[EM] General PR question (from Andy Jennings in 2011)

[Andy Jennings]

Yes, there is a tradeoff between proportionality and support.  Kristofer's
work speaks to that much better than I can.  But personally, I think
proportionality is paramount.  If you're choosing a "representative body",
then mirroring the electorate is the ultimate goal, isn't it?  I like
Monroe's metric.  If the voters can be divided up equally and assigned to
the winners in a way that each voter is perfectly happy with his
representative, to me that's a perfect representative body.

But any such method must be non-sequential, and the main problem with a
non-sequential method is the losers might be able to complain, "I would've
been elected if the council only had 4 seats, but since it has 5 seats, I
lost."  Is the answer, "Yes, the optimal 4-person council included you but
the optimal 5-person council didn't," good enough?


If I remember correctly, one of my goals in sending that email was to start
exploring what multi-winner outcomes felt intuitive to people.  A purpose
that you continued later on.  I wonder if you discovered the same thing I
did.  That not many people respond.  And that most of us don't have strong
intuitions about tricky situations in multi-winner outcomes.

If we could come up with a large set of multi-winner scenarios which had
answers that felt intuitive to most people, we could use it to evaluate all
existing systems and to quickly get a good handle on any new systems that
are proposed.

That's why I made a point to try to respond to your post, indicating which
answers felt best to me and how strongly I felt about them.

~ Andy

On Sat, Sep 27, 2014 at 4:28 PM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:

> I was thinking recently again about Andy Jennings's PR question (below)
> and available here
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-July/093278.html,
> which is about the trade of between proportionality and having candidates
> with strong support. Warren Smith (
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-July/126111.html)
> gave the extreme example of a 500-member parliament where two candidates
> each get 50% approval, and the others each get 0.2% approval. Perfect
> proportionality could be achieved by electing 500 candidates with 0.2%
> approval, but in many ways this would seem a perverse result.
>
> But the more I think about it, the more I think there isn't a
> non-arbitrary solution to the problem. What's the exchange rate between
> proportionality and support? There isn't an obvious answer.
>
> I proposed my own proportional approval and score system a few months ago (
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2014-May/098049.html
>
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2014-June/130772.html),
> and it purely bases result on proportionality, so would elect CDE in
> Andy's example but would also elect 500 candidates with 0.2% support in
> Warren's example. However, this also assumes that every possible winning
> set of candidates would be looked at and the most proportional one found.
> In practice, the system might be used sequentially. This would force
> through the most popular candidate, and then each subsequent candidate
> would be elected to balance it proportionally. This would elect the two
> most popular candidates in Warren's example, but would fail to elect CDE in
> Andy's example. But given that there may be no non-arbitrary solution,
> electing sequentially may be the simplest and least arbitrary way around
> the problems we have. It is also a solution that would likely be forced
> upon us due to limits on computing power when it comes to comparing all
> possible sets of candidates. Necessity may force the pragmatic solution
> upon us.
>
> Toby
>
>
>
> >Forest and I were discussing PR last week and the following  situation
> came
> >up.  Suppose there are five candidates, A, B, C, D, E.  A and B evenly
> >divide the electorate and, in a completely orthogonal way, C, D, and E
> >evenly divide the electorate.  That is:
>
> >One-sixth of the electorate approves A and C.
> >One-sixth of the electorate approves A and D.
> >One-sixth of the electorate approves A and E.
> >One-sixth of the electorate approves B and C.
> >One-sixth of the electorate approves B and D.
> >One-sixth of the electorate approves B and E.
>
> >It is obvious that the best two-winner representative body is A and B.
> What
> >is the best three-winner representative body?
>
> >CDE seems to be the fairest.  As Forest said, it is "envy-free".
>
> >Some methods would choose ABC, ABD, or ABE, which seem to give more total
> >satisfaction.
>
> >Is one unequivocally better than the other?
>
> >I tend to feel that each representative should represent one-third of the
> >voters, so CDE is a much better outcome.  Certain methods, like STV,
> Monroe,
> >and AT-TV (I think) can even output a list of which voters are represented
> >by each candidate, which I really like.
>
> >I also note that if there was another candidate, F, approved by everybody,
> >it is probably true that ABF would be an even better committee than CDE.
> Is
> >there a method that can choose CDE in the first case and ABF in the second
> >case?
>
> >Andy
>
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>
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