There is a fairly good chance that the City Council of Duluth will be putting ranked-choice voting (AKA instant-runoff voting) up for referendum sometime in the next five years. I sat in at one of the City Council meetings last week and listened to a task force Mayor Ness had formed talk about whether or not it should be adopted (they suggested that it should). I am personally in favor of the adoption, but it’s my hope that I can present the evidence below without bias. All data was taken from the links on this page.
When does Ranked-Choice differ from the current two-stage election?
There are a number of situations in which ranked-choice is exactly the same as the current primary+general election system. If there’s a simple majority, then they work the same way, and with no extra counting. If two candidates each have more than a third of the vote in the primary, then they also work the same way; ranked-choice eliminates all the lowest choices one-by-one to get to the top two, while the primary+election system just takes the top two without bothering to see how the votes add up.
The first situation where they differ is when no candidate would have had a simple majority in the general election. This isn’t supposed to happen in the two-stage system, because the primary is supposed to reduce the field down to only two candidates, but it’s still a remote possibility with a strong write-in candidate.
The second situation is when the primaries don’t yield two people who both got more than a third of the vote. If both candidates have a third of the vote in the primary, then they’re sure to be same two candidates that RCV would choose. That’s actually pretty common for any contested election in Duluth, as we’ll see.
Single-winner General Elections
Single-winner seats are chosen by the first-past-the-post method which follows the primary. I will start by considering the simple case (the general election), and then move on to the single-winner primaries. The general elections are what I would consider “democratic” if a simple majority of voters voted for the candidate (50%+1); that candidate is the sole member of the Smith set and therefore the Condorcet winner. Note that RCV does not always pick the Condorcet winner, it just has a better chance of selecting the Condorcet winner. (WBSRCV always picks the Condorcet winner if there is one.)
From 2011 to 1999 there were seven general municipal elections, held on odd-numbered years. A total of twenty-three seats were voted on. In every one of these cases, the election was decided by a simple majority rather than a plurality. However, we do not know whether these elections were truly “democratic” until we know whether the primary elections which preceded the general elections may have knocked the majority-preferred candidate out of the race.
Single-winner Primary Elections
Primary elections for single-winner seats choose the two top plurality candidates. These primary elections turn out identical under the RCV system if each of the two winners got more than 33%+1 of the vote. Note that this assumes honest voting and ignores the strategic voting problems that crop up under both two-stage first-past-the-post and RCV (though strategic voting under RCV will tend to be more honest).
The primary elections for municipal seats are held about two months prior to the general elections. Because primary election data from 1999 is not available, we will only be considering nineteen single-winner seats. Because a primary is not held if there are two or fewer candidates, we will only be considering twelve primaries. Because RCV and two-stage first-past-the-post operate in the same way if there are only three candidates, we immediately discount those primaries, of which there were six. Then we have to throw out those elections where the two candidates who went on to the primary had a large enough gap between them that a third candidate couldn’t have accumulated enough runoff votes. These races might have had a different outcome under RCV:
- 4th District Councillor Primary of 2009
- Mayoral Primary of 2007
- Mayoral Primary of 2003
A consideration of two of these races follows (the two mayoral races are pretty similar, and the analysis of why two-stage first-past-the-post is bad is the same either way). I offer the following caveat; this is a mathematical analysis. Because you cannot divine preference orders from first-past-the-post, even with a primary, this will show only the possibility that democracy was subverted, not the fact. It is possible that the two “best” candidates went through to the general in all three cases, though I think it is somewhat unlikely to have been true in all three cases, particularly the two mayoral primaries.
The 4th District Primary of 2009
Candidate |
Votes |
Percentage |
Matt Potter |
135 |
5.90 |
Kerry Gauthier |
1,006 |
43.97 |
Gordon Grant |
565 |
24.69 |
Heath Hickok |
472 |
20.63 |
Celia Scheer |
110 |
4.8 |
12,288 votes were cast in this election for five candidates. To democratically win your way into the primary (in the same manner that RCV would choose) took 763 votes. Kerry Gauthier was the only candidate to accomplish this. If you were the 764th vote or higher, you would have been better off voting for another candidate that you liked (ex. If your preference order went Gauthier > Hickok > Scheer > Potter > Grant, you would have cast your vote for Hickok if you had enough knowledge of how everyone else was voting – this is one way the system encourages what’s called favorite betrayal.). All votes for Potter, Hickok, and Scheer were wasted, as were all votes for Gauthier in excess of the 763rd vote (technically under this system, all votes in excess of the 473rd vote were wasted, but I will be using the more restrictive definition of “wasted”). That’s a total of 1,328 “useful” votes out of 2,288, which means 42% of the people who voted for that seat had about as much effect as staying home would have had. In this case, it is certainly possible one of the three eliminated candidates was the Condorcet winner (this is still possible under RCV too unless you adopt the variant known as WBSRCV – I imagine that’s a little too complex for election officials, even with the open-source code available to automate the pairwise calculations, and it’s less likely to pass referendum).
