Minority representation in multi-winner Score Runoff Voting
The multi-winner version of score runoff voting, which is intended to serve as a form of proportional representation, is described at http://www.equal.vote/pr and has some discussion at https://www.loomio.org/d/kgD4AJ8h/hot-off-the-presses-srv-pr- . Since one defining trait of proportional representation is its ability to represent minority groups (with “representation” defined as electing whoever the voters in question want to elect), I’ve run a few simple scenarios to see how well SRV does that.
The scenarios in this post all have the following elements in common:
- We’re looking at a district or town with 400 voters, where 5 candidates, ABCDE, are running for 4 positions.
- The voters are split into a majority group of 300 people and a minority group of 100 people.
- The minority group always gives a 5 to candidate A and lower scores (0-4) to everyone else.
- The majority group always gives a 0 to candidate A.
- Since there are 4 seats open, and 1/4 of the voters unanimously prefer candidate A to every other candidate, I grade the system PASS if it elects candidate A and FAIL if it doesn’t.
Notation etc.:
- To reduce visual clutter, I won’t show scores of zero.
- Bolding the “total scores” line means the candidate advances to the runoff. Bolding in the runoff means the candidate is elected.
- To keep the presentation simple, all ties will be broken A>B>C>D>E.
It’s possible this post has some minor transcription errors or formatting mistakes.
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Scenario 1: Voters only use zeroes and fives (bullet voting by minority group)
Minority group: A=5
Majority group: B=C=D=E=5
Round 1 individual weights: Minority=1.000, Majority=1.000
Round 1 group weights: Minority=100, Majority=300
Round 1 total scores: A=500, B=1500, C=1500, D=1500, E=1500
Round 1 runoff: B=0, C=0 (zero because none of the voters have a preference between B and C)
B is elected
Round 2 individual weights: Minority=1.000, Majority=0.500
Round 2 group weights: Minority=100, Majority=150
Round 2 total scores: A=500, C=750, D=750, E=750
Round 2 runoff: C=0, D=0
C is elected
Round 3 individual weights: Minority=1.000, Majority=0.333
Round 3 group weights: Minority=100, Majority=100
Round 3 total scores: A=500, D=500, E=500
Round 3 runoff: A=0, D=0
A is elected
Round 4 individual weights: Minority=0.500, Majority=0.333
Round 4 group weights: Minority=50, Majority=100
Round 4 total scores: D=500, E=500
Round 4 runoff: D=0, E=0
D is elected
_Results: BCAD are elected. _
Grade: PASS. SRV easily elects candidate A when the minority bullet votes.
Scenario 2: Minority group thinks candidate E is quite good, or is otherwise convinced to score candidate E almost as highly as candidate A
Minority group: A=5, E=4
Majority group: B=C=D=E=5
Round 1 individual weights: Minority=1.000, Majority=1.000
Round 1 group weights: Minority=100, Majority=300
Round 1 total scores: A=500, B=1500, __ C=1500, D=1500, __E=1900
Round 1 runoff: B=0, E=100
E is elected
Round 2 individual weights: Minority=0.556, Majority=0.500
Round 2 group weights: Minority=56, Majority=150
Round 2 total scores: A=278, B=750, C=750, __ D=750
Round 2 runoff: __B=0, C=0
B is elected
Round 3 individual weights: Minority=0.556, Majority=0.333
Round 3 group weights: Minority=56, Majority=100
Round 3 total scores: A=278, C=500, D=500
Round 3 runoff: C=0, __ D=0
__C is elected
Round 4 individual weights: Minority=0.556, Majority=0.250
Round 4 group weights: Minority=56, Majority=75
Round 4 total scores: A=278, D=375
Round 4 runoff: A=56, D=75
D is elected
_Results: EBCD are elected. _
_Grade: FAIL. SRV does not elect candidate A. _
This is the point where I expect some people to disagree with me. Every single member of the minority group gave candidate E a 4; isn’t that good enough? No, it isn’t. Representative democracy is about having the person of your choice at the table. There’s no reason why the minority group should settle for E.
