How Ranked-Choice Voting elects extremists
Instant-Runoff Voting is a voting method where voters rank candidates, who are then eliminated in a series of simulated runoff elections. It’s also known as “Ranked-Choice Voting” in the US, “Preferential Voting” in Australia, and “The Alternative Vote” in the UK (though there are many other preferential/ranked-choice voting systems, so I’ll use “IRV” here to avoid confusion).
It’s the most commonly-proposed reform in the US (the only reform that many have heard of, in fact), with the promise that it will eliminate the spoiler effect, promote consensus candidates, etc. Unfortunately, these claims are exaggerated, and IRV doesn’t really fix these problems. In this article, I’ll illustrate one of its worst failure modes.
In these diagrams, the voters and candidates are spaced along a one-dimensional opinion spectrum, and the voters prefer the candidates whose beliefs are most similar to their own. (This could be any spectrum of opinion, though, not necessarily the typical left-right political spectrum.) Of course, real political opinions are multi-dimensional, but the 1D case is easiest to illustrate, and the same problems happen in more dimensions, too.
The ideal voting system would be truly representative: When the population moves to the left, a more left-wing candidate wins. When the population moves right, a more right-wing candidate wins. If the population ventures out along some other dimension, the winner of the election should change along with them, so that it’s always choosing the best representative of the will of the people.
Unfortunately, most voting systems used in the real world do not behave this way when there are three or more strong candidates. First-past-the-post, Two-round system (“Jungle primary”), Contingent Vote, Supplementary Vote, and Instant-Runoff Voting (“RCV”) are all based around counting first preferences only, and therefore suffer from vote-splitting, which can eliminate the most-representative candidate and elect someone else instead, even though a majority of voters preferred the eliminated candidate over the winner.
In this animation, there are five candidates (represented by triangles), spaced along the political spectrum, each with different ideologies. The distribution of voters along the spectrum isn’t important — the same problem can happen regardless — but to make it as realistic as possible, the ideologies of the voters are represented by a bell curve:
With the population in this position, the Green candidate is the best representative of the will of the voters. Green has the highest approval rating, and would beat any other candidate in a head-to-head election, because in each case, they would appeal to a broader set of voters than their opponent:
Likewise, Blue would beat any candidate except Green, Orange would beat any candidate except Green and Blue, etc. When the preferences of the voters are combined, they show a clear, unambiguous order, with no cycles or ties: Green > Blue > Orange > Red > Yellow.
Yet IRV eliminates Green first!
This is because IRV ignores the opinions of some voters when choosing who to eliminate: It only pays attention to first-place preferences in each round, just like a FPTP election, which means it suffers from the same problems as FPTP in each round.
After Green is eliminated, voters who selected Green as their first choice have their second-place votes counted, which transfer to either Blue or Orange, depending on whether the voter was left or right of average.
Among the four remaining candidates, Orange and Blue are preferred by most voters over the more-extremist Red and Yellow, yet IRV eliminates them, too! Orange is eliminated, with their 2nd and 3rd-place votes transferring to Blue and Yellow, and then Blue is eliminated, with their 2nd and 3rd-place votes transferring to Red and Yellow.
Here’s an alluvial diagram showing how votes transfer outward from the more-representative candidates to the less-representative candidates in each round:
Now, in the final round, only Red and Yellow — the least-representative, most-polarizing candidates — are left. Among the remaining two candidates, Red has majority support from 51% of the electorate, and wins the election.
But this “majority support” only exists because all the better candidates were eliminated! If there are only two candidates left, there will of course be one that is preferred by a majority, even if voters dislike both candidates overall.
In this case, Red wins the election, even though:
- 69% of voters preferred Blue over Red
- 64% of voters preferred Green over Red
- 57% of voters preferred Orange over Red
- Red was ranked last by 49% of the voters
Is that really a democratic outcome?
Likewise, if the voters had shifted their opinions a small amount to the right, then Yellow, the opposite extremist (from the perspective of the voters), would have won the final round instead. Is it democratic for a small change in voter ideology to produce such a huge swing in power? Is it good for the stability of a government?
Does this happen in every IRV election? No. When used in a two-party system, in elections with only two strong candidates, the lesser fringe candidates will be eliminated correctly, and their votes will transfer to one of the main two in a logical, representative way. This is the scenario that people are thinking of when they say that IRV “eliminates the spoiler effect”.
