Are there other vote distributions and incomplete ballot scenarios that might derail arriving at three winners?
This is a continuation of last week’s post about Portland’s upcoming election using a new way of electing city leaders: ranked-choice voting for three representatives each, in four new geographic districts, or what is sometimes called proportional ranked-choice voting (RCV).
As I warned, this will be the more technical of the two posts. If all you want to know is how to correctly fill out your ballot, you don’t need to read this. However, I regularly come across Portlanders who have a tech or analytics background, and who want more information than just basic instructions. And many other people are curious for a deeper understanding about how all this works. This post is for them. It’s a long post for BikePortland, but each section can stand alone. I view the whole thing as a resource for the curious.
In preparing the post, I spoke or exchanged emails with four people: James Eccles, Voter Education Lead from the Portland Elections Office; Deb Otis, the Director of Policy and Research from Fairvote; my friend Dan, who has a PhD in Computational Neuroscience; and Chris Donnay, a Mathematics PhD candidate from Ohio State who will soon be starting as a lab manager at the Metric Geometry and Gerrymandering Group (MGGG). I decided not to summarize the written responses from the experts, it’s all there for you to evaluate, straight from the horse’s mouth.
At the very end of the post, I apply what I’ve learned to the Mayor’s race. Ready? Let’s go…
My question
One can easily construct artificial scenarios which have a close to zero probability of happening, but which theoretically might confound the RCV algorithm. For example, say 100,000 District 4 voters each rank only one candidate, and their choices are evenly distributed among the 30 candidates. All the candidates would pretty much receive the same number of votes, there would be no vote transferring, and also no clear winners. Obviously, that’s a possibility in the abstract, but also unlikely to happen in the real world. But are there other, more probable, vote distributions and incomplete ballot scenarios that might derail arriving at three winners?
My question to the experts ended up being some version of,
“Do you know of anyone who has modeled the probabilities of the vote not producing three (25% + 1) winners? One could imagine this happening if a significant number of voters didn’t fully rank 6 candidates, and if the vote totals were somewhat evenly distributed.”
Here’s how they responded:
Portland Elections Office
My first query was to the Portland Elections Office, and I received a nice long reply from City of Portland Elections Analyst and Voter Education Lead James Eccles:
One thing I will note is that our Elections Code is written such that we will always elect three winners as long as there are at least three candidates in the contest. We will continue with tabulation until either three candidates have passed the 25%+1 threshold or all but three candidates have been eliminated.
I do not know the exact mathematical probability of this happening, but our research has shown that it is a rare event. At some point it would become mathematically impossible, but even with voters averaging just over 3 rankings per ballot it is very unlikely.
Fairvote compiles all available cast vote records for US RCV elections and has authored some studies based on this data. A couple of important highlights from those studies include that “A median of 68% of voters rank multiple candidates” and that in elections with 5+ candidates that number rises to 74%.
A little further down that page referencing the same studies, they discuss the impact of inactive, or exhausted, ballots on the outcome of RCV elections. If a ballot reaches the point where it no longer has any rankings for active candidates, we consider it an exhausted ballot. They note that in a data set that includes 300 elections between 2004 and 2022 that although voluntary abstention (what we are talking about here) is the highest cause of exhausted ballots, it is still only occurring 7.8% of the time in multi-round elections. If the numbers in Portland follow this trend, our number of exhausted ballots would not be high enough to cause the outcome we are discussing. (They also make an important point here that in typical single-choice elections that result in a runoff election, the rate of voter participation greatly declines between the first and second election. Far more than we are likely to see in drop-off between the first and last round of tabulation in our elections.)
When we were first writing the election code for RCV in 2023, we also asked the Ranked Choice Voting Resource Center and Fairvote to conduct some additional analysis on our behalf related to how the number of rankings available might impact how many rankings a voter used. In the summary of those findings, they found that:
- “Ballots that allow more rankings tend to invite voters to rank more candidates.”