Also, remember the voters aren’t omniscient. Maybe the reason the minority scored both A and E highly is they wanted to elect both of them. That’s not an unreasonable aspiration if the majority thinks E is great and the minority is 40% of the population. So maybe the minority thought it was 40% but was actually 25%. In that case it should still be allowed to elect A; it shouldn’t be penalized for overestimating candidate A’s appeal.
So SRV easily passed scenario 1, where the minority bullet voted (E=0), and failed scenario 2, where the minority gave fairly strong support to a second candidate (E=4). Where’s the dividing line?
Well, let’s split the difference and see what happens.
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Scenario 3: Minority group thinks candidate E is so-so, or is otherwise convinced to give candidate E moderate support (maybe least of 4 evils?)
Minority group: A=5, E=2
Majority group: B=C=D=E=5
Round 1 individual weights: Minority=1.000, Majority=1.000
Round 1 group weights: Minority=100, Majority=300
Round 1 total scores: A=500, B=1500, C=1500, D=1500, E=1700
Round 1 runoff: B=0, E=100
E is elected
Round 2 individual weights: Minority=0.714, Majority=0.500
Round 2 group weights: Minority=71, Majority=150
Round 2 total scores: A=357, B=750, C=750, __ D=750
Round 2 runoff: _B=0, _ C=0
__B is elected
Round 3 individual weights: Minority=0.714, Majority=0.333
Round 3 group weights: Minority=71, Majority=100
Round 3 total scores: A=357, C=500, D=500
Round 3 runoff: C=0, D=0
C is elected
Round 4 individual weights: Minority=0.714, Majority=0.250
Round 4 group weights: Minority=71, Majority=75
Round 4 total scores: A=357, D=375
Round 4 runoff: A=71, D=75
D is elected
_Results: EBCD are elected. _
_Grade: FAIL. SRV does not elect candidate A. _
So, given the various assumptions used here, the dividing line is between E=1 and E=2.
Now of course these scenarios are contrived, so, hmm, how do I transfer this result to real life? Part of it depends on what happens when the majority isn’t giving a 5 to each of the candidates the minority doesn’t like. Maybe if a 1/4 minority group wants to elect 1 candidate in a 4-seat election, each voter in the group can afford to spend 1 or maybe 2 points total on other candidates who are likely to win. So a minority voter who liked candidates C and E could put A=5, C=1, E=1, and cross their fingers, hoping they weren’t watering down A’s score too much.
It’s important to remember that minority groups aren’t always explicit or well-publicized. The ideal of proportional representation is that all minority groups are represented, even ones that aren’t aware of their own existence.
With multi-winner SRV, it looks like minority voters need to have a somewhat sophisticated understanding of the playing field if they want to maximize their clout. As long as the minority is confident they have enough power to elect exactly 1 candidate, they should bullet vote as shown in scenario 1. If they think they might have more or less power than that, maybe they should consult a pollster who’s run some scenarios and can tell them, “If your favorite candidate is Garcia, a low risk vote is 5 points to Garcia and 1 extra point to your next favorite. For a high risk vote, add a second extra point. If you’re worried that everyone else who likes Garcia will go high-risk, you can ditch your own extra point to compensate. And remember you can give as many points as you want to Smith and Chang because neither of them will ever be in the top two.”
Those are my current thoughts on the implications of scenarios 2 and 3; by all means let me know if you disagree.
Sara Wolf Mon 27 Mar 2017 8:15AM
My conclusion is that in Fillard's example election above IRV-PR elects a spoiler 100% of the time and SRV elects a spoiler 1 in 3 times depending on strategic voting (Bullet voting is effective at helping elect your favorite if you sacrifice all your say over the other candidates in the process. It's questionable if this is actually worth it.) This means that SRV-PR doesn't do that great on the the Accuracy Criteria. IRV-PR miserably fails the Accuracy criteria. Both systems fail the Equality Criteria.
