# [EM] APR (10): Steve's 10th dialogue with Toby (Steve)

Toby Pereira tdp201b at yahoo.co.uk
Mon Dec 29 15:25:02 PST 2014

```Steve (and everyone)
Here's my latest reply! It's possible I've replied for a second time to some old comments, but you can have them anyway. (My new replies are untagged.)
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?
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.
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.
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.  > 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 you 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:?
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).   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?
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.  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?
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".  T:  That is why a balance of voters' preferences across all MPs is desirable rather than simply having their favourite elected.  S:  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.
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). 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.  S: Again, why is this more important to you than being guaranteed representation by your most trusted MP?
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.
T:   Because it gives voters more equal representation overall. People aren't necessarily just obsessed with their one favourite candidate as you seem to suggest.   S:  “Obsession” would lead a citizen to vote only for one candidate.  Instead, ranking allows each citizen to list any number of candidates according to how completely each is trusted to represent that citizen’s scale of values.  Again, especially with its use by APR, ranking allows each citizen to guarantee he will be represented by the MP who is ideologically closest to him.  S: 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?
It is true that someone won't necessarily get their favourite elected. But for example, if I scored one candidate 10/10 and teo others 9/10 each, I'd rather get the two 9s than the one 10 (assuming for now that each MP has equal weight).  T:  People are likely to have several candidates that they like similarly, and it makes sense for this to be reflected in the voting process.  S:  When this similarity occurs in APR, it is “reflected in the voting process” by these several candidates being ranking next in line to each other.
OK, but it is not reflected in the calculation process unless the candidate ahead in the rankings is eliminated.  T: Obviously it would be interesting to know in practice how people would vote using score and approval systems (how honest their scores would be) …   S:  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?
S:  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?
To put it simply, if a candidate is elected with a certain amount of power, 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 propoortionality is achieved if every voter ends up with equal representation. Otherwise it's measured on the total of the squared differences.
Also, it wasn't actually Simmons's method I was using, although it was him that set the problem - not that it's important. But to get ideal proportionality it would be computationally insane, but if you elect candiates sequentially, it would be quite doable and probbly very close to the ideal result.
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.
Toby
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