Last time I looked at single-winner elections, this time I will be looking at the multi-seat elections. Note that what’s actually being proposed is more properly called “single transferable vote”, but I’ll be calling it ranked-choice voting in order to maintain consistency. The multi-winner version does rely on ranking choices, so it’s not a total misnomer – just less accurate than it should be (for branding purposes).
How the Process Works
In a single-winner election, you vote for the person you think is best in the primary, the top two plurality winners go to the general, and then you vote for the person you think is best in the general. In a plurality-at-large election, you vote for the N best candidates, the field is whittled down to the N+2 candidates, and then you vote for the N best candidates again (where N is the number of seats open). In Duluth municipal elections in the past ten years, N has always been 2, as the only seats chosen this way are the four at-large council member positions, two of which are up for re-election every two years.
Current, Proposed, and Ideal Criteria for Multi-Winner Elections
The current system is two-stage plurality-at-large. Currently having the highest or second-highest plurality will get you one of the two at-large seats. Since every person has two votes, and there are four places on the ballot in the general election, you need a minimum of a third of the voters plus one additional voter to vote for you, assuming that every person casts both votes. (That’s a pretty big assumption; see the below section on bullet voting.) The lowest number of voters who wanted both candidates is a simple majority, and on this basis it’s actually pretty democratic (if you ignore the primary system, which hides some of the undemocratic nature of the system). The worst case scenario for the current general election system is when one of the candidates is broadly liked and the remaining three candidates are all scrabbling for the same pool of seconds votes. In that scenario, it’s possible that the second candidate chosen was only liked by a third of the voting population (something which is possible, but much less likely under RCV).
Under the proposed system, you rank all the candidates, and votes are re-distributed until there are two candidates who have more than 33%, and you declare those two the winners. The redistribution process works like this, and continues until all (both) seats are filled:
- If someone has more than the 33% needed to win, declare them the winner and find the sum of the votes in excess.
- Take votes-in-excess divided by total votes cast for that candidate to get a percent.
- Multiply the next-choice votes for each candidate by the percent we just found, and apply that to each of those candidates.
- If someone has more than the 33% needed to win, return to 1.
- Take the candidate with the least number of votes and redistribute their votes to the voter’s next choice.
- Go back to 1.
This is somewhat complex for the people who have to count the votes, but it’s pretty simple for the voters – just rank and let the system handle the rest.
Multi-winner ranked-choice voting ensures a couple of things. First, it ensures that “extra” votes for a candidate aren’t wasted. Second, it ensures that a tie among multiple candidates is broken properly. Third, it ensures that a large block of voters don’t win all the seats.
So what are the proper criteria for multi-seat representation? The biggest that the current system fails at, is ensuring that the elected candidates are representative of the voters. Under the current system, 51% of the population could have 100% of the seats, when instead you would probably want them to have 51% of the seats. Under multi-winner ranked-choice voting, the people elected to the seats are much more likely to be proportional (this difference would be much more pronounced if the four at-large seats were all chosen at once instead of two per year, but what can you do).
The second biggest criteria is that a small group shouldn’t be able to overpower the will of the majority because of differences in strategy. Here the two-stage plurality-at-large system somewhat fails; split votes can hurt you badly, and fielding too many candidates in the primary means that even a majority can be edged out by a minority that’s voting strategically. Of course in the end this difference in strategy means that everyone adopts the optimal strategy, and I’m really not sure how much of a concern this is in the current system.
To the elections!
When Does RCV Make a Difference?
There has been an at-large election every odd-numbered year for at least the last ten years (likely much further than that, but I wasn’t able to quickly find when the City Council adopted its current make-up and don’t know how at-large special elections are done). From the data available on this page, I will be looking at seven general elections for fourteen seats, and five primaries for twenty slots on the ballot (as there’s no data for 1999, and there weren’t enough candidates to require a primary in 2005). It’s somewhat hard to compare the two systems; in plurality-at-large a candidate can get (at most) 50% of the votes cast. However, the number of votes that a candidate gets doesn’t reflect the same thing as in RCV, because it’s a combination of the voters’ first and second choices – a candidate who gets all of the second-choice votes would not necessarily be sent on to get a seat under RCV (though it’s fairly likely). With that in mind, I won’t be comparing the two systems directly, instead only looking at the margins by which a winner is chosen.
General Elections
The general elections are routinely pretty close. No candidate in the history I’m looking at was elected to one of the at-large seats by having less than 25% of the vote, which means that no candidate in that history had less than half the first and second choices of the voters. Mathematically speaking, the lowest percent of the vote you could get and still win a seat is 16.7% (in ranked terms, which the current elections don’t have a way for you to express, you could actually win with 16.7% of second-choice votes).
It seems relatively rare for a candidate to break the 33% barrier; only three of the twelve contested seats have been won by candidates getting that high of a percent. Even lowering the barrier to 30% only raises it up to five of twelve. Remember that 30% of the vote is equivalent to about 60% of the first and second choice rankings – which is not a terribly good basis for electing someone, because it’s very possible that someone with 30% first-choice and 2% second-choice could lose to someone with 3% first-choice and 30% second-choice.
