Ranked choice voting
Common Core Standards and Mathematical Practices
7th Grade: Number Systems
7NS.A1 Apply and extend previous understandings of addition and subtraction to add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Mathematical Practices
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Modeling with Mathematics
Learning Objectives
Students will be able to...
Differientiate Ranked Choice Voting methods from majority and plurality voting methods.
Calculate the results of an election using different Ranked Choice Voting (RCV) methods.
Explain the differences between different RCV methods (Instant Runoff, Borda Count, and Condorcet Method)
Identify Pros and Cons of RCV methods.
Apply RCV methods to real world examples.
What is Ranked Choice Voting (RCV)?
In RCV, there are different methods to tally the votes, and we will discuss three of the most popular ones:
Instant Runoff Voting
Candidates are eliminated sequentially if they are in last place, until a final two are found. Then, the winner is chosen by simple majority.
IRV.pdfBorda Count
Ballot rankings are assigned point values, then total points are tabulated.
Borda Count.pdfCondorcet Method
Candidates are compared to each other candidate and the candidate who wins the most matchups wins the election.
See this page to learn about how ties are handled.
Condorcet Method.pdfStrange Examples
What are the pros and cons of RCV?
As the above examples suggest, RCV methods can be problematic. Watch this video to explore the problems with each voting method, and to introduce Arrow's Impossibility Theorem:
Pros / Why should we use RCV?
RCV more fully shows a given voter's full preference rather than simply their top choice as in plurality.
RCV could ensure a winner has the approval of the majority of voters.
RCV would eliminate the need for primaries.
Candidates are more likely to reach out to voters in-person.
A competitive RCV election can drive turnout.
Cons / Why don't we use RCV?
Voters could intentionally rank candidates to move a different candidate lower down.
Instant-runoff fails monotonicity.
Borda count does not satisfy the majority condition.
Borda count does not satisfy the independence of irrelevant alternatives.
Condorcet does not always generate a winner.
Where is RCV used?
Sample RCV ballot from Northern Ireland
In the U.S.:
RCV currently is used in cities and counties in California, Colorado, Maryland, Massachusetts, Michigan, Minnesota, New Mexico, Oregon, and Utah for mayoral and city elections primarily. RCV is also used statewide in Maine for their House and Senate elections, gubernatorial elections, etc.
In other countries:
Forms of RCV are used in Australia, Fiji, Malta, New Zealand, Northern Ireland, Papua New Guinea, the Republic of Ireland, Scotland, and the United Kingdom.
Check out this graphic that shows what years different U.S. cities have held elections using a form of ranked choice voting!
And here is a more detailed list with information about what elections in each state are determined by RCV.
Example of Local Elections:
In 2004, San Francisco began using Instant-Runoff Voting for local elections. Ranked-choice voting is used in all elections for mayor, assessor-recorder, city attorney, district attorney, public defender, sheriff, treasurer, and the board of supervisors.
Fun Examples of RCV
Colleges and Universities:
These colleges and universities use RCV. RCV is very common in student governments. Why do you think so many student governments use Ranked Choice systems instead of majority voting?
Eurovision:
Eurovision (the European song contest) chooses its winner based on "televoting" (people at home text or call in their votes) and jury voting (professionals from each country vote, too). Professional juries and televoters from each country each award 1, 2, 3, 4, 5, 6, 7, 8, 10, or 12 points to different countries. The televoting and jury scores are averaged together, and the country with the most points wins!
How is the Eurovision voting system a modified Borda Count method?
The Olympic Host City:
The Olympic host city is voted on by the International Olympic Committee. Here's a description from the vote for the 2020 host city:
"The eligible IOC members are asked to vote. In each round each participating IOC member may vote for only one city... If, after the first round of voting, no city obtains the absolute majority of the votes cast, as many rounds are held as necessary for a city to obtain such majority. The city receiving the least number of votes leaves the competition. The name of this city is made public straight away and the vote continues. If only two cities remain in contention, the one that obtains the greatest number of votes is elected."
What voting methods do you see in this process?
The Oscars:
The Oscars uses Instant Runoff Voting.
When the Oscars decides on the best movie of the year, is it more likely to choose a "safe" movie because of its voting method? Should the voting method be changed so that controversial movies can win?
Major League Baseball: MVP
The Baseball Writers Association of America uses a modified Borda Count method to rank their top ten players. First place is awarded 14 points and second through tenth are awarded 9, 8, 7, 6, 5, 4, 3, 2, and 1 points.
Is the MVP voting system the same as Eurovision's?
Further Resources
You can use this site to explore how IRV, Borda, and Condorcet function more visually.
You can use OpaVote to create a ranked choice election for your class.
You can listen to this podcast from the RCV Resource Center to learn more about the basics of RCV, drafting legislation, election verification, campaigning as a ranked choice candidate, etc.
FairVote is a great resource that we used throughout this module.
This video explains how instant runoff works.
Discussion Questions
Suppose you and your friends are planning to go out to eat. You love Indian food, but this is the second choice for most of your other friends and it does not have many first-place votes. A few others are advocating for Thai, and a few others for Mexican. You have a good idea of your friends’ preferences, so which voting method should you push for to influence the group to decide on Indian? Why?
Is there a state or local election near you that uses RCV? Is there a school or company near you that uses RCV?