Would like to revive discussion to see if there are any new opinions on MES---particularly a variant I'm calling "threshold" MES.
To quickly recap how it works (and I'll just use 5 star ballots to explain, but hopefully it's obvious how to generalize)
- Treat a rating of 5 as approval, < 5 as disapproval. Is any candidate approved by at least a quota of ballot weight? Great, choose the one who can be elected at lowest uniform cost by her supporters, and then subtract that amount of voting power from those supporters.
- If there is no candidate with at least quota of ballot weight, then treat a rating of 4+ as approval.
- Etc. down to 1+ as approval
If no candidate even gets a rating of 1+ stars from a quota, then default to just pick the highest scoring candidate and exhausting all ballots scoring them > 0.
A nice property it has: for every rating 0-5, it satisfies Proportional Justified Representation given approvals being above/below that rating level.
@andy-dienes I like this system. Is there a clear disadvantage to regular MES? There is a pretty clear simplicity advantage.
Please correct me if either of the following is wrong
- The subtracted voting power is done as "scaling" to the rest of the ballot
- The threshold will always decrease as sub sequent winners are elected.
@keith-edmonds The disadvantage would be that it respects linear / additive utility much less; for example it will not necessarily choose the score winner (although in practice probably will) and the distribution of utility (again, assuming it is linearly additive over sets) is not as proportional as in regular MES.
Personally, I've actually lately started to become of the opinion that linear / additive utilities make very little sense in the context of electing a proportional legislature, so I don't really see this as a big loss, but some might.
It is still proportional just in a different way (and more so, in some ways). Let t-PJR be PJR at the "approval threshold" t. Regular MES can and does regularly fail t-PJR for t > 0. To see what the difference implies: say we have two candidates with 5 stars from a block of two full quotas of voters. Regular MES only demands that the block get at least 2 winners scored > 0. This variant demands they get at least 2 winners scored exactly 5.
Maybe a bigger disadvantage, however, is that the outcome is even more sensitive to quota size. Regular MES has a 'boundary' at getting a quota of >0, but is mostly smooth with respect to score above that. This variant has a 'boundary' to reach a quota at every single score level. I have no idea how big of a concern this will be in the real world, especially given that candidates frequently win (and lose) by wide margins, but it is something to be aware of.
Another advantage is that I would speculate (with some confidence) that it is less manipulable by free-riding. Obviously it's basically impossible to test this with any kind of model that will generalize out-of-sample, but the nature of the thresholds certainly makes it seem very likely to be so.
- The subtracted voting power is done as "scaling" to the rest of the ballot
- The threshold will always decrease as sub sequent winners are elected.
The second point is definitely correct. I think the first one is too, but I'm not 100% sure I understand the question.
Anyway, these potential disadvantages notwithstanding, I think this is (currently) my favorite cardinal PR rule. Definitely open to changing my mind though.
The disadvantage would be that it respects linear / additive utility much less; for example it will not necessarily choose the score winner (although in practice probably will) and the distribution of utility (again, assuming it is linearly additive over sets) is not as proportional as in regular MES.
Does the system lower the threshold in integer increments? In later rounds the score could be a fraction.
I do like this system a lot and it is simple enough to be viable. It reminds me a bit of Sequential Monroe. I do not think Threshold MES is really the best name.
Ooh, so the thresholds will always be based on original scores. A voter with ballot weight 0.4 will contribute that 0.4 weight to all candidates they score a 5, then all candidates they score a 4 if none get a quota, then 3 etc.
I hope you still like it after this clarification! I like it a lot too, and I also find it pretty intuitive---possibly even more so than Allocated Score, but that's probably subjective.
Feel free to suggest a more evocative name I am not that creative.
@andy-dienes I understand that it is an allocation method so it is all or nothing unless on the split point. I also understand that you want to charge them all the same cost when it is on a split point.
