In this article, we'll take a look a some real-world RCV elections and see how they compare to plain old plurality elections.

San Francisco

San Francisco, California adopted ranked-choice voting in March 2002, and it has been used in every local election since 2004. Voters use a single-winner form of RCV, instant-runoff voting (IRV), to elect most local offices, including:

• Mayor
• Assessor-Recorder
• City Attorney
• District Attorney
• Public Defender
• Sheriff
• Treasurer
• Members of the Board of Supervisors

In 2020, RCV was used to elect several members of the board of supervisors (equivalent to city councils in Indiana). Let's take a look a one of these elections.

Board of Supervisors District 7

In this district, seven candidates competed for one seat. The first-choice votes were as follows:

If this was a straight plurality election, as in Indiana, the tally of first-choice votes shown above would be the end result. The candidate with the highest number of votes (Joel Engardio) would be declared the winner, even though over 75% of voters preferred someone else. The effectiveness of such an election would be relatively low, at 21%.

How does IRV work?

In general, voters rank the candidates in order from their most preferred to least preferred. Then everyone's 1st choices are counted. If any candidate has a majority of votes in any round of vote tabulation, then they have won and the election is over. But if no one has a majority, then the candidate with the lowest number of 1st choice votes is eliminated and their votes go to the voters' next highest choice. This process continues until a candidate has a majority of votes or only two candidates remain. In that case, the one with the greater number of votes wins.

By using ranked-choice voting, the effectiveness of this election was increased to 41.7%!¹ Basically doubling it! Thanks to ranked-choice voting, voters in San Francisco have more choices, more competition, and more effective elections.

The Euler diagrams comparing the effectiveness of the 1st and 6th (final) round for San Francisco's 7th district election.

Cambridge

Cambridge, Massachusetts has been using RCV for city council and school committee elections since 1941. For these elections, a multi-winner form of RCV is used: the single transferable vote (STV). This form of RCV is also a method of proportional representation, which ensures minority representation with majority control. For example, any group of voters that number more than one-tenth of the votes cast can be sure of electing at least one member of a nine-member council, but at the same time, a majority group of voters can be sure of electing a majority of the council.

The most recent RCV elections in Cambridge were the municipal elections held in 2019. Let's take a look at the results of that year's city council election.

City Council

In this election, 22 candidates competed for nine seats. The first-choice votes were as follows:

If this type of election were to occur in Indiana, plurality-at-large voting would most likely be used.² Using that system, the top nine candidates would win. Assuming this scenario, the effectiveness would be 53.3%. That might seem very good considering the effectiveness rates of the single-winner elections we've seen so far, but single-winner and multi-winner elections are different animals. As a a general rule, multi-winner elections will have higher effectiveness rates than single-winner elections.

How does STV work?

Just as in IRV, voters rank the candidates in order from their most preferred to least preferred. Once all the votes are in, a quota is calculated to determine the number of votes a candidate needs in order to win a seat.³ Any candidates who meet or exceed this quota are elected with any excess votes going to the voters' next highest choice. Then, just like in IRV, the candidate with the lowest number of votes is eliminated and those votes are transferred to the voters' next highest choice. Any candidates that now meet or exceed the quota from these transferred votes are elected and this process continues until all the seats are filled. In this way, STV maximizes vote effectiveness and minimizes waste.

Once you see how effective it is (see the diagram below), it's hard to ignore. The use of STV comes closest to the best case of 100% effectiveness than anything else we've seen!

The Euler diagrams comparing the effectiveness of the 1st and 15th (final) round for Cambridge's city council election.

But Wait … There's More!

If increased effectiveness isn't enough of a benefit to support ranked-choice voting, our next article will cover some of the other benefits that come along for the ride. Stay tuned!

Update: October 2023

While I had intended to write another article outlining some of the other benefits of RCV, life intervened and I haven't had the time to devote to this topic. That said, I do have good news to share. Greg Dennis of Voter Choice Massachusetts has republished his great article entitled Why I Prefer IRV to Condorcet. I strongly recommend this article to anyone who would like more insight into the benefits of IRV.

1. While San Francisco does not include exhausted ballots in their calculations, we are including them in ours in order to more accurately reflect the effectiveness of all votes cast—not just the votes continuing on to subsequent rounds of tabulation. In general, if exhausted ballots are excluded, the final effectiveness rate is higher than it would be otherwise. In this specific election, the effectiveness rate would be 46.9% with the exhausted ballots excluded. ↩︎
2. For the sake of the comparison, we are taking a simplified view of plurality-at-large elections and assuming all voters only vote for a single candidate. In a real plurality-at-large election, voters would have the option of voting for one or more candidates. ↩︎
3. In Cambridge, the Droop quota is used. ↩︎