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.
Clay Shentrup Mon 27 Mar 2017 3:32AM
that's why later-no-harm is considered an issue.
While I think LNH is an utterly nonsense criterion, it especially isn't applicable in multi-winner races. Because if you actually do believe {Green=5, Dem=4}, you want the aggregate legislative ideology that's approximately midway between Green and Dem. You don't necessarily want any particular Green in office—indeed if the Greens are popular, you may even want fewer greens because you're facing a legislature that's too Green. And that's true even if the Greens are your favorite party.
Aaron Wolf Mon 27 Mar 2017 4:02AM
Although it's not a crazy argument, the insistence that Green=5, Dem=4 means that I would be more represented by 5 green representatives and 4 dem ones isn't really fair. I might think "I agree 100% with everything the greens stand for and 80% of what the dems stand for" and would be happier with all green than any other situation.
I don't see how you can conclude exactly what the values behind the scores are without jumping to the unfounded conclusion that the scores are themselves the values. Clearly, it's just an abstract representation that carries little of the deeper values and has a lot of uncertainty about meaning. It could mean for a voter that they would like a 5/4 ratio of greens to dems in the representation, but it doesn't necessarily mean that.
Sara Wolf Mon 27 Mar 2017 7:42AM
@fillardspringrhyne
RE: "There is nothing remotely discriminatory or unequal about saying that 1/4 of the voters should be able to elect 1/4 of the seats in a legislature or city council while the other 3/4 of the voters elect the other 3/4 of the seats. No special treatment is being given to anyone."
If this was one person one vote and there were 4 seats I would absolutely agree! ...But, in this example there are 5 groups that ALL got at least a 1/4 of the vote but there are only 4 seats. In your 1st scenario 1/4 of the voters prefer Candidate A. 3/4 prefer Candidate B. 3/4 prefer Candidate B, 3/4 prefer Candidate C, 3/4 prefer Candidate D, and 3/4 prefer Candidate E. It makes a lot of sense that the top 4 should win the 4 seats.
If you look at it that B, C, D and E are all from the same party, and if this was a partisan election, then I understand your rational; Candidate A, (who is from a second party presumably,) deserves some representation too, but in this example the candidates are individuals and so are the voters. We aren't advocating a Party List type PR reform. So... Candidate E deserves to beat Candidate A because 3 times more voters prefer E over A. Any other outcome is a spoiler. A spoiler is any election that elects a candidate with less support than the ideal winner. Can anyone explain why A is not a spoiler in this example?
To help look at this from another perspective imagine this. We're still looking at Fillard's 1st example where 1/4 voted only A and 3/4 voted for ABCD and E. Candidate A is Green Party, Candidates B, C and D are Democrats, Candidate E is Bernie Sanders (or a Green Libertarian, you pick.) The Democrats all like Bernie so they also vote for him, but he is not a Democrat and his platform is totally different. In your scenario Bernie doesn't win even though his 3rd party was 3 times more popular than the Greens. Now the Independent's have 0 representation even though 3/4 of all voters voted for the Independent! What?? (Note: This is post-Trump PDX and nobody votes Republican anymore!)
If you want to say that A should get to win BECAUSE they have less support, that is essentially affirmative action. I support affirmative action in most cases, but as I said this could just as well be affirmative action or an unfair advantage for a minority group that does not deserve it. Candidate A could be Fascists, for example and E could be the Greens (now with more support than ever because people aren't aware they need to vote strategically.)
I'm absolutely NOT saying that PR is to blame for Fascists, or Nazis, or the existence of any other hate group. I'm blaming the spoiler effect in general for giving them more power than their real numbers should normally give them. Trump, case in point. Of course our current system is the worst for spoiler effects so as far as I can tell IRV-PR might be an improvement, (like IRV) but I'm not convinced that IRV-PR or SRV-PR is actually electing the best winners or being a fair and equal vote system.
The working definition that we have for equality in a voting system is this: "EQUALITY- The Voting System doesn’t favor some voters or candidates over others based on preferences, location, political party, etc."
Does PR in general as you are defining it meet that criteria? If it doesn't meet that criteria on purpose then how exactly do we justify that as fair? Are people arguing that giving an extra advantage to minority groups on all sides will balance itself out and lead to better legislation and governance?? I'm not convinced.
