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

Wed Oct 1 14:09:59 PDT 2014

Several points:

I think this is a productive discussion.

I generally like Toby's definition as a proportionality measure. However, I
think that there should be a majoritarian measure too (something like
summed utility for the whole candidate set), and some balance between
these. In other words, a method should come from somewhere on the Pareto
front.

I'm not sure that we'll be able to find a non-arbitrary way to pick a point
on the pareto front.

However, I think that delegated methods are promising in that regard. In
particular, if candidates are required to pre-declare some preferences over
the other candidates, and if this ordering must satisfy some criteria, then
I think that the chances of "pathological" examples can be minimized or
eliminated.

That should be balanced with concerns over complexity and transparency.
That's why, in designing PAL, I decided that rather than pre-declaring a
strict ordering, candidates should only pre-declare a "my faction" subset
of their party, and then an ordering over other parties.

This would leave the possibility of a proportionality/majoritarian tradeoff
within a given party. I think such tradeoffs should probably be resolved in
the majoritarian direction; since the "disadvantaged" voters from a
proportionality standpoint would still be getting fair representation at
the party level, and only have grounds for complaint at the faction level.

Obviously, this doesn't resolve cases like the pizza/fry-up example,
because you can't delegate to food items. For those cases, I think that the
sequential answer is good enough, though I understand why it's unsatisfying.

2014-10-01 16:47 GMT-04:00 Toby Pereira <tdp201b at yahoo.co.uk>:

> There are arguably situations where proportionality is desirable but not
> at the cost of overall support. I gave this example:
>
> 10 voters: A, B
> 10 voters: A, C
>
> With two to elect, I would argue that BC is the most proportional.
> However, imagine a group of people are deciding what to have for dinner on
> various days. They only have enough to have each particular meal once. For
> simplicity, Let's say there's 20 people and they have to decide for two
> days, and they vote approval style on the meals they like.
>
> 10 voters: pizza, curry
> 10 voters: pizza, fry-up
>
> This is effectively exactly the same vote as the other example.
> Curry/fry-up might be more "proportional" but it seems absurd not to have
> pizza on one of the days. Nothing is gained by preventing the other group
> from getting more enjoyment at no cost to yourself.
>
> So the question is - what is the best election method in cases such as
> this? I've struggled with this for a while because it requires a
> non-arbitrary trade-off between proportionality and positive support. I
> think my system of proportionality used sequentially would generally give
> good results, but it's a bit of a cop out and basically hides from the
> problem. There should be a reasonable non-sequential solution.
>
> Forrest Simmons's PAV would work reasonably well here (although I would
> argue with Sainte-Laguë rather than D'Hondt divisors), but it still fails
> independence of commonly rated candidates, and I don't know how to fix it.
>
>
>    *From:* Toby Pereira <tdp201b at yahoo.co.uk>
> *To:* Andy Jennings <elections at jenningsstory.com>; "
> election-methods at electorama.com" <election-methods at electorama.com>
> *Sent:* Monday, 29 September 2014, 13:42
>
> *Subject:* Re: [EM] General PR question (from Andy Jennings in 2011)
>
> One problem with saying that candidates must be elected non-sequentially
> is that it can (depending on how you measure proportionality) lead to
> monotonicity and Pareto violations. If there are two to elect with approval
> voting:
>
> 10 voters: A, B
> 10 voters: A, C
>
> I would argue that the most proportional result is BC even though everyone
> has voted for A. (Monroe would be indifferent between the three possible
> results, however.) Sequential electing is likely to lead to less failures
> of monotonicity, and perhaps less prone to strategic voting as a result.
>
> But in any case, sequential electing doesn't need to be billed as a system
> that gives better results (regardless of whether one thinks it does). It
> could simply be stated (probably truthfully in many cases) that it's
> unfeasible to check the proportionality of every possible set of
> candidates, and that close-to-optimal results would still be achievable
> with sequential electing. I don't have any data for that last statement,
> but most elections wouldn't be like the contrived examples we've come up
> with, and I'd be surprised if results ended up being massively different.
>
> Toby
>
>    *From:* Toby Pereira <tdp201b at yahoo.co.uk>
> *To:* Andy Jennings <elections at jenningsstory.com>; "
> election-methods at electorama.com" <election-methods at electorama.com>
> *Sent:* Monday, 29 September 2014, 0:35
> *Subject:* Re: [EM] General PR question (from Andy Jennings in 2011)
>
> Thank you for your responses Kristofer and Andy.
>
> The problem I have with the Monroe metric is that because it ignores how
> much you like or dislike the candidates that aren't the one it assigns to
> you, it can end up with lopsided (I would argue unproportional) results.
> When several candidates are elected in a proportional election, I don't
> think saying that each voter has exactly one representative is the best way
> to look at it. If I vote for several candidates who are elected, then I
> would feel that I have representation from all of them and would be in a
> better position than someone who has voted for just one elected candidate,
> but the Monroe metric would just see us both as catered for and leave it at
> that.
>
> In Andy's original example (see bottom), Monroe would consider ABC equally
> proportional to CDE, but clearly under ABC some voters are getting a better
> deal, whereas CDE is perfectly proportional (although with less support
> overall). That's why I came up with the metric I did for measuring
> proportionality, which looks at how you rate every elected candidate.
>
> With an approval ballot, if someone has voted for a particular elected
> candidate, then their representation from that candidate is 1/n where n
> people in total have voted for the candidate, and 0 if they haven't voted
> for them. A voter's total level of representation is the sum of their
> representation from each candidate. For v voters and c elected candidates
> in total, the mean representation for each voter is c/v (assuming that each
> elected candidate has at least one vote). Full proportionality is achieved
> if every voter has representation of c/v. The proportionality measure of a
> set of candidates is the average squared deviation from c/v for the voters'
> total level of representation (lower deviation being better). There's also
> a score voting version.
>
> If we look at the following approval election with two to elect:
>
> 10 voters: A, B, C
> 10 voters: A, B, D
>
> Monroe would be indifferent between any set of two candidates, even if it
> favours one faction over the other. My metric would rate AB and CD as the
> most proportional.
>
> Toby
>
>
>
>  *From:* Andy Jennings <elections at jenningsstory.com>
> *To:* "election-methods at electorama.com" <election-methods at electorama.com>
> *Sent:* Sunday, 28 September 2014, 17:48
> *Subject:* Re: [EM] General PR question (from Andy Jennings in 2011)
>
> 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
>
>
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