13th dialogue with Toby (Steve)

[Toby Pereira]

Steve and everyone
My newest comments have no tags.
T:  I suppose because a score system doesn't work on the same elimination basis as APR, it wouldn't be able to work in exactly the same way. But what you could do is allow the following three options for voters. One would be for the voter to give scores to as many candidates as they like (anyone candidate they ignore gets a default 0) and not transfer any power to their favourite candidate or anyone else. …  XS:  Do you agree that this option would not guarantee that your vote would not be entirely wasted, i.e. not even positively counting in the Commons through the vote of the MP could have otherwise been given your score by any eliminated candidate you had scored?
Yes. It is possible that none of the candidates you give a positive score to will be elected. However, see below.  T:  … They would also have the option of simply voting for one candidate and using that candidate's entire score set of the other candidates.  XS: Please clarify.  Do you mean this one candidate if eliminated would be required (some how) to give the score you gave to him to an MP?  If so, how exactly?
What I mean is that each candidate would have a pre-declared set of scores for all the other candidates. They would rate the other candidates in advance of the election. Then if I as a voter don't want to individually rate the candidates, then I cast a vote for my favourite candidate and indicate that I want to use their ratings of the other candidates rather than rate them myself.  T: … The other option would be for a voter to give scores (including zeros) to as many candidates as they want (these would be the ones they have specific views about), and then leaving the ratings of every other candidate to their indicated favourite candidate. As for whether I'm in favour of it, yes, I think it should work well.
 XS:  Again, do you agree that this option would not guarantee that your vote would not be entirely wasted, not even positively counting in the Commons through the vote of the MP given your score by this eliminated candidate whom you had scored?
It's possible that none of the candidates you give a positive rating to will get elected. Or, if you are using your favourite candidate's ratings, it's possible that none of the candidates they have given a positive rating to will be elected. However, under APR, unless you (or your favourite candidate) has given a complete ranking list of all candidates then this can happen in APR as well. Also if none of my ranked candidates are elected, but my favourite candidate's 78th ranked candidate is elected as my representative, I might well be justified in feeling that I'm not really represented in any way. The fact that someone gives a complete ranking does mean that someone will become their official representative, but it offers no guarantees about how well someone will feel represented by them. So you can be represented in APR by definition only and not in any real sense. I'm not saying that this is likely, but I don't think it is any more likely in an approval/score system either.  XS:  Still you fail to give a mathematical definition of “proportional”.  Without this, you cannot explain why the information below APR’s transfer line is important to you.  Similarly, you have not provided me with the formula by which all the information that would be provided by your approval/score voting would allow you to calculate what you would see as the optimal, “overall proportionality” in the Commons as a result of any such election.  Can you not provide this information? [I see you have attempted to provide this information below.]
Yes, I did provide the information below. I also described it (albeit more briefly) in previous e-mails and linked to a mathematical description of the approval system. It's probably best to read the whole e-mail before saying things like this. And also, if you weren't happy with the previous descriptions, you should have said that you weren't happy with them rather than ignoring them and just stating that I hadn't provided an explanation.
XS:  This correctly understands APR but I think it would be clearer to say that “A’s power is provided by two voters” rather than “split between two voters”.  Also, do you again agree that this option would not guarantee that your vote would not be entirely wasted, i.e. it will be wasted if none of the candidates you have approved or scored is sufficiently popular to be elected?
Yes, but see above on APR's limitations regarding being represented by APR's definition only.  XS:  Again, do you accept that according to your system it is possible that none of the candidates you have approved will be elected?  However, if any of these are elected, will each voter be able to know exactly to what “extent” he is represented by each of these MPs?  Will this also work for score voting?  If so, please explain how.
When the results of the election are published, the number of approvals or total score given to a candidate would be part of what is published, so you can know from that.  T:  The basic definition of proportionality is unchanged (each voter has equal representation), but how we calculate it is different from APR or STV methods generally. With approval voting, it is fairly simple. Each MP's representation is equally split [????shared????] among all the voters that have voted for them. With score voting, it is split proportionally to the score each voter gives. For example, candidate A is elected and has 1/500 of the parliamentary power. Two voters approved candidate A, so they each effectively have 1/1000 of the total parliamentary representation each plus whatever they might get from other candidates.
XS:  Correct me if my following understanding is mistaken:  Let us assume that your candidate A received only a number of approvals equal to one 500th of all the citizens voting in the country.  In this case, each citizen who approved MP-A has 1/500 of one vote in the Commons.  Again, assume that  this one 500th of all the voting power in the Commons was produced by 3,000 approvals.  However, a different group of citizens might elect MP-B with 4,000 approvals.  If so, each voter in this second group of citizens who gave their approvals to candidate B will have a smaller share in the one vote in the Commons held by MP-B.  This means that the share of the voting power in the Commons held by each of the voters for MP-B is less than the share held by the voters for MP-A.  Is this correct?    XS: If so, each citizen’s vote is not equal, “each voter does not have equal representation”.  For simplicity, I have assumed that each of the citizens voting for these two MPs only approved of one candidate.  However, the possibility of this inequality of representation would remain even if each had approved of more than one candidate.  Please explain why you agree or disagree.
It is correct that those represented by MP-A would in this situation have better representation than those represented by MP-B, and this disproportionality would be measured by the system. The overall most proportional set of candidates would be the set elected, but I am not claiming that you would be able to find a set of candidates that gives a perfect level of proportionality.
 T: …Voters' levels of representation for all candidates are added up. Exact proportionality is when every voter has the same amount of representation. That is what I mean by proportionality. The total of the voters' levels of representation will always be the same whatever the result (because it always equals the total parliamentary power), and so the average will always be the same. …  XS:  The meaning you give to the above words must be different from the one I see in them because I take them as just another way of expressing what APR offers.  However, I would like you to comment on my following attempt to rewrite your above words to show you how they could be used correctly to characterize approval, score, and APR systems from the point of view of each voter:  XS: In your countrywide approval election of a 500 member Commons, the 500 candidates who receive the most approvals are elected as MPs. The share that each approving citizen will have in the total power of the Commons is discovered by adding together each of the shares he has of each of the MPs he approved.  The more such MPs he has approved, the larger will be his share of total voting power in the Commons.  Because citizens may approve different numbers of candidates, and thus different numbers of MPs, approval voting (unlike APR voting) by no means guarantees that each voting citizen will have “the same amount of representation”, or any representation at all. 
That's not how it would work. It's not simply the 500 candidates with the most approvals that are elected. It would be the 500 MPs that would minimise the disproportionality as I have described it. For example, if 51 people approve A and B and 49 approve C and D, and two are elected, then it would be one of A/B and one of C/D, even though A and B have the most approvals.  XS: In any case, while the resulting voting power of each approving citizen may be different, the total voting power either of all approval, score, or APR MPs “will always be the same whatever the result because it always equals the total parliamentary power”.  At the same time, “the average” voting power of each approval, score, or APR MP will be one 500th of the total.  Of these three voting systems, only APR also guarantees that this total will also equal the total number of voting citizens in the country.
It only makes such a guarantee by defining some of the information out of existence when it comes to defining proportionality.  
T: …We can therefore measure disproportionality by adding up the squared deviations of representation levels of the individual voters from the mean level of representation.  XS: Here you are admitting that “individual voters” will have “deviations of representation levels from the mean”, i.e. each citizen’s vote may not count equally in an approval or score election, i.e. in the Commons. 
Yes. Proportionality would never be perfect in a system that uses this amount of information.  XS: Again in the light of the above attempt to rewrite your words, your above “measure of disproportionality” would usually show that there is some “disproportionality” in approval or score systems but none in APR.  This is true of APR because the total voting power in the Commons would be equal to the total number of voting citizens, each citizen’s vote being present in the weighted vote of his MP, i.e. each citizen’s voting power is one – exactly one of the voting population.
There would be no disproportionality in APR, but only under APR's own measure. As I have said previously, some voters might get chance extra representation by being better represented by MPs that are not their official representative. If I polled the voters in an APR election to find their scores (out of e.g. 10) for each candidate, and measured the APR result as if it was the result in a proportional score election, I would find disproportionality under that measure.
  
