The Case Against Ranked-Choice Voting: Part I
There has been an increase in interest in exploring voting systems other than the first-past-the-post (FPTP) system common in US elections. I consider this a welcome (although delayed) initiative. However, I'm concerned that efforts so far have focused exclusively on ranked-choice voting (RCV) at the exclusion of the alternatives. Although I strongly prefer RCV to FPTP, I think that there are significant drawbacks to RCV that haven't gotten enough public debate. I think this is the reason that in many cases voters have adopted RCV only to dump it a few years later.
In this post, I argue the case against ranked-choice voting, pointing out that it has many defects that are undesirable for a voting system. This post discusses these problems in theoretical elections. In the following post, I will show how these can or have happened in real elections. In a third post, I will discuss an alternative to RCV - approval voting - and show how it remedies many of the issues with ranked-choice voting.
Introduction to Ranked-Choice Voting
Ranked-choice voting is a system where voters rank the candidates in order from their favorite to least favorite. Then the votes are tallied for the top candidate on each ballot. If no candidate wins a majority of the votes, candidates with the least votes are eliminated and the votes then go to the next candidate on each of the ranked ballots. Thus it is like having an instant runoff election, which is why this process is also known as instant runoff voting. There are some variations to this approach (like how many candidates to remove each round), but this is the general idea.
Proponents of ranked-choice voting, such as FairVote, make many claims about the benefits of ranked-choice voting. They claim that it reduces strategic voting, provides more choice because voters don't have to worry about vote splitting, and prevents 3rd-party candidates from "spoiling" an election. Unfortunately, I don't think all these claims are true. Many of these negative effects still happen with ranked-choice voting. In this post, I will be simulating elections using VoteSim, a free and open-source library for simulating elections. The code to run the simulations in this blog post is available here.
Judging an Electoral Process
Before we get into looking at particular methods, I think it makes sense to discuss what makes a good or bad electoral system. It's hard to know exactly how to judge an electoral process. Part of it depends on whether the "correct" candidate won, and it's not always easy to know who that candidate is. However, I think some aspects of voting systems are clearly good or bad, so let's start with those.
Here are some things that I think are good:
The majority of voters approve of the elected candidate over any other candidate. Another way of saying this is that there is no losing candidate whom a majority of voters would have preferred over the winning candidate. Systems that do this are known as "Condorcet methods".
Voters can vote for their true preferences without worrying that voting in a different order would result in a better outcome.
The method should be easy to understand. There is a tradeoff between simplicity and sophistication that has to be carefully considered.
Here are some things that I think are bad:
Systems that allow for "spoiler candidates" where the addition of a candidate hurts the chances of similar candidates.
Systems that encourage strategic voting. This is the opposite of the point above about voters being able to vote their true preferences. In some systems, voters can get a result they would prefer by voting differently than their preferences.
These seem like fairly simple criteria where any system could allow the good and avoid the bad. But as we'll see, it is more difficult than it seems and many systems, including ranked-choice voting, fall short.
Drawbacks of Ranked-Choice Voting Systems
Ranked-Choice Voting Encourages Strategic Voting
Let's start with the idea of strategic voting.
Imagine a simple election between three candidates running for one position. We'll call the candidates Alice, Bob, and Charlie. Let's not worry about specific political parties, we'll just say that Alice and Charlie are in opposite camps and Bob is somewhere in the middle.
I'm going to use small numbers of voters for these simulations so the numbers are easy to follow. But you could imagine each "voter" actually being 1,000 or any other number of voters and the results would all be the same. Let's imagine there are ten voters. Four of the voters prefer Alice, four prefer Charlie, and two prefer Bob. All voters who prefer Alice or Charlie prefer Bob to the other camp's candidate. Those who prefer Bob prefer Alice as the second-choice candidate. Here's what the ballots would look like:
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Bob, Alice
Ranked ballot: Bob, Alice
Ranked ballot: Charlie, Bob
Ranked ballot: Charlie, Bob
Ranked ballot: Charlie, Bob
Ranked ballot: Charlie, Bob
Let's look at how this election would play out using ranked-choice voting.