But many of us want to end the two-party system, so that there can be three or more strong candidates, representing different ideologies, and IRV doesn’t cope well with this. As soon as one of the minor parties becomes more popular (because the voter population shifted towards their ideology), IRV can fail and elect unrepresentative candidates, sometimes changing the winner in the opposite direction of the voters’ movement.
For example, if the five candidates’ positions in the above election were slightly shifted, the more moderate Orange could win:
or the more moderate Blue could win:
or the consensus candidate Green could win:
even though the voters haven’t changed their ideological positions at all! The outcome of an IRV election with several strong candidates doesn’t do a good job of tracking the will of the voters; it’s essentially random, which is not what we want from a democratic reform.
When people say that IRV is “highly resistant to strategy”, this is what they mean: The outcome of IRV is highly random and unpredictable, making it hard to know whether strategically changing your support for a candidate will help them win, or help them lose. But the outcome isn’t even representative of the voters when they all vote honestly, which means that this is a bug, not a feature.
Better ranked-choice methods
The good news is that there are lots of other voting methods that don’t have this problem.
For purposes of illustration, I’ll start with a very small modification to IRV that fixes this particular problem (though it has problems of its own, and I’m not recommending we actually do this; it’s just an illustration).
Coombs’ method uses the same ranked ballots as IRV, and chooses a winner in a similar way: “eliminate the worst candidate in a series of simulated runoffs”. The only difference is that it uses a different definition of “worst candidate”:
- IRV: Eliminate the candidate ranked first by the fewest voters
- Coombs: Eliminate the candidate ranked last by the most voters
Yet this small change in definition has a huge effect on the outcome: The unrepresentative extremists are eliminated first, since they get ranked last by a lot of voters, and their votes transfer inward to the most-representative candidates:
Alluvial diagram showing the vote transfers toward the consensus candidate:
Green wins, which makes sense, since voters prefer Green over every other candidate (“Condorcet winner”), Green has the highest overall approval rating (“Utilitarian winner”), and Green is the closest match to the ideology of the electorate as a whole.
There are dozens of other voting methods that use ranked-choice ballots, which don’t have the huge problems that IRV has. If you really love ranked-choice ballots, pretty much any of these would be an improvement over IRV.
As another example, this ability of IRV to eliminate all the best candidates and elect the second-worst was actually noticed in 1882 by mathematician Edward Nanson, which spurred him to create his own variant instant-runoff method that doesn’t suffer from these flaws.
In the modern world, the most highly-regarded ranked methods seem to be the Condorcet methods known as Ranked Pairs and Schulze Method. These essentially do a simulated round-robin tournament, seeing if any candidate beats all the others.
Any of these methods would correctly choose Green in the above elections, and they aren’t affected by small changes in the positions of the other candidates. These are the same candidate ideology positions shown in the examples above, though now Green wins each time:
The downside of Condorcet methods is that they’re more complicated to calculate and explain, which might reduce voter confidence in the results. But if you want ranked-choice ballots and representative outcomes, that’s the price of democracy.
STAR Voting
Luckily, there are simpler alternatives that are still much better at finding the most-representative candidate than IRV. Instead of ranked ballots, they use rated ballots, which allow voters to express both strong and weak preferences between candidates, or say that they like two candidates equally.
The most promising rated method is STAR Voting, which is a hybrid of Score Voting and Instant-Runoff, providing much more representative outcomes while still being resistant to strategic voting.
In STAR Voting, you rate each candidate on a scale from “Worst” to “Best”, and you can give multiple candidates the same rating, or skip a rating to express a strong preference:
The tallying is simpler than IRV or Condorcet methods: Add up all the scores for each candidate, and select the two highest-rated as finalists. Then select the finalist who was rated higher by more voters.
In all of the above examples, the STAR finalists would either be Green/Blue or Green/Orange, and Green would win, as they should. If the population moves to the left, the winner will shift to Blue and then Red, if the population moves to the right, the winner will shift to Orange and then Yellow, as they should.
It’s simple to vote, simple to count, and the winner is always a much better representative of the voters.
I was told I should write a conclusion
Ok, so I guess it’s this:
Instant-Runoff Voting (“RCV”) is somewhat better than our current system, but it can still elect very poor candidates, in exactly the kind of elections that we hope to see more of in the future. There are dozens of other voting methods that have been invented in the following 150 years that work much better. Don’t push for IRV just because it’s the first voting reform you heard of, or because it “has momentum”. (First-past-the-post has the most momentum, after all, and it sucks.) Research the other options and choose one that actually produces a democratic, representative outcome. Because otherwise, what’s the point?
[All images created by me, and licensed as CC0, unless otherwise specified]