In our current system I believe that a number of 3rd parties truly deserve extra help because fear of the spoiler effect robs them of votes from their legitimate supporters, but I would like to fix this with a fair and equal system, not by giving them an unfair advantage.
By normal logic the 4 candidates with the most support should win the 4 seats. This is especially true with a score ballot where voters can actually show nuanced support for multiple candidates.
For comparison imagine that we just do an simple (non-reweighted) multi-winner score runoff election for each quadrant of PDX. This multi winner SRV election is just like SRV but we do one additional runoff with the remaining candidates until each seat is filled. This would elect the 4 candidates with the most overall support. This seems more fair to me, especially if we add in that each non-gerrymandered district elects 3 or so reps that are then accountable to their local constituents and who live in their districts. @nardopolo
Kristin Eberhard Thu 13 Apr 2017 5:17PM
@sarawolf - You said that A is a spoiler to E because E has more overall support. You clarified that by spoiler you mean a non-representative winner or candidate who wins even though another candidate has more support. By this do you mean a "non-representative" or "system failure" is a candidate who represents fewer voters than another candidate? In other words, are you saying a candidate is a spoiler if he wins a seat and prevents another candidate with broader support from winning that seat?
If I am understanding that correctly, then you would support a majoritarian system (where only candidates with broad or majority support win legislative seats) over a proportional system (where some legislators win legislative seats with only support from a minority of voters, beating out candidates with broader support).
Or am I misunderstanding what you are saying about spoilers?
Sara Wolf Mon 17 Apr 2017 8:09AM
Krisen, I think you are misunderstanding me. Sorry for being confusing. I meant to say "non-representitive winner" not "spoiler.
My point is that regardless of the system chosen there should be an agreed upon threshold of minimum support that a candidate should need to win a seat. I'm NOT saying that the majority party/group deserves all the seats. I AM saying that we need a method to evaluate what constitutes enough support to win a single seat in a multi-winner election so that we will know if a system picked the best winners and actually functioned how we'd hoped.
In a one-person-one vote situation it's MUCH more simple. If there were 4 seats you would need a vote from 1/4 of the voters (or maybe votes should be rounded to the nearest 1/4? Depending on how you choose to calculate that you get two different outcomes.)
In a more expressive system like IRV-PR it's not clear to me how to determine a threshold because there are likely to be more than 4 candidates that have support from 1/4 of the voters or more.
In a more expressive system with a score ballot, we could look at a 1/4 of the total of all the scores given to all the candidates together, divide by the number of seats available, and base the threshold on that. A candidate needs a 1/4 of the total scores given to win a seat.. Or something.. In Fillard's example here all the candidates have full support from 1/4 of the voters or more. In this case is it fair to choose the candidate with the least support, (A) so that everyone is represented by someone? Or should we choose the top 4 candidates that each had over a 1/4 of the voters support?
I'm not saying what is fair here, I'm asking, but until we have answers to these questions I don't see how we can justify any results as fair. I just think we need to recognize that in an expressive system there is good solid logic to justify a few different sets of winners or preferred outcomes.
Kristin Eberhard Mon 17 Apr 2017 5:20PM
@sarawolf - Thanks for the clarification, I'm relieved to hear you are not saying you want a majoritarian system.
But I'm still confused: by "one-person-one vote situation" do you mean plurality and top-two voting (each voter gets one vote) and IRV and STV (each voter gets one vote per round of counting) ? Because 1/4 of the vote is not the threshold to win one out of four seats in any of those systems.
In plurality, each of the four seats would be separately numbered (like Portland's city council seats) and the threshold to win is at least 1/3 of the votes if there are three candidates, and at least 1/2 if there are two candidates. Top-two is same as plurality but limited to two finalists, so the threshold is at least 1/2. Same for IRV--threshold to win is 1/2 of still-active ballots. In STV the candidates would run in a 4-winner pool and a candidate would need support from at least 1/5 of the voters to win one of the 4 seats (assuming the counting uses Droop quota).
The Droop quota threshold of support seems fair to me---any candidate who has attracted the support of more than 1/5 the voters should win 1/4 the seats.
