Allocated score (STAR-PR) centrist clones concern
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@toby-pereira Indeed, the source of the issue is going by total score. I emphasize Allocated Score (STAR-PR) because I'm concerned about proposals that people are really promoting rather than just any sort of potential system with this issue.
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@wolftune My understanding, correct me if I'm misremembering, is that a quota rule for cardinal methods like this is ensured if voters bullet vote, Party List style, but not necessarily if they don't. This seems like an edge case example of that, and it does seem like an edge case, but it raises good questions. (That I'm planning to post in a dedicated thread soon, when I have time to engage with the replies.) Namely, the definition of proportionality used for ordinal methods is pretty crude for describing Cardinal or Condorcet PR.
Cardinal PR (unlike Ordinal) can allow voters and factions to coalition naturally (even if the candidates or parties don't) by addressing vote-splitting, and they also combat the notorious PR polarization stagnation that academics warn about, but they can't also always fend off against the mythical homogenized centrist who everyone agrees is meh.
This is an example of why I like STAR more than Score, and we haven't fully applied those principles to PR.. yet. I still think a hybrid approach is the key to unlocking that next level.
Our STAR-PR committee looked at a few options for selection, including highest score (simplest) and Monroe (which I think would address this.) Highest score won out, but realistically the two were pretty well dead tied.
In any case, I think that Clones are a much bigger problem in hypothetical math scenarios than they ever will be in real life campaigns, and if a faction can really pull off running 2 or 3 clones that all break through and win over voters then that's frankly impressive. The reality is that if voter behavior doesn't do them in, limitations in campaign funding and volunteer power likely will.
I'd still take STAR-PR edge cases over STV edge cases, but I won't claim it's perfect and that nobody will ever come up with something even better. This is still the cutting edge of voting theory.
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There are a few methods that would address the problem, partly or fully.
Sara mentioned Sequential Monroe. In this method instead of looking at total score, you look at the Hare quota of ballots that gives the highest total score for each candidate. Because the G candidates have their score spread across all the voters, their score from a single Hare quota isn't very high.
Threshold Equal Approval starts off with five stars counting as an approval and will elect candidates that reach a quota of votes, and then only considers lower numbers of stars when no candidates reach the quota with five, four, three and so on.
Using the KP-transformation on a set of ballots to convert scores to approvals (and then using one of various approval methods) would mean that while a G candidate would still be elected first, the reweighting would be more severe on the fifth of a voter's ballot that approved G, so non-G candidates would still subsequently be elected.
COWPEA Lottery using scores as layers of approval is non-deterministic, but when a ballot is picked, the candidate given the top score on that ballot is looked at in preference to one with a lower score so the problem of score total would not apply.
Of these I think Threshold Equal Approval is the most fragile. If you add a few "irrelevant" ballots that only give scores to some other candidates not realistically in the running to win seats, then the A to F candidates suddenly don't have a quota of votes any more, causing the election of the G candidates.
Using quotas generally causes problems with irrelevant ballots. Also as it's possible for any number of candidates to have a quota of votes, the exact quota can seem arbitrary, and this is more the case with score voting than it is with ranked voting.
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@sarawolk said in Allocated score (STAR-PR) centrist clones concern:
In any case, I think that Clones are a much bigger problem in hypothetical math scenarios than they ever will be in real life campaigns, and if a faction can really pull off running 2 or 3 clones that all break through and win over voters then that's frankly impressive. The reality is that if voter behavior doesn't do them in, limitations in campaign funding and volunteer power likely will.
I'm not sure I really see this as a problem of clones specifically. If parties exist, then it's fairly normal for parties to field several candidates in a multi-winner election.
But I do think the particular voting behaviour in the example election is a bit "edge case", although it's still best to avoid vulnerability to it.
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I agree that this is an accurate description of how Allocated Score (and many other proportional Score-based methods) can work. However, I consider it an advantage of these methods rather than a problem.
Example votes for two-seat election:
10 votes: A5 C3 C3 D1 (two interchangeable C candidates)
10 votes: B5 C3 C3 D1
So, this is okay centrists Cs (times two candidates), split electorate in liking A or B (and opposing the other), and D thrown in to show that this could be realistic if D were a lesser-evil worse than C for everyone.What is better: electing two Cs, or electing A and B? While I lean toward the former for depolarization reasons, there's another argument that seems more powerful: The voters have indicated that the Cs are preferable. If a voter's main desire is to have at least one representative who shares her values, that voter is best off being very stingy in giving out high scores; giving C three stars doesn't make sense. Therefore, we should expect such a voter to not vote like this. However, if a voter wants the average winner to be as good as possible, but don't consider especially important to have a single representative she likes a lot, giving C three stars makes perfect sense.