Here is a simple hypothetical ranking scenario under which the two worst candidates were sent to the general (I’ve changed the names so as not to slight any of these candidates that I know nothing about):
Ranking |
Ballots |
Smith > Johnson > Doe > Bloggs > Miles |
135 |
Bloggs > Johnson > Smith > Doe > Miles |
1,006 |
Miles > Johnson > Doe > Smith > Bloggs |
565 |
Johnson > Smith > Doe > Miles > Bloggs |
472 |
Doe > Johnson > Bloggs > Smith > Miles |
110 |
This is highly simplified, of course, because not every person who has Smith as their first choice would have Johnson as their second choice, and some people will only vote if their first choice is in the running, but I don’t want to clog up this post with more math than I need to. Feel free to check these calculations if you are so inclined. It’s also – and I know I should stress this – entirely hypothetical. One of the great things about RCV is that you can get actual information out of the voting data, rather than just “I support, I do not support”. After an election using RCV, we can run lots of analysis on the data to figure out whether it’s actually making a difference and how, because we’ll be able to do actual (rather than hypothetical) comparisons.
In a hypothetical match-up between Smith and Bloggs, they both get all the votes from people who have them as their first choice, making it 135:1006. The people who would otherwise have voted for Miles prefer Smith to Bloggs, making it 700:1006. The people who would otherwise have voted for Johnson also prefer Smith to Bloggs, making it 1172:1006. The people who would otherwise have voted for Scheer prefer Bloggs to Smith, making it 1172:1116. Therefore, in a head-to-head between Bloggs and Smith, Smith wins. The rest of the calculated match ups in this hypothetical scenario follow.
Smith v Bloggs |
1172 to 1006 |
Winner: Smith |
Smith v Miles |
1723 to 565 |
Winner: Smith |
Smith v Johnson |
700 to 1585 |
Winner: Johnson |
Smith v Doe |
1613 to 675 |
Winner: Smith |
Bloggs v Miles |
1251 to 1037 |
Winner: Bloggs |
Bloggs v Johnson |
1006 to 1172 |
Winner: Johnson |
Bloggs v Doe |
1006 to 1172 |
Winner: Doe |
Miles v Johnson |
565 to 1723 |
Winner: Johnson |
Miles v Doe |
565 to 1723 |
Winner: Doe |
Johnson v Doe |
2178 to 110 |
Winner: Johnson |
These are all the pairwise matchups. As you can see, both Miles and Bloggs actually lose the majority of their matchups, because outside of their core of supporters, no one really likes them. Miles loses every match up, while Bloggs loses all but one. The Smith set here only has one candidate: Johnson, who wins in every single head-to-head matchup. That means he’s the Condorcet winner, and should probably have (with these made up preference rankings) won the election.
In RCV the election would play out like this: Doe has the fewest votes, so he’s eliminated and his votes go to Johnson. Potter then has the next lowest vote total, so he’s eliminated and his votes also go to Johnson. Finally, Miles is eliminated and his votes go to Johnson, which pushes him over simple majority and makes him the winner. (The WBSRCV variant works a little differently, but in this case would still elect Johnson. There are other cases where two-stage first-past-the-post, RCV, and WBSRCV all elect different people, but they’re thought to be somewhat rare – and without a ranking system in place, we don’t actually have the data to see whether or not they’re rare.)
Mayoral Primary of 2003
That’s probably enough for you to get the picture, but I did want to touch on one of the most suspect of the (single-winner election) primaries. See for yourself:
Candidate |
Votes |
Percentage |
Charlie Bell |
4,760 |
20.65 |
Herb Bergson |
4,930 |
21.39 |
Joanne Fay |
879 |
3.81 |
Greg Gilbert |
4,429 |
19.21 |
Thomas Huntley |
2,847 |
12.35 |
Vernon LeTourneau |
1,670 |
7.24 |
Jim Stauber |
3,536 |
15.34 |
This is pretty obviously not a good way to pick out candidates, as we have a huge number of wasted votes. Only 42% of the voters decided on which two candidates were going to be in the general election. No wonder turnout for the primaries is so low if you have such a large chance of being disenfranchised. The difference between second and third is 331 votes. The number of votes that went to someone in 4th place or lower was 27 times that; those are people who should have engaged in favorite betrayal and voted for someone that they liked less than the person that they voted for (or who engaged in strategic voting but miscalculated the outcome due to incomplete information).
Conclusions So Far
I think this answers the “Does it even matter?” question fairly well. Two-stage first-past-the-post is only a good system when you already have broad consensus on who the top three candidates are – and the measure of a voting system should not be how it responds to consensus, but how it responds to discord. This is all from the viewpoint of whether or not the system is democratic; there are numerous reasons to adopt RCV beyond mere arguments of whether or not the system is electing the right people, such as the fact that consensus-building has to happen prior to the vote rather than at the voting booth. If you’ve heard someone say, “I like him, but I don’t think he can win”, you know what I’m talking about. The evidence is also pretty good that RCV would save the city money, especially if the public school elections move to IRV (or one of its variants) as well, which is always a plus.
To Be Continued
I will be going through the multi-winner at-large elections some time in the future. Those work a little differently, and there are different conclusions to be drawn from the data.
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Would Ranked-Choice Voting Make a Difference in Duluth Municipal Elections? Part 1