Unless I'm missing something I can't support either system. :( Is it possible to have a PR system that gives every voter an equal vote and that allows and incentivizes you to vote your conscience?
Fillard Spring-Rhyne Mon 27 Mar 2017 3:16PM
Okay so let’s think back to the March 5 demo of multi-winner IRV. We’re electing 2 flavors of ice cream to serve at our party.
You have a ballot and a slip of paper that says “ONE VOTE”. You mark your ballot. The flavor you marked '1' is called and you walk over to stand with that group.
The victory threshold is 8 votes, and there are 10 people standing in the mint chocolate chip group. So I declare mint chocolate chip elected -- the first of two winning flavors. What do I do next?
Answer: I confiscate the votes of the people in the mint chocolate chip group. (And as their “change”, I provide a replacement slip of paper for each of them representing 2/10 of a vote.)
Why? What’s the justification for taking away the votes of the people whose favorite flavor of ice cream has just been elected? How does that make the party we’re planning any better or worse?
(I don’t mean to ignore all the rest of your comment but this is all I have time for right now. Also I think it makes sense to start by seeing what you think about this.)
Mark Frohnmayer Mon 27 Mar 2017 11:46PM
@fillardspringrhyne writes: "So, given the various assumptions used here, the dividing line is between E=1 and E=2." -- this is important. If the majority and minorities are truly monoliths, the minority can get their proportional representation (one candidate of the four) and tip the representation within the strong majority to the candidate they least detest amongst the strong majority's slate.
This is scoring, not ranking. IRV and STV rigidly cling to Later No Harm and get non-monotonicity/favorite betrayal as a result. SRV and SRV-PR let you express meaningful support (in the runoff sense) while taking very little risk as a voter. If you give more than token support, it means you are actually offering more than token support.
I disagree with @wolftune and @clayshentrup that the runoff step is unnecessary in the multi-winner case. It measurably improves VSE in the single-winner case, so it stands to reason that it'd be more representative in the multi-winner case as well, and no counter argument has been offered to refute that. Particularly when you have a strong majority -- the runoff votes of the minority start to really matter after the majority has captured a couple of seats. This would make all candidates care at least a little bit about the electorate as a whole, rather than just trying to appeal to a faction of voters, which would likely make for a more functional governing body.
My only real problem with PR at this point is that the measuring stick isn't clearly defined. I'd love to see a credible measure of multi-winner VSE that takes into account both the overall representative accuracy (i.e. VSE) as well as proportionality (how well are individual voters or factions represented).
Sara Wolf Tue 28 Mar 2017 12:11AM
I get how IRV-PR works. SRV-PR and Score based PR is fundamentally different because you can show ties and support for multiple candidates at the same time. You are saying that in IRV-PR the Mint people are already winners so they get less of a say later, but in the SRV-PR original example you gave there is no way to know that Candidate E is actually the same as candidates B, C and D. As a voter I may well prefer E and be an E party voter but since there are 4 seats available I gave my top 4 all a top score. (B, C, D and E.) This is good strategy for me and it lets me help choose all the winners since they will all represent me. A voter who in SRV-PR voted BCDE = 5 and A=0 might have given this ranking if the election was in IRV-PR: E-1st, D-2nd, C-3rd, B-4th.
Let's stick to analyzing the original example and not mix metaphors. We should look at the same set of voters and the same election for IRV-PR in depth too but that's a whole other analysis.
Fillard Spring-Rhyne Tue 28 Mar 2017 3:43PM
Sara: I'm not questioning whether you understand the mechanics of multi-winner IRV. I'm questioning whether you understand why some people (like me) claim it's vastly preferable to even the best winner-take-all systems. That’s why I went back to the ice cream example and asked why taking people’s votes away was justified; it seemed like the most effective way to convey the concept, provided of course that you chose to engage with what I said.