In cumulative voting, candidates would run in a 4-winner pool and each voter would have 4 votes (so, #not# a one-person-one vote situation), and support from 1/5 of voters is necessary but not sufficient to win. In Cumulative (and, so far as I can tell, in SRV too), if some of that 1/5 of voters also express a lower level of support for any other candidate, then their favorite might not win. In other words, a candidate must not only attract a minimum level of support, but must also ensure that support is monolithic; that his voters will only support him and no one else.
This seems problematic to me.
Under STV, a candidate only needs to reach the threshold and does not need her voters to exclusively support her. Voters could rank for their favorite (lets say, African-American) candidate first, and rank their next favorite (lets say, white candidate who has expressed support for more productive approaches to criminal justice) second without worrying about harming their favorite. An African-American candidate could tell voters to rank her first and also rank whoever else they like. She could even run in a slate with the criminal-justice reforming white candidate, talking about Black Lives Matter and the harms of mass incarceration on the campaign trail and asking progressive voters to rank them 1 and 2.
But under SRV, African-American voters would have to withold support from any white candidates in order to get one African-American on the city council. An African-American candidate might have to campaign by saying "if you want me to win, vote for me and no one else." Voters who like her best would need to give her a maximum score and falsely express no or minimal support for any other candidate, or else risk causing her to lose (even though a critical mass of voters gave her a top score). It would be hard for candidates to come together, bring voters together, and amplify media coverage of important issues they share in common, because the math would require them to tell voters to give them a max score and not to express support for anyone else.
Aaron Wolf Mon 17 Apr 2017 6:06PM
Under STV… without worrying about harming their favorite
Yes, that's the later-no-harm argument, and it's not entirely crazy or anything. But this framing ignores the spoiler concern.
Here's how a spoiler would work in STV: The African American voters don't constitute enough of a block to get their 1st choice included but they think they'll at least then help support their 2nd choice. However, because that 2nd choice doesn't get enough 1st choice votes, they get eliminated early. It's possible that the 2nd choice of the African American voters is also the 2nd choice of other blocks of voters. It's easy to have a scenario where the African American voters get neither 1st or 2nd choice but look at the situation and recognize that if they did favorite-betrayal by dishonestly switching their 1st and 2nd choices, that would make their 2nd choice actually win. If they learn to do that, then it will falsely show the African American candidate as having less support than they really do, further undermining their clout.
Basically, this is what has been discussed back and forth for so long here. If you get later-no-harm, you empower favorite-betrayal as a strategy. Of the two issues, there are positive things about allowing later-harm (that some say even outweigh the negatives) and nothing positive about favorite-betrayal.
I should clarify that I believe all bad scenarios are less likely in any form of PR than in single-winner elections. There's just less space for the worst-case scenarios to play out, so I don't think worrying about them in any form of PR should be the main worry.
Anyway, side-note, see what you think of this: http://blog.opavote.com/2016/06/guest-post-rethinking-stv-fundamentals.html ?
Adam Zielinski Mon 17 Apr 2017 9:22PM
Kristin,
Isn't it inaccurate to say that under SRV, "African-American voters would have to withhold support from any white candidates in order to get one African-American on the city council?"
If white voters and other non black voters of color express at least some non-zero score support for the African American candidate(s), there is no reason they couldn't win. So that assertion would only be true if all white voters monolithicly gave zero support to the african american candiates.
So I think it is true to that SRV does incentivize all candiates to have at least some appeal to a broader range of voters, I think this is a feature and not a bug.
I think it is desirable for white candidates to try to appeal to black voters, as you illustrated in your example, but I also think it is desirable for black candidates to try to appeal to white voters.
Rather than have an election system where it would be possible to elect someone who only appeals to a narrow base and no one else.
Kristin Eberhard Mon 17 Apr 2017 11:52PM
@wolftune I'm not sure why you say there is "nothing positive" about favoring favorite betrayal over later no harm. Seems to me that being able to safely offer support for candidates beyond your favorite is quite positive--it gives voters more voice, additional candidates more support, and encourages candidates to reach out to voters beyond their base because they might get an additional vote from them.
Do those not seem positive? Or did I misunderstand you?
Aaron Wolf · Sun 26 Mar 2017 8:56PM
Devil's advocate: that's why later-no-harm is considered an issue. The 2 Green voters in the 3 voter scenario are harming their ability to get majority Green representation by admitting to like the Dem. All the arguments about why later-no-harm shouldn't be prioritized or emphasized apply etc. not getting into that, just making the point for this contrived example…