I was thinking that a voter with a ballot weight 0.4 will contribute that 0.4 weight to all candidates they score a 5, BUT the 5 would be sequenced as 2. This means a person who scored the same candidate 3 would be taken first. There is a strategic issue around this but I don't recall the details. We encountered it when designing Allocated score. I suggest you look into the issue. It is linked on electowiki here but the link is broken since the CES forum has been taken down.
@keith-edmonds I guess I should probably just walk through an example so I make sure we are talking about the same algorithm. I am envisioning anybody scoring at or above the split point spends the same amount of ballot power, so you will not necessarily get fully allocated.
I'll use the example you linked; found the profile in wayback machine:
...... A B C
21: 5, 0, 0
41: 0, 4, 5
38: 0, 3, 0
S2 is same as the first, but the last block of 38 voters is 0, 5, 0
And the issue was for Allocated Score (sorted by original score) that S1 elected BBBAB and S2 elected BBCAC. Then fixing Allocated Score to sort by weighted score meant S1 elected BBBAB and S2 elected BBBAC, so there was a smaller incentive to free-ride.
Let's look at what happens in t-MES.
To elect 5 winners in S1
In round 2, we can keep threshold = 5 stars, and C can still be elected at a price of 20/41 per voter. Elect [C]
In round 3, we can keep threshold = 5 stars, but only A has a quota. Each of those 21 voters spends 20/21 voting power. Elect [A]
No candidate gets a quota of ballot weight at threshold = 5, so lower it to threshold = 4. Now B gets 41 * 1/41 = 1 ballot weight of support. No good. Lower it again to threshold=3, now including that block of 38 voters, B gets total support of 39.The uniform price is 19/38 (so the block of 41 voters gets fully exhausted). Elect [B]
No candidate gets a quota of support, even if we lower to threshold=0 . In this situation it makes sense to me to just default to weighted score. Elect [B]
And we can show that S2 yields the same outcome, CCABB, so there is no incentive to free-ride for that last block of voters when even in AS there was a small incentive.
And by the way, this example is a good one to demonstrate how it does not necessarily respect linear utilities. Personally, I think CCABB is the "correct" choice: it provides each block of voters with their favorite candidate, and the number of representatives they get is proportional to their size. But, if you take linear utilities too literally, it may seem that B should be chosen since it can represent the middle block of 41 "almost as well." The problem, in my opinion, of thinking this way, is that it seems very likely to me to encourage the middle block of voters to min-max their vote between B and C (and similarly to encourage C's campaign manager to run negative ads against B)
As mostly a sidebar, to see what I mean by "threshold-PJR," try setting threshold=5. Then the middle block of voters all approve C and no other candidates, and constitute two quotas, so an outcome satisfying 5-PJR must elect C at least twice.
Likewise, the top block of voters all approve A and no others, and constitute one quota, so A must be elected at least once.
Set threshold=3, so the last block of voters all approve B. To satisfy 3-PJR, then B must be elected at least once.
This gives us CCAB. The last candidate we have leeway to choose, and I think clearly B makes the most sense in this specific example, but in general this will depend on what you do once nobody gets a quota.
OK good. It does not seem to have that issue. Thanks for humouring me, I could not quite remember the reason for not wanting to order by original score
I would think this is the better result but whatever. To explore this I find the following example which I often refer to illustrative.
Consider this 5 winner example with clones for each candidate
Red: 61% vote A:5, B:3, C:0
Blue: 39% vote A:0, B:3, C:5
RRV Gives ['A1', 'C1', 'A2', 'B1', 'B2']
MES Gives ['A1', 'A2', 'A3', 'C1', 'B1']
SSS Gives ['A1', 'B1', 'B2', 'B3', 'B4']
Allocated score Gives ['A1', 'B1', 'A2', 'B2', 'A3']
STV Gives ['A1', 'A2', 'A3', 'C1', 'C2']
What does your new system give?
@keith-edmonds On this profile it gives AAACB (so same as regular MES). If the pcts are 59-41 instead of 61-39 then it gives AACCB. But of course this is an example intentionally constructed to be right on the edge.
