Posts made by Lime
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RE: Optimal cardinal proportional representation
@toby-pereira said in Optimal cardinal proportional representation:
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.
Right. I suppose that's what I meant by disliking the idea of making an underrepresented group worse-off just to make the overrepresented one even worse-off.
@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.
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RE: 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.
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RE: Optimal cardinal proportional representation
@toby-pereira said in Optimal cardinal proportional representation:
99: AC
51: AD
99: BC
51: BD
1: C
1: DI'm not really seeing what the problem with electing C & D here is supposed to be It seems like a gain for only 2 voters, so I might be missing something, but I'm not seeing what would make that bad.
@toby-pereira said in Optimal cardinal proportional representation:
Right, but it's debatable whether a voter's utility is purely determined by approved candidates elected.
I'll briefly set aside the "approved" part and focus on score voting more broadly (since voters rarely have dichotomous preferences).
I'm not sure why the distribution of like this would particularly matter. The way I'd model is that each candidate is assigned a utility equal to the (importance-weighted) probability that they'll break a tied vote in my favor. I'm not sure why it would be better for me to have a legislator who casts votes that represent my interests less often, or why it would be better for me to have a legislator supported by fewer voters.
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RE: What Multiwinner Method To Push For Local Boards?
@jack-waugh said in What Multiwinner Method To Push For Local Boards?:
Is monotonicity equally so important for the multiwinner context as it is in the single-winner context?
Yes—it makes no sense that, if I give a candidate an extra star, we respond by deciding the candidate is "too good to win" now. It also makes honest voting impossible (because ranking A over B is no longer the same as giving A more support, so you can't give A the correct level of support without knowing everyone else's exact ballot).
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RE: Approval Voting as a Workable Compromise
@gregw said in Approval Voting as a Workable Compromise:
@lime said in Approval Voting as a Workable Compromise:
I basically agree, but I think we should probably try to squeeze out at least a "Combined approval voting" (-1, 0, 1) option to make Burr candidates a bit less harmful.
Would -1, 0, 1 lose the Majority Criterion? If so would that make much difference in compliance with state constitutions?
I don't really think of Woodall's majority-favorite property as being applicable to cardinal systems, since it's based on comparisons of candidates. I also doubt it's written into any state constitutions.
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RE: Optimal cardinal proportional representation
@toby-pereira said in Optimal cardinal proportional representation:
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?
General concern about transformations. My worry is transforming score ballots to approval ballots discards information about which voter gave which ratings, so I'm not sure it will preserve the stable winner set properties of PAV.
@toby-pereira said in Optimal cardinal proportional representation:
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.
Oh, definitely, harmonic voting is great! (Although it needs a less intimidating name.)
@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.
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RE: Optimal cardinal proportional representation
@toby-pereira said in Optimal cardinal proportional representation:
@lime said
I'm not 100% sure about this myself—won't any transformation of the ballots discard some information? I'm not sure if applying the KP transform to range retains the core-approximation properties that make PAV so appealing (i.e. 2-approximation of the core, and satisfying core with enough similar candidates).
Can you remind me exactly what these mean?
And I'm glad you liked the post!
K-approximation means K Hare quotas would prefer another committee (instead of just 1).
And if every candidate has infinitely many clones, you can guarantee the method will choose from the core (see here).
I'm wondering if some method can keep these properties in the score voting case.
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RE: Optimal cardinal proportional representation
Thank you so much for this post! It's great
@toby-pereira said in Optimal cardinal proportional representation:
There are several possible methods of converting an approval method to a score method, but the KP-transformation keeps the Pareto dominance relations between candidates and allows the methods to pass the multiplicative and additive versions of scale invariance, so my current thinking is that this is the optimal score conversion.
I'm not 100% sure about this myself—won't any transformation of the ballots discard some information? I'm not sure if applying the KP transform to range retains the core-approximation properties that make PAV so appealing (i.e. 2-approximation of the core, and satisfying core with enough similar candidates).
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RE: What Multiwinner Method To Push For Local Boards?
Agreed with Toby, PAV is solid.
OTOH, I'll point out if they're using STV already that STV is by far the most complicated proportional representation algorithm out there, if they actually understand it and haven't just tricked themselves into thinking they understand it.
To see whether they understand it, ask if they use Warren, Meek, or Wright's method. (If they say Gregory's method, you can hijack the committee by building a coalition of strategic voters. )
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RE: Approval Voting as a Workable Compromise
@jack-waugh said in Approval Voting as a Workable Compromise:
In that case, I hope the default is -1.
Agreed
@cfrank said in Approval Voting as a Workable Compromise:
@lime I think unfortunately that changing the voting system at all is squeezing a lot. It might not do well to try something more complex to start. Even minor peculiarities can be difficult to overcome in the face of the political status quo.
I actually mention this mostly for public approval reasons; empirically, people tend to prefer scales with more options unless they're badly-presented (e.g. people get annoyed if they're given 20 separate bubbles and forced to look through them to find the one they prefer. People also prefer buttons to sliders).
More categories doesn't mean a system is more complicated, though. (If it did, people wouldn't be able to comprehend numbers bigger than 10!)
