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!