To generalize this instance a little, if in general you have two factions with some preferred cands, and then some compromise candidates, each faction will get preferred cands up to their vote share, rounded down (aka lower quota), and then the remaining seats will be filled by compromise.
for Red vote share 41% up to 59%, the outcome is AACCB
for Red vote share 61% up to 79%, the outcome is AAACB
for Red vote share 81% up to 100%, the outcome is AAAAB
And I suppose there are special cases (which won't occur in real elections) when the vote share is exactly divisible by the quota, in which case the winners will be what you'd expect.
@andy-dienes OK that is what I would have expected. I think this is now my second favourite system (second to SSS but we do not need to side-track). It meets the basic criteria I look for
- It is simple enough to be explained in a referendum to laypeople
- It has an underlying ethos which makes sense. It is not the linear utilities like SSS but it is reasonable and consistent.
- It gives a high level of proportionality
- It gives good voter expression (ie cardinal ballots)
Unless there is a large flaw I am missing (like nonmonotonicity) I think you should run it past experts who are not on here (ie Piotr and Jameson) to see if they have comments.
It is quite similar to Sequential Monroe Voting so I would take a good look at that. The two finalists in the last Committee on voting methods was this and SSS. Allocated score was sort of reinvented as a compromise between the two.
Possible names for this system
- Threshold Allocation Voting
- Proportional Threshold Selection
- Something else with the words Proportional, Threshold, Allocation, Justified.
@keith-edmonds Awesome! I agree with all of your summary points.
I imagine Piotr will approve, since it is substantially similar to his design of MES on ranked ballots (except of course we use cardinal ballots). Also, he may be sick of me at this point, lol , but if it looks like others are buying in as well we should definitely run it by him to verify.
It is definitely similar to seq-Monroe, but instead of using the mean of the Hare quota it uses the min, and it has a built-in way to tiebreak. I do like this method more since, as you say, I think it has a more consistent ethos and a high level of guaranteed proportionality.
Hopefully the name will be STAR-PR , but a name like that sounds good too. I sometimes visualize this method like an iceberg, since you start with the threshold high and only see the 'tips' of the ballots, then uncover the 'body' of the ballots as you lower the threshold. Not sure if Iceberg Voting is particularly evocative though. Maybe "floating" fits in with those words, something like "Floating Threshold Voting"
Edit: Reddit user /u/OpenMask suggested Scoring Threshold Allocated Representation for STAR, lol
Let's see what others think in the call in a few weeks!
multi_system_fan last edited by
@andy-dienes seems like this method comes from US and comparable context. Then it seems like interesting for 3-7 seats. The Netherlands has 150 seats for 20 parties. This method allone does not make much sense since it would be (almost) identical to other proportional systems. So some in between step or other solutions seems neccesary in this context.
@multi_system_fan Definitely---the goal here is a non-partisan PR method using scored ballots. And I agree that if your number of seats to elect is greater than maybe 9 or so at the most, probably you should either split it up into smaller districts or use a party-list method!
I'm worried about the strategic implications of this. In the single-winner case this is Majority Approval Voting (assuming you're using the Droop quota), and even with more winners this has all of those strategic issues.
- Suppose you are part of a faction that comprises ~1.2 quotas and has fielded two candidates, one of whom you like more than the other (you hate every candidate outside of your faction). Your faction is very likely to win one seat, but it won't win two. Here you want to have your ballot count only as an approval for your favorite as far into the tabulation as possible, so you shouldn't give your second choice a score greater than 1. Even bullet voting is reasonable; if the vast majority of voters in your faction are giving their second choice a 1, bullet voting is the only way to make your ballot count in the decisive round. (This is, of course, the chicken dilemma.)
- Suppose there's a two-party system. The other party has both moderates you tolerate and extremists you hate, and you'd rather they elect more moderates than extremists. Still, the main thing you want is for your party to win more seats than them. Here, giving even a 1 to a moderate candidate in the opposing party is a big mistake. It won't make a difference at all until all scores of 1+ are counted as approvals, and at that point you still want to favor your party's candidate over the opposing moderates.