A world in which the Cs win by getting three stars from everyone is a world in which everyone is happy with this. Broadly speaking, whether it's better to elect a diverse collection of extremists or a less diverse collection of moderates is a difficult question. Allocated Score (unlike STV, Sequential Monroe, and Block STAR) lets voters answer it rather than embedding a particular answer to it into the tabulation algorithm.
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@marcus-ogren while I recognize that there are pros and cons here, the core issue is that elect-all-acceptable-centrists is not so reasonable to call "proportional representation".
I think the weighting toward consensus candidates and PR are working toward different approaches to representation. I'm okay with saying that Allocated Score is a balance between consensus and PR. That seems more fair than saying it is PR. At least given the examples.
I'm concerned with fair and transparent presentation of what a voting method is. I think that concern is independent from discussion about how good a method is for various goals.
The extreme case of lots of clones that only got 1-star does seem still to be essentially a failure for Allocated Score, but I don't see it as realistic.
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To simplify things a bit, I'm going to use scores out of 1. We have 3 parties - A, B and C - and the following ballots:
100: A=1, B=0, C=x
100: A=0, B=1, C=xThe question to you all is: At what value of x are AB and CC equally good?
If we use PAV with the KP-transformation and the usual D'Hondt divisors, then the answer appears to be 0.67 (well 2/3 to be precise). If you use the Sainte-Laguë divisors, the answer appears to be 0.75.
I also looked at COWPEA and COWPEA Lottery also with the KP-transformation, and the point where the weights or probabilities are balanced (A and B at 0.25 each and C at 0.5) is when x is the square root of 0.5, so 0.707.
These numbers seem to me to be in the right ballpark. I think any method that elects CC for any x over 0.5 is doing PR wrong. (Late edit - "any" as in "all". A method is doing PR wrong if it always elects CC when x is over 0.5, even if it's over by a tiny amount, like 0.501).
A maximally polarising method would obviously require x to be 1 before electing CC. This might seem also wrong, but I suspect that this sort of method is likely to be less susceptible to strategic voting. COWPEA using scores as layers of approval would elect A and B with equal weight and C with no weight.
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At what value of x are AB and CC equally good?
Yes, but another question is: at what value of x can we be comfortable calling CC "proportional"? Anything less than x=1?
I think any method that elects CC for any x over 0.5 is doing PR wrong
Do you mean under 0.5?
Anyway, I do think again there's two issues: what is fair to call "proportional" and what method is good for representation, and those do not need to have the same answer.
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@wolftune said in Allocated score (STAR-PR) centrist clones concern:
Do you mean under 0.5?
Anyway, I do think again there's two issues: what is fair to call "proportional" and what method is good for representation, and those do not need to have the same answer.I meant over 0.5, but I meant "any" as in "all". E.g. if x=0.51 and CC get elected, I'd say it's not a very good result.
But anyway, I'd say if CC gets elected for x<0.5, then it's a bad result whether it's PR you want or not.
But as for your question of what can be called proportional, all voters will be equally represented under AB or CC regardless of x, so arguably it's proportional regardless of x. But it might be an idea to try and come up with some PR criteria for score voting. There's quite a lot around for approval voting.
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Okay, so your "over 0.5" idea for "wrong" is contrasted with <0.5 being worse than "wrong" (in your words, "bad" is worse than "wrong" it seems). This is a confusing way to put things.
As for terminology, yes, there's a question of what it means to be proportional. I don't think "everyone is equally represented" is enough. That would mean electing everyone's least favorite is still proportional. I think proportional needs to mean something like if there's a clear block of voters enough to have a quota of a seat, that block gets to elect whoever they prefer.
IMO, Proportional Representation means that whatever blocks happen to emerge in the stats are used to elect representatives as a contrast with geographically-drawn seats. PR should give the same results as if we could identify the voting blocks and designate them as we do with geographic districts for single seats. Or at least it is in this direction.
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@wolftune said in Allocated score (STAR-PR) centrist clones concern:
Okay, so your "over 0.5" idea for "wrong" is contrasted with <0.5 being worse than "wrong" (in your words, "bad" is worse than "wrong" it seems). This is a confusing way to put things.