- “In races with 3 winners, voters tend to use 2-3 rankings. However, the races with three winners are also the ones that have rank limits. So, in races that attract a similar number of candidates but allow more rankings voters tend to rank 3-5 candidates.”
These were both factors in our decision to have six rankings in Portland elections.
Fairvote
Fairvote is a nonpartisan national organization which promotes ranked-choice voting (RCV) and proportional RCV, and which advises cities and states across the country. Fairvote’s Director of Policy and Research Deb Otis responded to me via email (emphases hers):
I don’t know of any modeling on the likelihood of any winners finishing below the 25% threshold, but we do know that it’s possible. If that happens, the candidate who is the “last one standing” closest to the threshold will be elected. From my perspective, that’s not really a problem. The nice thing about proportional RCV is that the vast majority of ballots will count towards at least one winner, even if they become exhausted before the count is complete. So even with a crowded field and a six-rank limit, most ballots will be impactful and most voters will have someone they ranked earn a seat.
For reference, the average number of ranks used in the Cambridge MA city council and school board races in 2023 was 7.3 and 4.6 ranks, respectively. 85% of people ranked one of the top 3 winners.
So I’ll bet some modeling on likelihood is possible, but I also don’t see that as the marker of whether RCV was successful at giving more voters a voice and giving more groups a seat at the table. So even with a crowded field and a six-rank limit, most ballots will be impactful and most voters will have someone they ranked earn a seat.
My friend Dan
Dan got his PhD in Computational Neuroscience, and now works analyzing big data sets using statistical tools. He mentioned to me when we talked that he had once taught a college-level math class which had a unit in voting schemes. He started our conversation by saying, “No voting method is perfect.” What can trip voters up with RCV is that the “winner” might not be the first choice of a plurality of voters. Second-ranks can pull a candidate who didn’t have the most first-rank votes over the 25%, or 50% threshold. This might not seem fair to some voters.
“What can trip voters up is that the “winner” might not be the first choice of a plurality of voters. This might not seem fair.”
— Dan, my (very smart) friend
To be honest, I had contacted Dan hoping to coax him into doing some quick-and-dirty data modeling, but he put that notion to rest in short order, saying that without a way of limiting the inputs, the possibilities became “astronomical” and not possible to analyze.
Metric Geometry and Gerrymandering Group
The last person I spoke with was Chris Donnay, a mathematics PhD candidate who will soon begin working with MGGG. (MGGG is the group which advised the Charter Reform Committee on the different voting schemes and district configurations that would give the most Portlanders an electoral voice.) Chris told me, “I’ve never seen Single Transferable Vote (STV) not produce the target number of winners, with either real or synthetic data sets.” He agreed with my friend Dan that this is a difficult modeling problem, and that it can become a “combinatorial explosion,” but that MGGG had empirical data which allowed them to limit the parameters, and that, yes, the group had done a partial model.
Chris was confident that the Portland elections would work, but added that there are often “some surprises” the first time a city or state uses RCV. He mentioned the same issue that Dan did, that sometimes the candidate who receives the most first-rank votes doesn’t end up being the winner.
What all this might mean for the Mayor’s race
I could see the issue that both Dan and Chris mentioned, of the candidate receiving the plurality of first-rank votes not becoming the “winner,” happening in the race for mayor.
Let’s assume that Commissioner Rene Gonzalez is the front-runner. It’s not a stretch to imagine Gonzalez garnering most of the 1st-rank votes, say 38%. And perhaps Carmen Rubio coming in a close 2nd, with 35% of the 1st-rank vote.
But there also seems to be a sizeable “anyone but Rene” contingent. If it goes into a second round of tabulation, and more voters who ranked Keith Wilson or Mingus Mapps as their first choice, go on to rank Rubio, rather than Gonzalez, as their second choice, possibly Rubio could cross the 50%+1 threshold with more votes (1st-rank + 2nd-round transfer votes) than Gonzalez receives. That would make Rubio the winner despite Gonzalez receiving more 1st-rank votes. And I could see that being controversial among people new to this system.
Get ready to rank!
Thanks for reading.