These are simplified examples, but the simplicity is not necessary for such problems to manifest. I'm not claiming that it's never strategically optimal to give a candidate a 4, but it's pretty atypical. It's strategically optimal to use lower scores than other voters do, such that they're supporting both their own favorite(s) and your favorite(s) while you're only supporting your favorite(s). The only equilibrium involves 5s for a voter's favorite(s) and low scores for everyone else.
Under Threshold MES, voters who ignore strategy lose a lot of influence, and when voters are strategic the expressive power of the 5-star ballot is mostly wasted. I am pessimistic about it reducing political polarization any more than any other PR method would; I actually expect it to be worse than STV in this regard since parties would be heavily incentivized to get their voters to not give candidates from any other party a score greater than 0 and this would encourage divisive attacks. Similarly, candidates would be incentivized to play exclusively to a party's base (and perhaps to some "sucker" voters in other parties who vote as would make sense in single-winner STAR).
@marcus-ogren Hi Marcus,
In the first example (chicken dilemma) that is going to be an issue for any proportional method. In fact, I would maybe even go as far to say that if such strategy is not a consideration, then your rule isn't proportional.
Fundamentally, if you have one quota of voters, half of whom like A > B and the other half of whom like B > A, then only one of them can get elected, and both factions will try to exaggerate their preference between the two.
To that end, I believe this rule deals with this kind of situation better than many of the others we've discussed. I believe that because of its guarantee to give what I am calling Split Justified Representation (SJR), which is basically lower-quota even for parties who face intra-party vote-splitting (like this chicken dilemma example). It says if there is a T-cohesive group, each voter approving B out of some set of T candidates, then they will get at least B winners.
Even in the worst case where they chicken-dilemma each other into oblivion and one half rates A: 5, B: 1, others: 0, and the other half rates A: 1, B: 5, others: 0, then still one of either A or B is guaranteed to win. The same is not true for, e.g. Allocated Score.
Perhaps this is a philosophical disagreement more than a mathematical one, but I believe throughout this entire design process of evaluating cardinal PR rules there has been too much bias towards 'centrist' or 'moderate' candidates, and this is another example of that. If the voting method selects too many moderates, then voters will start exaggerating their positions more and more; if the opposing party is half moderates and half crazies, then that's unfortunate, but it means I would expect the elected committee to be 1/4 crazies, since that's what proportionality means.
By way of example, I strongly strongly feel that in the following instance (for 0 < x < 20)
40 + x%: A5, B3, C0
60 - x%: A0, B3, C5
That the best, most fair, most intuitive, and most proportional outcome is AABCC. If you select BBBBB like some more linear-utility-respecting rules would, then all you're doing is telling voters to make their ballots as exaggerated as possible.
I also have to admit I might not be seeing the same strategy you are, but this assertion
in this regard since parties would be heavily incentivized to get their voters to not give candidates from any other party a score greater than 0
does not make a lot of sense to me. By the nature of the proportionality guarantees (t-SJR, for example), as long as the party can coordinate some threshold score above which to put their candidates, then they can be guaranteed their lower quota, but that threshold definitely need not be 0. For example, a rule of thumb could be "use scores 3,4,5 for intra-party preference, and scores 0,1,2 for other-party preferences."
I do not mean to say that such incentives do no exist; they do, and they have to because you cannot have proportionality without them. But I would expect such issues to be at most as bad, and probably strictly less bad, than they are in the linear-utility-respecting rules like MES, SSS.
@andy-dienes Okay, you're right about the chicken dilemma and other voting methods - STV avoids it, but I don't know what else does. But note that, if voters "chicken-dilemma each other into oblivion" it doesn't mean everyone votes A: 5, B: 1, (or the reverse) it means that everyone votes A: 5, B: 0 (or the reverse). The incentive for the more extreme version is pretty significant, though this isn't all that different from Allocated Score in the same scenario.