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RE: Approval Voting as a Workable Compromise
I basically agree, but I think we should probably try to squeeze out at least a "Combined approval voting" (-1, 0, 1) option to make Burr candidates a bit less harmful.
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RE: Simple anti-chicken modifications to score
@sarawolk said in Simple anti-chicken modifications to score:
More likely they are linked to the RCV lobby's campaign to sabotage STAR Voting for Eugene, Measure 20-349, which people start voting on this week. (see pgs 9-26)
I promise you that nobody in the election-methods mailing list is particularly positive on IRV.
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RE: Smith // Score
@jack-waugh said in Smith // Score:
@lime, yeah, you could. There is a little bit more risk that the workers in one precinct get tired and keep everyone waiting.
Maybe a useful policy would say conduct the election with computers and the Internet, let the result go into effect, then verify everything by hand. It might be easier to check a proposed outcome than to compute it from scratch.
The Essential set almost-always has 3 candidates, so the method can be made 3rd-order summable except when the election gets ridiculously close.
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RE: What does STAR Voting do when 2nd place is tied?
@cfrank said in What does STAR Voting do when 2nd place is tied?:
If we were being engineers about choosing a high quality candidate to win the election, we could even compute the distribution of scores, take the candidates whose scores exceed some elbow point, and find the Condorcet winner among those candidates with the top scoring candidate as the backup if no Condorcet winner exists. That’s basically a generalization of STAR with a dynamic front-runner selection method.
What about a 50% cutoff? That would also dramatically reduce the incentive for turkey-raising—no point in pushing up a bad candidate to help them make the runoff, since now that doesn't eliminate another contender.
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RE: Simple anti-chicken modifications to score
I don't think that reply addressed any of my concerns. I'm worried about STAR's potential for turkey-raising. It's completely possible that STAR is great at avoiding favorite-betrayal, reduces the rate of LNH violations, and does lots of other good things, but is still vulnerable to turkey-raising (later-no-help violations).
@sarawolk said in Simple anti-chicken modifications to score:
When will we stop ignoring the forest for the trees and recognize that both have important pieces of the puzzle and that a hybrid approach like STAR makes more sense than telling people that their concerns are invalid.
Smith//Score is a hybrid approach just like STAR, by the way, and I offered several other hybrid approaches that could improve on STAR in my post.
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Simple anti-chicken modifications to score
STAR has been extremely divisive on the EM-list. Lots of people have some very harsh things to say about it. This wasn't just the usual jockeying from perfectionists, and I think I've come around to the other EM-listers on this. The opposition to STAR seems to be common to both cardinal and Condorcet supporters. Everyone seems to agree either Smith//Score or plain Score would be better than STAR.
Most of these criticisms boil down to STAR managing to break every criterion in the book. Adding a runoff destroys favorite betrayal, later-no-help, participation, . It does this in to try and prevent a strategic voting dilemma that:
- Has never been observed in an actual election (and is even named after an election where it notably didn't happen),
- Is probably rare,
- Would incentivize party elites to clear the field in the first place to avoid this, and
- Seems almost impossible to accomplish without any other candidate noticing and retaliating.
Personally, I was supportive of STAR until @SaraWolk's comment about the possibility of candidates not running in cloned pairs made me think through its potential turkey-raising problems. Burt Monroe has argued (very convincingly, in my opinion) that any system that fails turkey-raising will eventually be repealed. It doesn't matter that the expected value of a strategy is negative: empirically, parties push turkey-raising strategies even in systems where risks of blowback are extremely strong, e.g. the Democratic party's support for extreme Republican nominees in primaries, or their refusal to put up an alternative to Gavin Newsom in the recall.
It's true that criteria are worst-case guarantees, and what we care about is the average case. But for something as complex as a political system, we don't know the average case. Simulations are unrealistic and we've never run elections with STAR. All we know is in the worst case, STAR might do very badly.
If nothing else, these dramatic criteria failures severely limit the possibility of receiving endorsements from economists and social choice theorists. Few, if any, voting theorists who hear about STAR's criteria failures are eager to endorse it.
This leads me to suggest the following alternatives to STAR in its current form, which attempt to eliminate the small (but potentially disastrous) risk of turkey-raising.
- Provide a small reward to ballots that rate multiple candidates above 0. D2.1 does this by granting a single antiplurality vote to voters who give multiple approvals. A full antiplurality vote sounds too strong, but maybe something else would improve on it, e.g. down-weighting bullet votes to give only 4 stars to the favorite instead of 5?
- Using trimmed-means instead of the average rating.
- Smith//Score and Score DSV both received strong praise on the EM list as alternatives to STAR, especially if combined with a tied-at-the-top rule.
- Limit STAR runoffs to allied candidates (described elsewhere).
- Limit STAR runoffs to candidates who have strong mutual support (i.e. actual chickens or clones). For example, the runoff could consist of the score winner, paired against the candidate whose score is most positively correlated with the score winner's (across ballots).
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RE: Smith // Score
@jack-waugh said in Smith // Score:
@lime, but on the other hand, rescaling is not practical, because it would require reexamining the ballots. The people need precinct-summable systems to maintain security against fraud.
Can be done in two passes. The first pass identifies the Smith set, and then a second pass identifies the Score winner.