ROUND 1
Candidate Votes Status
----------- ------- --------
Alice 4 Active
Charlie 4 Active
Bob 2 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Alice 6 Elected
Charlie 4 Rejected
Bob 0 Rejected
Alice won the election and the Charlie voters are disappointed. They would have been fine with Bob, but are not happy with Alice. Let's reimagine that election but now, the voters for Charlie are going to be more strategic. Two of the Charlie supporters change their ballots to vote for Bob as their first candidate and Charlie as their second candidate. Let's see how this plays out.
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Bob, Alice
Ranked ballot: Bob, Alice
Ranked ballot: Bob, Charlie
Ranked ballot: Bob, Charlie
Ranked ballot: Charlie, Bob
Ranked ballot: Charlie, Bob
ROUND 1
Candidate Votes Status
----------- ------- --------
Bob 4 Active
Alice 4 Active
Charlie 2 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Bob 6 Elected
Alice 4 Rejected
Charlie 0 Rejected
Now, Bob wins the election. This isn't exactly what the Charlie voters wanted, but they prefer it to having Alice win. But the problem is they got it by voting disingenuously. They voted differently than their true preferences and got a better result. Thus, in this case, ranked-choice voting benefited people who voted strategically.
Ranked-Choice Voting Doesn't Always Result in the Favored Head-to-Head Candidate
As mentioned above, one measure of a good voting system is that the result of the election is the same if it was a head-to-head matchup of the winning candidate and any other candidate. But ranked-choice voting doesn't do this. To see, let's go back to the ballots that got Alice elected.
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Bob, Alice
Ranked ballot: Bob, Alice
Ranked ballot: Charlie, Bob
Ranked ballot: Charlie, Bob
Ranked ballot: Charlie, Bob
Ranked ballot: Charlie, Bob
ROUND 1
Candidate Votes Status
----------- ------- --------
Alice 4 Active
Charlie 4 Active
Bob 2 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Alice 6 Elected
Charlie 4 Rejected
Bob 0 Rejected
Let's calculate what the results would have been in a head-to-head election.
Head-to-head Election Results:
Alice: 4
Bob: 6
Head-to-head Election Results:
Bob: 6
Charlie: 4
In the ranked-choice election, Alice won, but we can see that in a head-to-head election, Bob would have won against either Alice or Charlie.
Ranked-Choice Voting Allows for Election Spoilers
As I said above, one undesirable aspect of voting systems is if they allow for "spoiler candidates". The best way to check if there was a spoiler candidate is to remove a losing candidate from the election and see if it changes who won. If so, then by entering the election they "spoiled" it for the other candidate. To see it in this election, let's imagine Charlie didn't run by taking the ballots from before but removing every instance of his name from the ballots.
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Alice, Bob
Ranked ballot: Bob, Alice
Ranked ballot: Bob, Alice
Ranked ballot: Bob
Ranked ballot: Bob
Ranked ballot: Bob
Ranked ballot: Bob
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Bob 6 Elected
Alice 4 Rejected
Bob wins. But when Charlie was in the election, Alice won. Therefore the candidacy of Charlie spoiled the election for Bob.
Ranked-Choice Voting Allows for Candidates to Receive Higher-Ranked Votes but Have Worse Outcomes
This is a very odd situation and I didn't believe it until I really studied the data. But there are times when a candidate can receive higher-ranked votes and end up doing worse in an election.
Let's imagine the scenario of a primary election with four candidates in it, each candidate hailing from one of four districts. The four candidates are Alice, Bob, Charlie, and Dan. Alice is from District 1, the largest district, and has lots of experience; she is considered the frontrunner for the race. Bob is from District 2, which is slightly smaller, but also has lots of experience and is the other main contender. Charlie is from District 3, which is smaller than 1 or 2. He isn't well-known outside of his district. Dan is the candidate from District 4. He is popular in District 4 but completely unknown outside of it.