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There is a lot of hand wringing about “too many candidates” in the press and amongst commenters and political consultants who made a living on the previous system. It is important to keep in mind that in this election we are electing an entirely new City Council. That is part of the reason we have so many candidates and it won’t be repeated. Moreover it is commonplace for new voting systems like RCV to initially attract a lot of new candidates. After a cycle or two the number of candidate filings tends to decrease. Lastly having more Portlanders out there selling their ideas and learning how to build and run political campaigns can only be good. It is helping build and enlist the tremendous amount of talent and expertise that has been left on the sidelines under our existing form of government.
Journalists often don’t like the chaos of democratic politics. It is partly understandable because they have the job of making sense of it all. But unfortunately sometimes that makes them biased in favor of making it less messy which often means less participatory and representative. So I say relax and don’t stress it if democracy looks a little the messy and chaotic, it is often evidence that it is more authentic.
BTW. BIkeportland is doing a great job with few resources covering the candidates and the election. Readers should support this.
I feel like it only seems controversial to people who either haven’t thought about it for more than 15 seconds, or people who just want their person to win and they can think of a way to say they should have won. They’re trying to contrive a reason (in this scenario) Gonzalez should have won.
RCV, even with whatever imagined / hypothetical flaws this new system may have, will give better results. There is no reason to think the minority of voters who voted for candidate A should get their way over a majority who voted for “not A”. That would be unfair, and it’s the tyranny you get with first past the post nonsense.
The main threat that I see is that the voters do not think the winner won “fairly”. The system is somewhat opaque to the casual observer, and we all know people who are resistant to the facts.
As I point out in other posts, you can also get that with ranked choice voting. There is a danger in believing your own propaganda. Its simply false to claim that ranked choice voting eliminates the need for strategic voting or even guarantees the most popular candidate will win.
Thank you for this comment, John V. The word count on my post was getting a little high, so I probably didn’t express clearly enough that neither Dan nor Chris (nor myself) consider the 1st-rank plurality issue to be a problem. James Eccles, from City Elections sent this to me earlier today:
And from downthread with the Sarah Palin/Alaska comment, that is exactly how RCV is supposed to work.
It’s worth correcting that RCV does not remove the spoiler effect – it reduces (this is good) and obscures (this is less good) it:
https://en.wikipedia.org/wiki/Spoiler_effect
“85% of people ranked one of the top 3 winners.”
15% of votes being wasted (not counted) does not seem like a good outcome at all.
If the Charter commission had not decided, at the very last minute, to ignore the voting system choice of their own subcommittee there would be no possibility of exhausted votes:
https://www.starvoting.org/wasted_votes
*had decided, at the
I don’t understand your “wasted,” “not counted” framing. It seems to me that it means that 15% of the voters didn’t rank a candidate who ended up winning. Isn’t that a much better outcome than, say, 49.9% of the voters being unhappy with the outcome? Or as you out it, having their vote “wasted” and “not counted.”
I used a term that is commonly used as synonyms for “exhausted votes”.
For example even Fair Vote describes RCV exhausted votes as wasted votes:
https://fairvote.org/the-wasted-votes-wheel/
PS: I dislike first-past-the-post wasted votes too so don’t at me about the quote
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‘“not counted” framing’
Once again this framing is commonly used “framing”.
https://www.starvoting.org/wasted_votes
The votes are “not counted” in the deciding vote which has always been a flaw in PR RCV and has been the cause of many voting pathologies. For example, RCV will likely be repealed in Alaska this November due to the candidate who was most broadly acceptable in the vote count not winning (a Condorcet failure).
Seems like they should tweak it rather than fully repeal it.
I don’t think you should even have this discussion without mentioning the Alaska congressional races. The one candidate that had the support of the majority of voters didn’t win. That was because a lot of the third place candidates didn’t vote for the other candidates, but most of the second place candidates voters did vote for the third place candidate giving him votes from an overall majority.
