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@lime said in Optimal cardinal proportional representation:

@toby-pereira said in Optimal cardinal proportional representation:

COWPEA isn't really a voting method as such though (it's more of a theoretical thing), but COWPEA Lottery could be used as a method. Optimal PAV Lottery would be computationally too hard to be a method I think, although theoretically interesting.

That's surprising. I know there are local councils and similar that use weighted votes, but I can't imagine any legislature or council (especially a small one) using a random method.

Which bit is surprising? I'm only saying that COWPEA Lottery could be used (i.e. there would be no computational problems) - not that it's likely to be. In any case, from my point of view, I don't have a problem with non-deterministic methods in some situations.

@lime said in What Multiwinner Method To Push For Local Boards?:

@toby-pereira said in What Multiwinner Method To Push For Local Boards?:

Well, SPAV is purely approval whereas SPAV + KP is scores, so which ends up being more proportional might depend on exactly how you define proportional and also how people vote in practice. There's always been the question with score voting of whether some voters will lose out by casting a more honest ballot but losing out strategically.

Thus my question in another thread, about whether Harmonic voting might lose the stable winner set properties of PAV. The stable winner set seems like it could provide some very strong strategy-resistance properties, similar to Condorcet in single-winner elections.

I don't think its strategy resistance is as strong as it would be with ranked ballots. With approval voting, you still have to decide whether to approve candidates you don't like as much because you think they've got a better chance of being elected.

Schulze STV uses ranked ballots and reduces to the Schulze Condorcet method in the single-winner case. It's probably more strategically robust than an approval-based method that satisfies core stability.

@lime In the example I gave, electing AB would mean that 300 of the 302 voters would have approved exactly one elected candidate, whereas electing CD would mean that all 302 would have approved exactly one elected candidate. So by that measure, CD would be better.

But - under AB, 150 people have approved A and 150 have approved B. Under CD, 199 have approved C and 103 have approved D. So CD is a disproportional result in that the 103 D voters wield a disproportionate amount of power in parliament. Or perhaps more relevantly, the D party has only about 1/3 of the support but half the power. AB would be more balanced in that respect. Methods that use a measure of proportionality rather than satisfaction (e.g. Phragmen) would tend to elect AB.

This doesn't matter in the purely optimal case, because PAV would elect CD but in the respective proportions. COWPEA would elect all four in varying proportions. If these were real-life votes, it would be likely that AB and CD focus on different issues. A and B are opposed on the issues that they focus on. C and D are opposed on the issues they focus on. By electing all four, COWPEA would be making sure that the issue space is better covered.

COWPEA isn't really a voting method as such though (it's more of a theoretical thing), but COWPEA Lottery could be used as a method. Optimal PAV Lottery would be computationally too hard to be a method I think, although theoretically interesting.

@gregw said in What Multiwinner Method To Push For Local Boards?:

@toby-pereira

I admit I am desperately seeking voting systems that are appealing and accurate. So I do appreciate the help I have received on this forum. When I first decided to advocate for better voting systems I had no idea how difficult the choices would be.

I think that voters will prefer Score ballots over Approval ballots, but I could be wrong. Has anyone done any polls on this?

Is there any reason to think SPAV would be more or less proportional than SPAV + KP?

Well, SPAV is purely approval whereas SPAV + KP is scores, so which ends up being more proportional might depend on exactly how you define proportional and also how people vote in practice. There's always been the question with score voting of whether some voters will lose out by casting a more honest ballot but losing out strategically.

@gregw said in What Multiwinner Method To Push For Local Boards?:

@toby-pereira said in What Multiwinner Method To Push For Local Boards?:

If you're using scores it's probably better to use a cleaner system like SPAV + KP or Phragmén + KP.

Thank you for your analysis of quotas and the suggestion of SPAV + KP.

Concerning SPAV and SPAV + KP:

Would SPAV with Jefferson give too much favor to large parties and/or tend towards block voting?
Would Webster give too much favor to small parties?
Would a Score election using SPAV + KP make any difference regarding the possibility of block voting and the use of Jefferson or Webster?

I would say that Webster gives objectively the most proportional result (wrongheaded arguments in favour of Huntington-Hill elsewhere on this forum notwithstanding) rather than favouring small parties. Jefferson does favour large parties, but it is more strategically robust. Large parties or factions can deliberately split up and force a Jefferson result under Webster voting if they can co-ordinate well enough.