This depends on the exact preferences of the crazies. If they all insist on being represented by another crazy and the moderates are viewed as being virtually the same as the other side, then yes, proportionality means electing the crazies. There's no getting around this. However, if the crazies would feel very well-represented by a crazy and also reasonably well-represented by a moderate, electing moderates instead of crazies seems consistent with PR. In the latter case, I think electing moderates is strongly preferable to electing crazies; not because of the labels, but because I think the preferences of voters in other factions should have some nonzero influence on which of them is elected. And I think this is very important; disincentivizing candidates from further alienating opposing voters is a big deal for depolarization, and I believe the vast majority of the benefits of electoral reform stem from depolarization.
I also have to admit I might not be seeing the same strategy you are, but this assertion
Suppose every party uses this rule of thumb. Then, if I score the candidates in my party other than my favorite a 2, I can both get the security of supporting those candidates as a backup plan while having a much bigger influence on which candidates within my party win. I can also help my party more by refusing to give anyone outside my party more than a 1; that way, in the round of 2+, my party benefits from approvals from other parties while other parties don't benefit from my approvals, and I get the bit of added security of supporting more acceptable parties with a 1. The rule of thumb you describe is not a strategic equilibrium.
I see strategic voting in Bucklin voting as being approximately, "only rank candidates you'd vote for under Approval Voting". Threshold MES is similar, but with "only give candidate you'd vote for under a proportional form of Approval Voting a nonzero score." I expect any voting method for which this is true to be very slightly worse than STV at depolarization.
I think your example and my first example have a common problem: they're too clean. Realistic strategic voting involves a mix of getting your faction to win as many seats as possible, get the best people within your faction to win those seats, and getting the most tolerable people in opposing factions to win their seats. Strategic voting centers around making good tradeoffs, in toy examples with only three types of candidates can't capture the tradeoffs you'll find in more realistic elections. (This is really annoying, because anything that can properly capture these tradeoffs will be too complicated to be a good toy example.)
STV avoids it, but I don't know what else does.
Right, exactly and STV does not satisfy Justified Representation, which is (personally speaking) my minimal demand for proportionality. Anything which gives Justified Representation will exhibit a chicken dilemma.
it means that everyone votes A: 5, B: 0 (or the reverse). The incentive for the more extreme version is pretty significant, though this isn't all that different from Allocated Score in the same scenario.
I'm still not sure I'm seeing why there's an incentive to do so; if they all vote A5B0 or A0B5, then very possibly neither candidate will be elected, which is far worse for the group than either one.
Let's look at more abstractly the game of chicken because I think there is something a little subtle going on here.
Even in the case that we have
- Two identical groups of rational agents
- A larger payoff for either group if they defect (so defection is best-response for each individually)
That does NOT necessarily mean that the incentives will result in both groups defecting, because a simultaneous best-response is NOT always an equilibrium. Chicken is a classic example of an anti-coordination game, and there are multiple strategic equilibria involving unequal strategies for the two groups (and also mixed equilibria involving defecting / compromising with some probabilities).
How that's relevant to voting, is that just because there is a coalition split half A>B and half B>A, we shouldn't assume that the steady-state strategic equilibrium will be both sides burying the other. More likely is one side capitulates, and which side that will be is essentially random (in this example).
Then, if I score the candidates in my party other than my favorite a 2, I can both get the security of supporting those candidates as a backup plan
The rule of thumb you describe is not a strategic equilibrium.
Well, maybe, but one could also speculate that if you score your backups a 2, but other voters use higher ratings for their candidates, then all seats might be filled before the threshold reaches 2, so you don't have that "security." I'm not saying that this is an unreasonable concern per se, but I don't think the incentives are nearly so cut-and-dry as you are making them out to be.
only rank candidates you'd vote for under Approval Voting
disincentivizing candidates from further alienating opposing voters is a big deal for depolarization
Well, kind of yeah, but this intentionally the design. I included a very brief similar discussion in the (pretty janky) electowiki page I made just to have something to reference, but this method entirely rejects the assumptions that scores should be linearly additive over sets, or averaged over voters, etc, and instead treats the scores as thresholds for lower quotas of representation.