The result was that a heavily partisan district elected a candidate that the majority rejected. She was simply rejected by fewer voters than the second place candidate. By contrast the third place candidate had the support of a majority, but was the first choice of fewer than the first two candidates and therefore eliminated.
I would not trust any of the groups that are proponents of ranked choice voting to provide objective evaluations. The danger is that 25% of people only rank people who are not among the final four. That guarantees someone will be elected with less than 25% of the vote.
When you have 30 candidates for three seats, that seems like a fairly easy thing to have happen. The only real question is how many truly competitive candidates there are to share the vote. By competitive, I mean someone who might get one of six rankings from 25% of the voters in their district.
The other, larger issue, is how the council will function when to get reelected someone only needs to keep the votes of 6.25% of the voters from one part of the city. They don’t need to worry at all about what the other 93.75% of the voters in Portland think.
Its going to be a wild ride and I think anyone who believes they know how this will really work is fooling themselves. And the folks who are claiming they do know are fooling everybody.
Thanks for bringing up the Alaska example
FUBAR is the word that comes to mind when thinking about this new system.
The only people that seem to be excited for this new system are voters who think there is now a real possibility that their far out wacky candidate, that wouldn’t win the popular vote in a million years, now has a chance to win, and that should worry everyone.
The only reason a “far out wacky candidate” might actually have a chance to win in the new system is because in reality they weren’t far out or wacky, people were just afraid to vote for them because they thought they might not win. Now they can vote for who they want to win instead of who polls or the Oregonian tells them is going to win. It’s unambiguously better. Maybe some other forms of RCV are better in unlikely edge cases, but the worst system is first past the post.
That is just not true and is probably the most dangerous fallacy of the RCV advocates. All you need to do is look at the Alaska vote. People voted for the “far out wacky” Republican Palin and ranked the alternative Republican Begich second. Since Palin finished ahead of Begich all the people who voted for Palin first and Begich second ended up represented by a Democrat elected with a minority of the votes. If they had ranked them in the other order, Begich would have won with a majority of the vote.
And so cometh the 2024 initiative to rid Alaska of the scourge of RCV.
If the RCV election results really does reflect “the will of the people”, and the system is “unambiguously better”, this repeal should go down in flames.
You are re-writing Alaska’s election. From NBC news in 2022–(via Google):
Obviously Palin did not have the support of the majority of voters.
RCV working as designed.
No it did not.
The Alaska election violated the most fundamental rule of election fairness (Condorcet) and also showed how RCV can result in a very large percentage of votes being wasted. It was a fustercluck and RCV will likely be repealed in Alaska as a result of this failed election.
I would not use the term “majority” but it was clear that right-wing wacko was the preferred candidate of most voters.
https://arxiv.org/abs/2303.00108
It’s a good paper, thank you for citing it. I don’t know the details of how Portland has implemented eliminating candidates. But all the voter information will be available in a data structure, and they are re-tabulating the vote every day, with the total votes received to-date.
It seems obvious to me that in the multiple-winner elections, the transfer of votes which will be most significant will be the over-flow votes from a strong winner. For example, let’s say a top-ranked candidate wins with 41% of the total 1st-rank vote. That leaves 16% of the total first-round votes to be redistributed down, making the 2nd-ranks of those 41% winning voters very important.
The elimination and redistributing up of the candidates with the least votes will most probably be insignificant.
Kudos on the Condorcet reference, can I mention John Rawls?
My politics has strong affinity with his theory of justice, so please mention Rawls more.
If I were the programmer writing this up, I wouldn’t eliminate a candidate who still had a possible path to victory through the entirety of the rankings in the voter table. Does that make my code a STAR implementation? Seriously asking.
I mean, some folks clearly won’t be receiving enough votes in the total table to be viable. They can be culled immediately.
STAR voting scores all candidates from 0 to 5 stars and there are only two rounds (scoring, runoff) and everyone who voted has their vote counted.
I’m convinced that we should use STAR voting. It has been my opinion from early on that the new system we’re about to try isn’t the best, just that it’s better than what we had. Why we didn’t go for something that works better, that is hard to understand. But I wasn’t about to vote against the new system and lose all the things I like about it.