Here’s the short answer to whether ranked-choice voting would ever have made a difference in the municipal multi-winner general elections: we have no way of knowing, but it’s possible that the outcomes of all but one of them would have been different. The one exception to this is the 2011 election, which would have had the same outcome no matter what arrangement of hypothetical first and second choice votes you use. It’s also incredibly unlikely (though mathematically possible) that Don Ness would have lost the 2003 election. To make that election come out with Ness as the loser using ranked-choice methods, we would have to make some very specific assumptions about who voted in what way and what their ranks are.
So with the caveat that we can’t really know what people meant by their vote, let’s look at what I think is probably the most telling number; the difference in percent between second place and third place – in other words, the difference between getting a seat and not getting a seat.
| Year | Second | Third | Difference |
| 2011 | 35.92 | 13.14 | 22.78 |
| 2009 | 25.45 | 24.91 | 0.54 |
| 2007 | 26.52 | 24.16 | 2.36 |
| 2005 | 23.78 | 22.61 | 1.17 |
| 2003 | 25.90 | 22.67 | 3.23 |
| 2001 | 25.62 | 23.33 | 2.29 |
Looking at that data, it certainly seems that some of these races were quite close – some within 200 votes. So with one exception (2011), we can see that all of these were close – close enough to have made a difference. In nearly all these cases, we have “wasted” votes far in excess of the maximum cap set by the ranked-choice method (33.3%+1). In fact, we have “wasted” votes that are in most cases an order of magnitude higher than the difference between the winner and the loser (considering a “wasted” vote as one which did not go to one of the winners or the person in third place).
Theoretical Results
So let’s talk about what the actual differences in outcome would be in between the two systems in a purely theoretical world. Imagine that we’re looking at a utopia that has all the solutions to all of life’s problems … except for one. This one problem is the only issue that the elections are about. There are extremists on both sides of the issue, but the people themselves make up a bell curve, with the majority of people in the center (though leaning slightly to one side).
So what does two-stage plurality-at-large produce? If we pretend that there are a hundred candidates in the running, two-stage plurality-at-large will elect two people who are close to the center but a little bit to the left (same as the population as a whole). So far that sounds pretty good. Who does this implementation of ranked-choice voting elect? Most likely it’ll take one person from slightly to the left of the issue and one person from slightly to the right, if we assume infinite ranking and that every person will rank candidates according to how close they are to the voter’s preference (ex. If my first choice is 5, I will rank like so: 5>4>6>3>7>2>8).
Here’s another hypothetical situation: we have the same utopia as before, with the same single issue that they base their entire election one. But this time, instead of public opinion being a bell shape, it’s an upside down bell shape. In other words, there are almost no moderates at all, and pretty much everyone is far to the right or far to the left, with a very slight preference for left over right.
In this hypothetical, two-stage plurality-at-large will produce a perverse result; it will give both seats to people on the far left, even though they only make up a slim majority. Ranked-choice voting, on the other hand, will elect one person from the left and one from the right. (It’s arguable that the best outcome here would still be to take two people from the middle, because they’re most likely to find some kind of compromise. There are a couple of voting systems that produce that outcome, such as the Schulze Beatpath method, Simpson-Kramer method, or Tideman method. Those are all ranked-choice methods, but none of them are being proposed in Duluth, so I’m skipping them for now.
In the real world, there are hundreds of different policies, incomplete information, and a limited selection of candidates. As one might expect, this complicates things immensely. The principles are generally the same though; the system we have now tends to take people from the middle if there’s general agreement and from one extreme if there’s disagreement. This implementation of multi-seat ranked-choice voting tends to take people from either side of the middle if there’s general agreement and from both extremes if there’s disagreement.
So which is better? In a vacuum, I don’t think I would prefer one over the other. When it’s paired with single-seat first-past-the-post and a fairly pervasive oppositional mentality, I think I like the ranked-choice system a lot more. I think people in general would like it more as well; see Question 28 of this Suffolk University poll of Massachusetts about whether people see the benefit to having one Democratic senator and one Republican senator. That is, unfortunately, the best that I can do as far as data on that issue; if you’ve got more hard data on that issue, I would love to take a look.
Extra: Does Bullet Voting Happen?
Bullet voting is when you only use one of your multiple votes. There’s good reason to do so; let’s say that you really really like one candidate and feel pretty good about a second one. If you vote for both, there’s a decent chance that the candidate you feel pretty good about will win at the expense of the candidate you really really like. The more people bullet vote, the more the election tends to have unrepresentative outcomes.
So, does bullet voting happen? It’s hard to say. In theory, the number of ballots cast should be equal to half the number of votes. If there’s a difference between the two, that doesn’t necessarily mean that bullet voting took place. It might mean that people didn’t vote for any candidate, usually if they lacked information about who was running and what they stood for, but wanted to vote for some other race. I would guess this is usually not the case in these municipal elections, because there usually aren’t items on the municipal ballot that are hugely more important and/or exciting than the councilor seats (with the exception being the mayoral seat, but even that isn’t much more popular).
I put all the data into a spreadsheet in Google Docs for both the primary and general elections. In short, the worst case scenario is that about 16% of the voters in the general and 14% of the voters in the primaries are bullet voters. Take from that what you will. I think the number of “true” bullet voters (those who are bullet voting intentionally even though they have an opinion about who their second choice is) is probably more likely 6-7%, and that’s about the level it’s at in those elections where one of the only things on the ballot is the council memberships.
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Would Ranked-Choice Voting Make a Difference in Duluth Municipal Elections? Part 2