Remember that with the linearly-additive interpretation of scores, parties are punished if their voters are not maximally cohesive and if they try to express any intra-party preference, so it is "polarizing" in a different way. I think it would help me if you give specific-yet-parameterizable examples of types of situations where this rule will do poorly, but a more utility-based one will do well.
Strategic voting centers around making good tradeoffs, in toy examples with only three types of candidates can't capture the tradeoffs you'll find in more realistic elections.
Agreed. My favorite kinds of examples are those that don't depend too particularly on the exact numbers (this is what I mean by "parameterizable" ) as I think they give some of the best pictures of how a method actually behaves. Maybe to distinguish we can call these "scenarios" rather than examples, and I like to give them names; probably we should compile a battery of these and make some kind of chart for what different proportional rules do.
- Chicken dilemmas
- Center squeezes
- Highly polarized clusters
- Justified representation
- Laminar vote splitting: a coalition all agree with its top ratings on some popular candidates, but lower ratings fragment into independents and sub-parties.
- Compromise vote splitting: a coalition's top ratings are fragmented over independents and sub-parties, but their lower ratings all agree on some popular candidates.
- Cyclic (down-ballot) vote splitting: some mix of the above two
@andy-dienes I agree with you that the chicken dilemma is nowhere near as bad as it's often made out to be; I've written about it for single-winner voting methods and the mitigating factors for Approval Voting there should apply to a lot of chicken dilemmas under PR as well.
There are obviously some cases where you should give a candidate who isn't one of your favorites a high score, such as when your favorites are dark horses with virtually no chance of winning a seat. But in single-winner Approval Voting, when most voters are voting for a lot of candidates it makes sense for you to vote for fewer candidates and vice versa. I'm pretty sure the dynamic is still present here, and, conditional on all the seats being filled before the threshold reaches 2, doing something akin to bullet voting seems like it should typically be a good strategy.
I think it would help me if you give specific-yet-parameterizable examples of types of situations where this rule will do poorly, but a more utility-based one will do well.
There are two parties, Left and Right, and two sub-factions within each party, Moderate and Extremist. So you have Far Left, Center Left, Center Right, and Far Right. There are 2 candidates within each sub-faction. The sincere preferences for a Far Left voter, on a 0-5 scale, average 4.5 for Far Left candidates, 3.8 for Center Left, 1.5 for Center Right, and 0.1 for Far Right (different voters within each sub-faction have slightly different preferences). For Center Left voters it's an average of 3.8 for Far Left candidates, 4.5 for Center Left, 1.5 for Center Right, and 0.1 for Far Right, and for voters on the Right it's symmetrical. The is substantial uncertainty over how many voters are in each sub-faction, so we don't know how many seats the Left will win altogether. (We could also suppose that ~10% of voters are completely non-partisan and will ignore the factions altogether, for the purpose of incentivizing free-riding, though we don't really need that for this analysis.) You can treat the numbers of voters and candidates in each sub-faction as tunable parameters, and the uncertainty is another parameter.
Here's how I see it going under some different voting methods:
- STV: Voters can't really benefit from strategy. The preference for voters on the Left for Center Right over Far Right is irrelevant, except maybe for the final seat.
- PAV, SPAV, MES with Approval ballots, etc.: Voters are best off either voting for all the candidates in their party (since they care more about winning more seats for their party than about optimizing who wins within their party) or only voting for their sub-faction (since these voters are the ones who affect which candidate within a party will win, and doing so doesn't reduce your party's expected number of seats won by all that much). I don't have a great feel for what the equilibrium looks like quantitatively, but voting for a moderate in the opposing party is a terrible move. The preference for voters on the Left for Center Right over Far Right is even less important than under STV.