Haha - they were separate posts with informal language though!
As for terminology, yes, there's a question of what it means to be proportional. I don't think "everyone is equally represented" is enough. That would mean electing everyone's least favorite is still proportional. I think proportional needs to mean something like if there's a clear block of voters enough to have a quota of a seat, that block gets to elect whoever they prefer.
Arguably that means you would have to elect AB whenever C gets less than the max score. Unless you count all the voters as a single block that prefer CC to AB. But then you get the debate over what counts as preferring when you have two or more candidates. Is it correct to just add up your scores of AB and CC to determine which you prefer?
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The above examples illustrate two issues. Keep in mind that the goal of some supporters of cardinal PR is not to satisfy a strong form of Proportionality for Solid Coalitions (PSC); but to elect one moderate centrist, and a representative for each solid coalition with a quota of supporters. This should often be an achievable goal as the number of candidates entitled to a seat under PSC is usually less than the number of seats to be filled. But by starting off with awarding a seat to the overall score winner electing a moderate is prioritized over PSC.
A second issue, seen in the second example, is that a candidate receiving only low scores can beat a candidate that is clearly entitled to a seat under PSC. This is due to a downward shift in what constitutes a neutral score as the number of seats increases. What I mean by neutral score is the minimum score that a candidate must exceed to be entitled to a seat if everyone bullet votes. This would be the corresponding score to the vote exceeded in the Droop Quota. For 0 to 5 score this would be 2.5 for a single winner election, 1 ⅔ for two winners, 1.25 for three, 1 for four, etc. For a six seat election in the above example a score of 1 isn't a low score of disapproval it's a modest score of approval.
What could be done about these issues?
1: Educate voters on strategy.
Allocated Score will achieve a proportional outcome, if all voters engage in bullet voting. Rating all candidates that the voter doesn't approve of with a score of zero is essential. The ballot options could be changed from (0, 1, 2, 3, 4, 5) to (0, 0, 0, 3, 4, 5) to stress the point. The description of STAR-PR doesn't have the top-two runoff step of STAR so there's no incentive to use intermediate scores as it is.2: Award seats to candidates that qualify for seats based on their top scores alone first. For example: count only the ratings of 5 cast then seat the candidates that have a score of 5 times the Droop quota, following a procedure similar to the first round of PR-STV. Afterwards this would switch to Allocated Score instead of the elimination round. This should prioritize proportionality, while preserving some of the attributes of Allocated Score. Intermediary rounds could be included, counting scores of four and five and a round counting scores of three, and five in a Bucklin like manner. This would ensure that even parties that split their vote between multiple candidates would get priority over an overall score winner. There would be a confirmation process to handle surplus votes and make sure votes aren't counted twice, that would seat individual candidates sequentially, but this would fundamentally change the process from a series of single winner elections to rounds of multi-winner elections. Multiple candidates could meet the Droop quota to win the round, but the ballot deweighting process could result in not all winners being confirmed.
3: Transform the scores to adjust for the shift in the neutral point.
By adjusting the scores before they are tallied voters can score on the more familiar scale used for single winner elections and have them corrected for the distortion caused by having multiple winners.
Example: four winner election 0 to 5 ballot. The neutral score would be 1. The balance test for the equal vote criteria also changes for multi-winner. Instead of the familiar one vote canceling one vote, four votes in opposition are necessary to cancel each vote in favor(see balance test below). A score of zero remains zero, 1 becomes ⅓, 2 becomes ⅔, 3 becomes 2 ⅔, 4 becomes 3 ⅔, and 5 remains 5. Consider if four voters give a candidate a zero and one a five. Total score will be 5 and the average score will be 1. If four give a 1 and one a 4. Total score would be 4 * ⅓ + 3 ⅔ = 5 and an average of 1. If four give a score of 2 and one a 3. Total score would be 4 * ⅔ + 2 ⅓ = 5 and an average of 1. With these adjustments in place the potential harm to a preferred candidate of giving a lesser candidate an intermediate score will be on par with single winner systems.Balance Test for Score (Based on Droop Quota rather than majority, to be applicable to any number of winners) : There shall be a set of ballots of size one plus the number of seats to be filled, such that if one of the ballots is cast any way possible the other ballots can be cast to cancel out the vote leaving the average scores for each candidate unchanged. The ballots shall be scored such that, scores of approval on one of the ballots shall be countered by the opposing score of disapproval on the other ballots, and a score of disapproval shall be countered by the opposing score of approval on one of the other ballots and the score of disapproval shall be shared with the remaining ballots.