District 1 is the largest and wealthiest district of the four in the region. The voters prefer the mainstream candidates, Alice and Bob. They have seven voters who all rank the candidates: Alice, Bob, Charlie, and Dan.
District 2 is somewhat smaller but very similar to District 1. Traditionally, the entire region has been represented by candidates from either District 1 or District 2. District 2 voters are similar to District 1 voters, except that they prefer their hometown candidate, Bob. They have six voters who all rank the candidates: Bob, Alice, Charlie, Dan
District 3 is smaller than 1 and 2 but is still fairly wealthy and the citizens feel generally included in the region's governance, although the representative is rarely from this district. The voters prefer their candidate, Charlie, but would also accept Bob or Alice. Out of those two, they prefer Bob because they see District 1 as too large and powerful already and don't want it to have more power. They have five voters who use the following ranking: Charlie, Bob, Alice, Dan
District 4 is smaller and much poorer than the others and the voters there feel completely ignored by the mainstream candidates. The elections have gone to candidates from Districts 1 and 2 for ages and they want something, anything, different. They have three voters and their ranking is: Dan, Charlie, Bob, Alice.
Ranked ballot: Alice, Bob, Charlie, Dan
Ranked ballot: Alice, Bob, Charlie, Dan
Ranked ballot: Alice, Bob, Charlie, Dan
Ranked ballot: Alice, Bob, Charlie, Dan
Ranked ballot: Alice, Bob, Charlie, Dan
Ranked ballot: Alice, Bob, Charlie, Dan
Ranked ballot: Alice, Bob, Charlie, Dan
Ranked ballot: Bob, Alice, Charlie, Dan
Ranked ballot: Bob, Alice, Charlie, Dan
Ranked ballot: Bob, Alice, Charlie, Dan
Ranked ballot: Bob, Alice, Charlie, Dan
Ranked ballot: Bob, Alice, Charlie, Dan
Ranked ballot: Bob, Alice, Charlie, Dan
Ranked ballot: Charlie, Bob, Alice, Dan
Ranked ballot: Charlie, Bob, Alice, Dan
Ranked ballot: Charlie, Bob, Alice, Dan
Ranked ballot: Charlie, Bob, Alice, Dan
Ranked ballot: Charlie, Bob, Alice, Dan
Ranked ballot: Dan, Charlie, Bob, Alice
Ranked ballot: Dan, Charlie, Bob, Alice
Ranked ballot: Dan, Charlie, Bob, Alice
ROUND 1
Candidate Votes Status
----------- ------- --------
Alice 7 Active
Bob 6 Active
Charlie 5 Active
Dan 3 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Charlie 8 Active
Alice 7 Active
Bob 6 Rejected
Dan 0 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Alice 13 Elected
Charlie 8 Rejected
Bob 0 Rejected
Dan 0 Rejected
Alice wins the election.
The next election comes along and it's the same candidates and the same voters. However, during this campaign, Alice decided to reach out to District 4 and put extra effort into getting their votes. Through her hard work, she convinces them to put her second (behind Dan) on the ballot. So the voters from District 4 preferences are now: Dan, Alice, Charlie, and Bob. Given that Alice won the previous election and her approval has only increased, how would this affect the results?
ROUND 1
Candidate Votes Status
----------- ------- --------
Alice 7 Active
Bob 6 Active
Charlie 5 Active
Dan 3 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Alice 10 Active
Bob 6 Active
Charlie 5 Rejected
Dan 0 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Bob 11 Elected
Alice 10 Rejected
Charlie 0 Rejected
Dan 0 Rejected
Stunningly, this change has knocked Alice out of office. The only change here is that voters ranked Alice higher, but now she's lost an election that she otherwise would have won. In election parlance, this is known as violating the "monotonicity criterion".
Results from Real Races
In this post, I've looked at simplified examples to highlight specific issues. After reading this, one could easily argue that these are obscure edge cases that would never happen in a real election. However, these results are more than merely theoretical. In the next post, we'll look at a real ranked-choice election, the 2009 election for mayor of Burlington, Vermont, and see that these defects are present.