XS:  As I see it, your above complicated attempt at an explanation does not remove the validity of the conclusion I offered for your consideration in my above “XS:” comment immediately preceding this one.  If you think that conclusion is not correct, please explain.
That there will always be some disproportionality? Yes, but this would also happen in APR if measured by the same metric.  XS: Also, because such a mathematical explanation would be much more difficult for most citizens to comprehend, in contrast to the relative mathematical simplicity of APR, I would see it, instead, as proving an argument that APR should be preferred both over approval or score systems.
It's something to consider, but I don't think citizens all understand how STV works, and it is used in some places anyway.
XS:  Please specify and explain the “flaws” in APR that you still see in the light of all the above points.
Well, the bottom line is that APR doesn't use all the information about what voters think of the candidates. If I was coming at this afresh, without having a system already in mind, I would have thought that the more voter preference information that is used, the better the result can potentially be, without worrying exactly how to define "better" or "more proportional". This is why I have suggested score voting. Whether the particular method I described does the job or not is beside the point, because this is really a discussion about APR. The main point is that APR doesn't use all the information and another system (whether the system I described or not) might, so APR could end up lacking something as a result, including in the examples I gave in previous e-mail about some voters getting chance extra representation that isn't officially recognised by APR.
It would be interesting to compare APR with a proportional score system in the following way: have an election held under APR, but also poll the voters on what scores they would have given to the candidates if it had been a score voting election to find what would have been the winning result under these circumstances. Then measure the proportionality of each result using the score system to see which does better. You might say I'm stacking the odds in favour of the score system by using the score system to measure proportionality, and it's right to an extent, but it would be interesting to see how much the weighted power feature of APR worked in its favour.
Toby
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