4:Only count a fraction of the votes for each candidate.
Sequential Monroe avoids the issues by only counting the top Hare quota of ballots for each candidate. With the vast majority of low scores left uncounted, the results are largely unaffected by the distortion of scores in multi-winner elections. However, with little more than the candidates core supporters contributing, the results will lean less moderate until the final round.What if STAR-PR was not a misleading name; and included an automatic top-two runoff based on all ballot preferences before each selection was finalized?
With the current version of Allocated Score if all voters make use of intermediate scores it will destroy any semblance of proportionality. If all voters resort to min-max voting to protect proportionality the runoff will be irrelevant. More likely voters most interested in getting a particular candidate or party elected or dead set against a particular candidate, will resort to min-max voting while voters torn between objectives will make use of the full range of scores. Vote splitting among min-max voters could result in parties failing to get a seat, and the voters making full use of all scores will have an outsized influence in getting their lesser evils elected.
Score based PR systems have the potential to provide a balance between different interests. With some of the above changes in place, parties with a quota of supporters should get one of their top two candidates elected, even if they split their votes between multiple candidates, but could end up with the one preferred by voters overall, rather than the one preferred by party members.
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@k-shenefiel said in Allocated score (STAR-PR) centrist clones concern:
For a six seat election in the above example a score of 1 isn't a low score of disapproval it's a modest score of approval.
I object to the entire premise that any of these voting systems say anything about approval/disapproval. I want "approval voting" changed to "choose-any voting". Except for a system like 3-2-1 that asks about approval explicitly, all these systems of rating and ranking are relative. Voters might approve of all or none of the candidates. We can only discuss "preference".
The idea of encouraging bullet voting and not using low scores seems to me to show the whole system to be flawed rather than be a solution. It's a bad workaround at best.
The description of STAR-PR doesn't have the top-two runoff step of STAR so there's no incentive to use intermediate scores as it is.
That's a problem IMO. At the very least, this undermines the credibility of the label "STAR-PR".
Award seats to candidates that qualify for seats based on their top scores alone first. … Afterwards this would switch to Allocated Score instead of the elimination round. … [the rest of your suggestion 2]
That seems (by first impression) to be a potential real solution.
Your suggestion 3 might make mathematical sense, but I think it's too complex for public-perception to go well.
My inclination is that the check-top-scores-first and award seats by quota and then do Allocated Score… that seems optimal. It brings in a bit of later-no-harm. It makes it safe to express preferences for non-first-choice candidates. Without this top-scores-checked-first step, any block large enough to get a seat can force their favorite by bullet-voting.
The whole point of STAR vs plain score is to give the majority their wish no matter what. STAR brings a weak sort of later-no-harm which disrupts the pressure for majority to bullet-vote in plain score. Effectively, "don't worry about bullet-voting to force your favorite, we'll give it to you no matter what if you have a true majority, so you can express preferences and not worry about strategizing". And while STAR is not strictly Condorcet, it's effective enough to achieve this reduction of bullet-vote pressure.
STAR-PR needs to keep this core point. We don't want voting blocks to feel regret that they could have forced a preferred outcome by bullet-voting. Simply giving seats to any blocks with enough 5-star votes seems the answer to me.
I don't think this is inherently obviously good, just as I don't think majority-winners in single-seat elections are necessarily good (compared to consensus candidates with wider support). However, I support STAR in its majoritarian emphasis because that encourages honest preference expression. STAR-PR needs to follow the same pattern, to achieve the same overall effect.
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In the context of political parties, where a voter can only affiliate with one party and vote for one party, it's fairly easy to define proportional as you say, @wolftune, that "if there's a clear block of voters enough to have a quota of a seat, that block gets to elect whoever they prefer."
This is a simple and transparent result, which has value, but it's not necessarily the best result, because we know that voters are not factional hardliners that agree with their parties only and disagree with everyone else 100% all the time.
For a better example we can take 6 parties with candidates; Red, Orange, Yellow, Green, Blue, Purple. Blue voters would give Blue 5 stars, but also like cool colors in general. Orange voters love Orange but also like warm colors like Yellow and Red. Red voters also like Orange but also like Purple. These parties supporters also tend to like Brown, though it's not a color on the color wheel and thus not a real party in Colorland. Lets also say that Red and Purple voters actually slightly prefer Ultraviolet and Infrared, though those colors make no sense to most voters.
