Proportional Ranked Choice Voting Example

Proportional ranked choice voting (also commonly known as "single transferable vote" or "choice voting") gives voters the freedom to rank candidates in order of choice and maximizes the effectiveness of every vote to ensure that as many voters as possible will help elect a candidate they rank highly. It minimizes wasted votes and the impact of tactical voting, allows voters to have more choices, and encourages positive campaigning and coalition-building. It upholds both the principle of majority rule and of fair representation of those in the minority. Because of its proven history, its emphasis on candidates rather than parties, and its ability to allow voters to express their full, honest preferences on their ballots, ranked choice voting is the form of fair representation voting best suited for use in U.S. elections.

To Vote

Under ranked choice voting, voters rank candidates in order of choice. They mark their favorite candidate as first choice and then indicate their second and additional back-up choices in order of choice. Voters may rank as many candidates as they want, knowing that indicating a later choice candidate will never hurt a more preferred candidate.

To Determine Winners

To find out who wins, votes are counted in a series of rounds to ensure that as few votes as possible are wasted. Each round, one of two things happens: either a winning candidate is identified and elected, in which case the votes they received in excess of what they needed to win transfer to their next choices; or the candidate in last place is eliminated, in which case votes for that candidate transfer to their next choices. Additional rounds take place until each seat is filled.

First, we need to know how many votes are enough to guarantee victory, which we call the election threshold. That threshold is the number of votes that mathematically guarantees that the candidate cannot lose. For example, if three candidates will be elected, the threshold is 25% of votes. That's because if one candidate has more than 25% of the vote, it is impossible for three other candidates to get more votes than them (because that would add up to more than 100% of votes). If four candidates will be elected, the threshold is 20% of votes. If five candidates will be elected, it is about 17% of votes.

Initially, every vote counts for its first choice only. If enough candidates have more votes than the threshold to win so that every seat is filled, then those candidates win and the vote counting is over. Otherwise, votes are counted in rounds as follows:

If any candidates have more votes than the election threshold, they are elected. The number of votes they received in excess of the threshold then are added to the totals of continuing candidates. This works by adding a fraction of each vote for the elected candidate to the totals of the candidate ranked next. For example, if a candidate has 10% more votes than the election threshold, every one of their voters will have 10% of their vote count for their next choice. That way, voters aren't punished for honestly ranking a very popular candidate first.

If no candidate has more votes than the election threshold, the candidate with the fewest votes is eliminated. When a voter's top choice is eliminated, their vote instantly counts for their next choice. That way, voters aren't punished for honestly ranking their favorite candidate first, even if that candidate cannot win.

The process of counting surplus votes and eliminating last-place candidates repeats until all seats are filled. Here is a flowchart that summarizes the process:

This method of counting is performed by hand in many places, though it can also be quickly administered using existing voting machines.


The chart below shows the results of a partisan race using ranked choice voting. Six candidates are running for three seats in a hypothetical district where 9,200 votes are cast. Candidates Cathy Chan, Armando Perez, and Brad M. Jackson are Democrats, while candidates Hannah Murphy, Charles Lorenzo, and June Smith are Republicans. The district is majority Democratic; the Democratic candidates collectively earn 60% of first choices. However, there are a substantial number of voters who prefer the Republicans.

In this simulation, Perez is the most mainstream Democratic candidate, while Jackson and Chan have support among Democrats, Independents, and even some Republicans. Similarly, Lorenzo and Smith are both mainstream Republicans, while Murphy has support among Republicans, Independents, and some Democrats.

With 9,200 voters, the election threshold is 2,300 votes (25% of 9,200).


Round 1: Armando Perez has more votes than the threshold and wins the first seat.

A count of first choices elects the most popular Democratic candidate, Armando Perez. Perez has 200 more votes than the threshold, so 200 votes will transfer to other candidates. This will work by transferring 8% of every Perez voter's ballot to its next choice (because Perez's 200 surplus votes divided by his 2500 total votes = 8% of each vote). Of the 2,500 voters who ranked Perez highest, 1,250 ranked Cathy Chan next; 1,000 ranked Brad Jackson next; and 250 ranked Republican Hannah Murphy next. As a result, Chan's total increases by 100 votes (8% of 1,250); Jackson's total increases by 80 votes (8% of 1,000); and Murphy's total increases by 20 votes (8% of 250) in the following round. Perez keeps the other 92% of every ballot as his vote total, which is equal to the election threshold of 2,300 votes.