- Threshold MES: Analyzing strategic voting under Bucklin-based methods is a pain, in general, since it depends so heavily on the details of what other voters are doing. Here though, I think we can get a good approximation to optimal strategy just by noting that every round is basically an MES election, and since voting for an opposing moderate is a bad idea under MES it's a bad idea in every round here. For a Far Left voter, I think it's best to give 4s and 5s to Far Left candidates, some combination of 0s, 1s, and 2, to Center Left candidates, and 0s to everyone else. A rigorous analysis is extremely difficult, but I'm confident that opposing moderates should be given 0s. This favors moderates no more than the voting methods that use Approval ballots.
- Allocated Score: First, let's suppose that voters are giving scores of 3-5 to all the candidates in their party. In this case, giving 2s to the opposing moderates is sound; you're unlikely to end up in their quota, but it will help them a lot against the opposing extremists. That said, giving the opposing moderates 2s does hurt your party in the final round. And you could help your sub-faction the most by giving everyone in it a 5 and everyone else a 0 (and if enough voters do this it means that giving opposing moderates 2s could easily land you in their quotas). There are several competing interests to consider, and ultimately I think voting about honestly makes the most sense so long as other voters are doing the same.
- Allocated Score with runoffs in each round: Similar to Allocated Score, but the benefits of giving candidates (including those in the opposing faction) different scores are heightened. The runoffs also reduce the cost of giving 4s to moderates in your faction if you're an extremist since there could be a runoff between one of your moderates and one of your extremists.
Of these methods, I think it's only Allocated Score and Allocated Score with runoffs that favor moderates an appreciable amount when voters are competent at strategic voting.
I like your idea of creating a bunch of named scenarios for proportional methods akin to the chicken dilemma and center squeeze for single-winner voting methods. I think computer simulations are ultimately best for making quantitative comparisons (at least usually), but named scenarios are great for understanding what's going on.
The sincere preferences for a Far Left voter, on a 0-5 scale, average 4.5 for Far Left candidates, 3.8 for Center Left, 1.5 for Center Right, and 0.1 for Far Right
I do really want to emphasize that one of my main theses for this design is that the mere existence of 'sincere' utilities for each candidate, when in a proportional multiwinner context, feels somewhat nonsense to me. Even if one is a staunch utilitarian, I think ultimately voters should be modeled to have utilities over decisions that the committee makes and not the individual members of the committee; that is, I think it is much too strong an assumption to presume that it is even possible in the first place for a voter to assign 'sincere' utilities to each candidate such that their utility for any set of those candidates is equal to the sum of candidate utilities.
I prefer to think of this method (which I am now calling Threshold Equal Approvals because @Keith-Edmonds suggested a rename and that spells TEA , haha) as instead interpreting each score as answering the question "would you like to be inside or outside this candidate's 5 (or 4/3/2/1)-star coalition"
Anyway let's consider the scenario you suggest (I guess we can name it "Single Peaked 1d" ?)
Far Left: A > B > C > D
Center Left: B > A > C > D
Center Right: C > D > B > A
Far Right: D > C > B > A
Let's say the percentages of the electorate are respectively w, x, y, z%. This is (kind of) an instance of laminar vote splitting---at least if there is some candidate popular among the entire Left wing, and likewise for the Right. To me, I would prioritize the guarantees in this order
- Left gets at least (w+x)% seats and Right gets at least (y+z)% seats
With TEA, I actually agree with your assessment that it will usually be best for Left to only rate Left candidates, and the same for Right (unless they feel strongly about certain independents or certain candidates in the other party). But that's not a function of the method, that's just due to the way the profiles are set up where there are two very clear coalitions. The proportionality guarantees mean that no matter how much strategic jankery happens, as long as Far Left voters give Far Left cands higher scores than Center Left cands and vice versa, and all Left voters give Left cands higher scores than Right cands (and again, vice versa), then both 1. and 2. have to hold.