In a quota rule PR election where there are 6 winners is it fair if Brown, who is liked by all and highest scoring overall never wins? When parties overlap and Venn Diagram, who is to say which is the "real" faction? Is a winner set the most representative if Ultraviolet and Infrared win, even though they were disliked by every other faction, while Red and Purple were also loved by their supporters but were also well liked by their peers?
My point is that real voters have nuanced preferences, so an expressive 5 star PR method can and should take the strength of those preferences into account. (Allocated Score does this in determining which voters get allocated to a given winner. Adding runoffs to the winner selection, or doing Monroe Selection would do this even more, with some added complexity.)
As said above, the definition of PR that we use for List PR or STV, if applied to a score ballot, would say that if a quota bullet votes then they will win a seat. That works for ordinal methods, but it specifically selects for polarizing winner sets and could care less about electing candidates who represent more voters when possible. This also might allocate voters and consider them represented by a candidate who they ranked 5th and dislike, or who they only voted for as a lesser evil.
We could also aim for a stricter proportionality criteria that does recognize and reward consensus candidates, particularly if they are alternatives that are representative for factions that slightly prefer a highly polarizing or antagonistic option.
A reasonable definition of high spectrum PR might be that "if there's a clear block of voters enough to have a quota of a seat, that block gets to elect the most widely supported of the candidates they like." Another way to think about that is that "that block gets to elect the least polarizing of the candidates they like." (Q: what score is a candidate who is "liked" by a voter? 4? 3?)
This guarantees the most representative proportional winner set possible and likely would find the most effective but still diverse winner set. It doesn't guarantee that everyone gets their favorite. It does get each faction an advocate who is likely to be more effective with the larger elected body, however.
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@sarawolk I think 100% of your arguments apply to plain score voting as being preferred to STAR. If everyone is honest, plain score is better than STAR for all the reasons you express. I agree with the values and the balance you describe. However, I think all the justifications for STAR over plain score also apply to adding the first step of block-allocation based on 5-star counts over plain Allocated Score.
Do you see my point about how the runoff in STAR is a balancing factor and discouragement of strategizing in the same way as the adjustment to STAR-PR that came up here?
We don't need to discuss whether brown should win, because the argument that brown should win is also an argument for brown getting elected in single-seat elections even when the majority has a more polarizing favorite. So, again, if you accept the reasons for STAR over plain score, then all the same reasons need to be dealt with in determining the best STAR-PR instead of going with a score-PR that doesn't address what STAR was invented to address.
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@wolftune
I noticed something similar with reweighted range voting when I tested it years ago. I had simulations with a "gray party" that got the same medium score from every voter, alongside colored parties that got the maximum score from their party voters and the minimum score from everybody else. I noticed that as I varied the score for the gray party, it would suddenly "explode" from having no seats to having all the seats.I devised a fix, which I later learned was the Kotze-Pereira Transform.
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@isocratia Yes, as I mentioned above, the KP-transformation "protects" the high scoring part of someone's vote from being deweighted when a candidate they gave a lower score to gets elected. Also it simplifies the process in that you just have to use an approval-based PR method rather than having to work out what to do with the scores.
Also, rather than electing sequentially starting with the highest scoring candidate, you can potentially avoid the favourite-of-nobody candidates from getting elected by using other algorithms (like e.g. MaxSwapPAV, mentioned in this thread) that get closer to the "optimum" set without necessarily having to try out every combination of candidates.
One problem with the methods that elect a candidate and then remove a quota of votes is that they often don't actually have a way of measuring a set of candidates. They use a process rather than a measure and therefore can't decide which set of candidates is better when given two in isolation.
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I don't like the idea of getting rid of "favorite of nobody" as an end in itself. The goal I'm describing is to elect the clear favorite of a quota-sized block. There's no goal of stopping the election of consensus non-favorite candidates, and I would oppose making design choices based on that goal.
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@wolftune Sure, but I was referring specifically to the favourite-of-nobody candidates in this scenario and the fact that they could all get elected.
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@toby-pereira that doesn't change my point. Blocking someone's election just because they are nobody's favorite is not a goal I support at all. Being the top favorite of anyone is not the point in itself. A candidate that is nobody's favorite and that everyone really still highly approves of is likely a good candidate to elect as long as any quota-sized blocks of voters get their favorites.