Is it not possible now to revise the system again to switch to STAR? It seems like it would be a much simpler transition. Voters still do pretty much the same thing.
My expectation is that none of the edge cases are going to come up in this election. It’ll seem like it works well most likely. I wonder if people will be uninterested in changing it again if it appears to work.
I am doubtful that with 30 candidates anyone is going to get 41% of the top ranked votes. I think 10% is more likely. But it will be interesting to see how it really works.
I’m enjoying the discussion, Ross. When I use numbers it’s usually just to come up with a simple illustration for a point I’m making, not because I think they are realistic.
One thing I learned at the League of Women Voters event is that there will be analytics available for the public to query the election results. So how it plays out will be transparent. I can’t wait to see.
With the STAR versus STV discussion, I think one aspect which is not getting mentioned is that there is much empirical data for how people behave when voting. Political scientists have entire careers researching that stuff.
But we are discussing this in the abstract as if every voter were an independent widget, not influenced at all by others, and that is far from the case. That’s real clear if you look at the small donor data (even though they are way behind with the data entry). Every district has a candidate far ahead of the others in fundraising. I can’t help but believe that will win them more than 10% of the vote (except in D3, where I’m not sure how Steve Novick’s greater name recognition will compete against scores of tiny contributions gained from social media and email lists).
No, but Begich did.
Spell this out for me like I’m a 6th grader. How did the candidate with 27.8% of the vote in the first round have majority support?
I don’t really care about the content of this discussion, but it is telling that even interested and knowledgeable folks get tripped up over the lingo and ramifications of the numbers, so explaining to someone who is confused and somewhat skeptical why their favored candidate lost and convincing them there were no shenanigans when votes from their candidate were given to one they don’t like is going to be our new springtime hobby.
There are some people who have an ideological and partisan investment in convincing us RCV in Alaska was a failure and should be reversed. I think they are simply wrong, either in the conclusion that the system didn’t work as designed or that it was a failure. To be sure, no new system can be judged by one election. There has to be learning by doing. It is understandable that some voters under RCV will learn that if they don’t rank more than one candidate they are forfeiting part of their vote in a more representative voting system. RCV is not perfect. There are better voting systems. But RCV is an undeniable improvement on first past the post, the system often favored by those who just don’t want more representative voting or participatory government. RCV is better precisely because it asks more of voters in exercising their vote: it moves us toward a system that encourages and rewards rather than discourages and punishes deeper and more meaningful engagement.
Your mayor example doesn’t actually catch the most likely possibility. Gonzales finishes first, Rubio second and the Mingus and Wilson voters refuse to vote for either one. Rubio because of her ticket problems and Gonzalez because they disagree with this politics. You have a perfect Alaska scenario only with two candidates with majority support losing to Gonzalez who the majority rejected.
The most likely possibility is that the “anyone but Rene” group picks Wilson or Rubio.
Unless they are also in the “anyone but Rubio” camp. In which case they choose Wilson and Mapps. If the Wilson and Mapps vote is smaller than the Rubio vote, then those ballots will have no effect on the outcome. It won’t matter how many Rubio voters had Mapps and Wilson ranked as their second choice.If even 10% of people vote only for Mapps and Wilson you can easily end up with neither of the candidates still standing having a majority of those voting.
I am assuming Gonzalez wins, but Rubio could win with the same effect with large numbers of Gonzalez voters ranking Wilson or Mapps and not Rubio.
Maybe you should look up the definition of majority vs. plurality. Maybe I will then understand what you are trying to say. Only one candidate can have majority support and they are elected.
No, not when people have more than one vote, albeit only one effective vote, because they can rank more than one candidate. Many candidates can have majority support and yet a candidate lacking it can win the election with a plurality.
Oh great, we already had an electoral college system that gave us presidents who didn’t win the popular vote, and now we are going to have local elections where mayors and city council members who don’t win the popular vote are elected. What a sad joke.