You provided your definition of “spoiler” (thank you) and yes candidate A is a spoiler by that definition. But it’s a winner-take-all definition, one that PR rejects. Similarly you use the phrase "normal logic" to refer to winner-take-all principles, which here in the USA are considered normal and righteous (part of the national story we tell ourselves). If these are your expectations then yes the PR results will surprise you.
I’m sorry my remarks these past couple months haven’t properly explained why I claim PR is important. There have been other issues to deal with. If you or anyone else would like a proper explanation, please let me know. (I’d prefer phone or in person.)
Fillard Spring-Rhyne Thu 30 Mar 2017 5:44AM
Mark (@nardopolo) says:
"If the majority and minorities are truly monoliths, the minority can get their proportional representation (one candidate of the four) and tip the representation within the strong majority to the candidate they least detest amongst the strong majority's slate [by giving said candidate a sore of 1]."
The ability to give a score of 1 to a second candidate without undermining your support for your first candidate depends on things that even an educated voter is unlikely to know. So I disagree with this quote.
Mark Frohnmayer Thu 30 Mar 2017 9:54PM
@fillardspringrhyne writes: "The ability to give a score of 1 to a second candidate without undermining your support for your first candidate depends on things that even an educated voter is unlikely to know. So I disagree with this quote."
Are you sure? I think it's interesting that when you picked a "perfectly proportionate" electorate - i.e. exactly 75%/25% electorate split with 4 seats. What happens if factions are 1/5 and there are 5 seats? Does the minority still get 1 seat and the ability to tip a runoff? That'd be cool.
SRV, at its foundation, follows Smith's Proportionality Theorem, so it is proportional by definition.
That said, it is entirely up to the voter whether he or she wants to stick with the faction and get guaranteed proportional representation, or compromise by giving some degree of support to another faction's candidate. This could be a GOOD THING, particularly when there aren't many seats and there are lots of distinct minorities. It allows a candidate of a dominant faction to make an overture to a minority in order to gain his or her seat. In doing so, the dominant faction candidate is saying, "Hey, I'm going to listen to, and represent, you guys too."
But again, it's entirely up to the voter to make this call.
Do you trust voters enough to let them score the candidates however they choose? Because all SRV-PR attempts to do is reflect the desires of the electorate as expressed by their scores.
Kristin Eberhard Thu 13 Apr 2017 5:18PM
@nardopolo - is "Smith's Proportionality Theorem" this http://rangevoting.org/RRV.html or something else?
Clay Shentrup Tue 28 Mar 2017 5:11AM
IRV and STV rigidly cling to Later No Harm and get non-monotonicity/favorite betrayal as a result.
Well, it is possible to create a system that passes LNH and FBC or monotonicity I believe.
It measurably improves VSE in the single-winner case, so it stands to reason that it'd be more representative in the multi-winner case as well
"Stands to reason" is extremely weak here given the inherent differences with multi-winner systems. Whereas the increased complexity is definite.
This would make all candidates care at least a little bit about the electorate as a whole, rather than just trying to appeal to a faction of voters
A) This is antithetical to the idea of PR in the first place.
B) You can accomplish the same effect by just electing fewer candidates per district or setting C to a value > 1.
Aaron Wolf · Tue 18 Apr 2017 3:07AM
Two things:
You've correctly described STV spoiler scenario. But is it a problem with SRV-PR? I don't know. I don't really get SRV-PR, haven't taken the time to grasp it fully. But my impression is that you're judging it incorrectly. SRV is for single-seat elections. SRV-PR is based on Reweighted Range Voting with an added runoff stage.
My point wasn't "nothing is positive about accepting favorite-betrayal as more tolerable than later-no-harm". My point was that if we ignore the intrinsic trade-off between these two concerns, there are positive things about later-harm in and of itself. In other words, if we knew for an absolute fact that nobody would ever do favorite betrayal, there are still reasons to accept later-harm (i.e. reject later-no-harm criterion). The same is not true in reverse.