@lime Who would you elect in the following election with 2 to elect:

150: AC
100: AD
140: BC
110: BD
1: C
1: D

Edit - I can give a more extreme example:

99: AC
51: AD
99: BC
51: BD
1: C
1: D

@gregw said in What Multiwinner Method To Push For Local Boards?:

@toby-pereira said in What Multiwinner Method To Push For Local Boards?:

If you're using scores it's probably better to use a cleaner system like SPAV + KP or Phragmén + KP.

By cleaner do you mean better criterion adherence or less complex?

Probably both. When Allocated Score was chosen to be the "STAR-PR" method, there were a few other options that worked in the same basic way. That is - they elect a candidate and then remove a quota of votes, and then go through the same process until the seats are filled.

But I would say that quota-removal is a very clunky way to go about PR. Quotas are essentially arbitrary, especially as later-elected candidates might not reach a full quota so get elected more "cheaply". I discussed the problem of quotas here as well. My conclusion was that essentially quota removal methods are just a poor man's Phragmén.

The other thing is that the difference between the methods that went up for consideration to become "STAR-PR" was all about how they dealt with scores. For approval voting, they were all essentially the same method. But scores are messy to deal with, and all these methods (including Allocated Score) had their own unsatisfactory and messy way of dealing with these scores. The KP-transformation simply cleans it up. It's a consistent way of dealing with scores that takes away the weird edge cases and discontinuities that the other methods threw up. And then you just use your base approval method once the scores have been converted to approvals. See my post here as well.

@lime said in Optimal cardinal proportional representation:

@toby-pereira said in Optimal cardinal proportional representation:

By the way, COWPEA fails the multiwinner Pareto criterion in the example I gave above, so might have core failings as well. Certainly in the IIB version of core (where you ignore voters who are indifferent between competing sets and just look at the proportion who favour each one of those who have a preference), it would fail. But I don't see this as a failing of COWPEA, just a different PR philosophy.

This is a much bigger hangup for me personally. If everyone agrees a different committee would be better, then leveling-down (making some people worse-off, just to make the outcome more equal/proportional) strikes me as wrong.

Right, but it's debatable whether a voter's utility is purely determined by approved candidates elected. A voter is better represented in parliament if they share their representative with fewer other voters. So in the example up the thread:

250: AC
250: AD
250: BC
250: BD
2: C
2: D

A and B are more attractive options to most voters.

@gregw said in What Multiwinner Method To Push For Local Boards?:

@jack-waugh said in What Multiwinner Method To Push For Local Boards?:

For a county board of supervisors, for example, what's a nice simple multiwinner system to suggest?

Would Allocated Score (STAR_PR) work well?

If you're using scores it's probably better to use a cleaner system like SPAV + KP or Phragmén + KP.

@lime OK, I'm not sure how the KP-transformation would affect these things. Do you specifically think it's likely to be any worse than any other transformation, or is it general concerns about any transformation that hasn't been demonstrated to pass these things?

In any case, I definitely think PAV + KP is better than RRV or SDV because of its scale invariance, and I don't see any particular advantages of these methods over it.

There is also the probabilistic transformation, which I see as inferior to KP as well. Someone might give scores of 9 and 1 (out of 10) to 2 candidates A and B respectively. KP would split the voter as follows:

0.1: -
0.8: A
0.1: AB

The probabilistic transformation would give:

0.09: -
0.81: A
0.09: AB
0.01: B

This wrecks both Pareto dominance and scale invariance.

By the way, COWPEA fails the multiwinner Pareto criterion in the example I gave above, so might have core failings as well. Certainly in the IIB version of core (where you ignore voters who are indifferent between competing sets and just look at the proportion who favour each one of those who have a preference), it would fail. But I don't see this as a failing of COWPEA, just a different PR philosophy.

By the way, since PAV with infinite clones passes core (which it doesn't with a limited number of candidates), I presume the optimal version probably is properly proportional (passes perfect representation). I might update my paper with this in at some point.

Also, in the optimal scenario, both Phragmén and Monroe would be unsuitable as contenders. Both would be indifferent between an infinite number of different candidate proportions. They are concerned only with perfect representation, and this is very easy to achieve in the optimal case with any proportions allowed, and they have nothing to say to distinguish between them. Monroe is also essentially the Hamilton version of Phragmén (which can be made D'Hondt or Sainte-Laguë), so essentially the same but with more IIB failures.