Conversely, in Allocated Score (with or without runoffs), we can only get guarantees 1. and 2. if every Left voter min-maxes their candidates. And in fact if they start peppering 2s to the opposing party I think it's quite likely that they will lose seats. If I am not mistaken, it seems you are mostly concerned that TEA does not incentivize voters to express much preference over candidates in opposing parties; I have the converse concern that Allocated Score does not incentivize voters to express much preference over candidates in their own party.
I have to admit, when I read statements like
I think it's only Allocated Score and Allocated Score with runoffs that favor moderates an appreciable amount
It feels like we are jumping straight to guarantee 3. from above, and skipping 1. and 2. which I personally view as more significant. Again this might come down to a philosophical disagreement, but I do not think that "favoring moderates" is a good thing when proportionality is the goal; I do not think any types of candidates should be favored except for those best representing the electorate in miniature, so to speak.
Although, I am worried we might be starting to go in circles , not that this is any fault of yours or mine, it is just the nature of these kinds of discussions when they're one-on-one. Maybe we should try to get more (and fresher) eyes on the problem.
I do really want to emphasize that one of my main theses for this design is that the mere existence of 'sincere' utilities for each candidate, when in a proportional multiwinner context, feels somewhat nonsense to me.
In principle, I fully agree with you. In practice, I think assigning utilities to each individual candidate works pretty well. An individual voter will only have a marginal effect on the outcome; questions that cause the individual-candidate-utilities model to break down (such as comparing between electing 5 candidates you love, 3 candidates you love and 2 candidates you hate, and 2 candidates you love and 3 you hate to a five-person committee) become irrelevant (at least usually). If a single ballot can cause at most one of the winners to be different, I can't think of an example off the top of my head where the model of having individual utilities of each candidate and maximizing the sum over all the winners breaks down.
Left gets at least (w+x)% seats and Right gets at least (y+z)% seats
I have two major points of disagreement. First, I place no intrinsic value whatsoever on having guarantees; all I care about are results and incentives. I am completely indifferent between having a result occur with it being guaranteed to occur and it occurring without a guarantee. Second, I consider the second point to be undesirable. In my example, voters have somewhat stronger preferences for who wins within the opposing party than within their party, and I don't think the weaker preferences should take precedence over the stronger preferences. Also, points 2 and 3 are in direct conflict, and I care about point 3 because it encourages depolarization.
The proportionality guarantees mean that no matter how much strategic jankery happens, as long as Far Left voters give Far Left cands higher scores than Center Left cands and vice versa, and all Left voters give Left cands higher scores than Right cands (and again, vice versa), then both 1. and 2. have to hold.
The stringent conditions (e.g. "all Left voters") make these guarantees seem weak to the point of irrelevance; "strategic jankery" that is well-justified and outside your allowed parameters will void these guarantees entirely. And strictly speaking, I don't think these guarantees are strong enough to prove what you want. Like, if most Left voters give the Left candidates a score of 3 and Right candidate a score of 0, but slightly less than a full quota of Left voters give the Left candidates a score of 5 and the Right candidates a score of 4, these latter Left voters will function like Right voters who will fill the quotas of Right candidates. Contrived, I know, but still. you need to assume a lot, including some pretty unreasonable things, in order to get a mathematical guarantee.
Conversely, in Allocated Score (with or without runoffs), we can only get guarantees 1. and 2. if every Left voter min-maxes their candidates. And in fact if they start peppering 2s to the opposing party I think it's quite likely that they will lose seats.
True with respect to guarantees (though I don't care about guarantees). As for the latter point, more precisely they can lose seat. Most of the seats will be decided by the filling of quotas; so long as their voters don't fill the quotas of opposing candidates, giving 2s to the opposing party is only harmful for winning the final seat. Still a solid argument against giving out these 2s, but I don't think it's an overwhelming one.
I think our big disagreements are (1) Should a voting method favor moderates over extremists? and (2) Are formal guarantees valuable? Our disagreements seem to be more over what a voting method should do than over what certain voting methods will do. I am not particularly optimistic about coming to an agreement on these points, but I think the agreements we have reached are valuable.