Round 2: June Smith has the fewest votes and is eliminated.

After Perez's votes transfer to their next choices, no candidate is above the threshold. As a result, the weakest candidate, June Smith, is eliminated. Votes counting for Smith are added to the totals of their next choices. Of the 1,000 voters who ranked Smith highest, 580 ranked Hannah Murphy next, 300 ranked Charles Lorenzo next, 100 ranked Cathy Chan next, and 20 ranked Brad Jackson next.

Round 3: Brad Jackson has the fewest votes and is eliminated.

After Smith's votes transfer to their next choices, still no new candidate is above the threshold. Now, the weakest candidate is Democrat Brad M. Jackson. He is eliminated, and votes counting for him are added to the totals of their next choices. Of the 1,450 voters who ranked Jackson highest among the remaining candidates, 1,250 ranked Cathy Chan next; 150 ranked Hannah Murphy next; and 50 ranked Charles Lorenzo next. Some of these voters may have ranked Armando Perez or June Smith next, but as those candidates are elected and eliminated respectively, ballots that would count for them move on to their next choice instead. (Note: 80 of Jackson's votes are not whole votes; they are the cumulative total of the 8% of the 1000 votes that transferred from Perez in round 1. Those 80 votes do not transfer as whole votes. They transfer as the 8% fractional vote that was with Jackson, to whomever is next on any given ballot, contributing to the total transfers as described).

Round 4: Cathy Chan has more votes than the threshold and wins the second seat.

After receiving the lion's share of back-up support from fellow Democrat Brad Jackson, Cathy Chan is well over the threshold and is elected. She has 900 more votes than the threshold, so 900 votes will transfer to other candidates. This will work by transferring 28.125% of every vote (or partial vote) counting for Chan to its next choice (because Chan's 900 surplus votes divided by her 3200 total votes = 28.125%). Keep in mind that some of Chan's votes are already fractional votes because they were transferred to Chan after Perez was elected in round 1 (or they transferred first to Jackson after round 1 and then to Chan after round 3). The new transfer value for those votes is 28.125% of 8%, or 2.25%. For simplicity, this example assumes these fractional votes transfer based on the same probabilities as Chan's full-value votes. Of the 3,200 votes counting for Chan, 50% ranked Murphy next, 10% ranked Lorenzo next, and 40% did not rank any other active candidates. As a result, Murphy gains 450 votes (28.125% of 50% of 3,200); Lorenzo gains 90 votes (28.125% of 10% of 3,200); and 360 votes (28.125% of 40% of 3,200) are inactive and do not contribute to any other candidates. 

Round 5: Hannah Murphy has more votes than the threshold and wins the last seat.

After Chan's votes transfer to their next choices, Hannah Murphy has more votes than the threshold and wins the last seat. Because all three seats have been filled, the vote counting can now end; there is no need to transfer Murphy's surplus support.

Final Results: The winners are Democrats Armando Perez and Cathy Chan and Republican Hannah Murphy

The winners are Perez (D), Chan (D), and Murphy (R). If this were a single winner election, the most mainstream Democrat (Perez) easily would have won, leaving all others unrepresented. Instead, two additional candidates are elected, both of whom are rewarded by coalition-building among the district's remaining center-left and center-right populations. Voters were split 61% Democratic and 39% Republican by first choices, and they elected 67% Democrats and 33% Republicans. In the end, 96% of voters can point to a candidate whom they supported and helped elect. 

Had these three seats been elected by block voting, in which every voter casts three votes for the three candidates they support, the Democrats would have almost certainly swept all three seats, because each Democratic voter could vote for all three Democratic candidates. In fact, even if the three seats were elected by the single vote system, a weaker form of fair representation voting, Democrats still would have swept all three seats due to the Republican vote being split among three candidates.

Had these three seats been filled by dividing the district into three single-winner districts, the outcome would depend on how the district lines were drawn. The districts could have been drawn to elect two Democrats and one Republican, or they could have been gerrymandered to over-represent either party. Regardless, the district elections would probably not be competitive, and each district's primary election would likely weed out the candidates who won by coalition-building.

By using ranked choice voting to elect three seats, the election results fairly represent the district's diversity after a competitive election without any opportunity for partisan gerrymandering.

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