RCV 101
Ranked-choice Voting is an increasingly common way to vote.
Ranked-choice Voting
“Ranked-choice voting” (RCV) is a term used in the United States to describe a family of voting and vote counting methods in which:
Voters rank candidates in order of preference; and
Votes are counted in rounds that sequentially elect or eliminate candidates and progressively draw on more information from voters’ ballots.
RCV is different from the more common plurality systems used in American elections in that is asks for more information from voters—a relative ranking of the candidates—than plurality systems, which ask only for binary preferences: a filled in oval versus an empty oval.
The Common RCV Variants
The term “Ranked-choice Voting” (RCV) typically refers to one (or all) of three variants in the United States:
Instant Run-off Voting (IRV, aka the “Alternative Vote”)
Single Transferable Vote (STV)
Preferential Block Voting (PBV, aka the “Utah Variant”)
The characteristics all variants share are that:
Voters rank candidates.
Vote counting proceeds in rounds.
The unique effects of the RCV variant are greater as more voters rank candidates more fully.
RCV variants fundamentally differ in most other respects, presenting a choice for reformers, legislators, and administrators about which variant best fits their needs.
IRV is the main RCV system that is suitable for contests in which there can only be one winner, like contests for mayor, governor, or president.
For offices where multiple winners could be elected from the same set of candidates, such as city councils, school boards, state and federal legislatures, and other legislative bodies, IRV, STV, and PBV are all options.
Instant Run-off Voting
A majoritarian system for electing a single winner, either at-large or in districts, in which voters get a single vote and rank candidates in order of preference. To win a candidate must receive a majority of votes.
After voters cast their ballots, votes are tallied. If a candidate wins a majority of first rankings, they win. If no candidate wins a majority of first rankings, a second round of vote counting – an “instant run-off” commences. The candidate with the fewest first rankings is eliminated and ballots with that candidate as their top choice will have their next choice counted. Votes are tallied and the process continues until one candidate has more than half of the remaining vote.
A plurality system for electing multiple winners, either at-large or in districts, in which voters rank candidates in order of preference. To win, a candidate must receive a majority of the votes in that given round of counting.
When electing the first winner, voters’ first choices are tallied as they would be under IRV until a candidate is elected. To elect the second and subsequent winner, ballots are retallied using the IRV process as if the elected candidate(s) had not run for office, with each ballot counting for the highest ranked candidate that has not been elected.
This process continues until the desired number of candidates have been elected.
Preferential Block Voting
Single Transferable Vote
A proportional system for electing multiple winners, either at-large or in districts, in which voters get a single vote and rank candidates in order of preference. To win, a candidate must receive a threshold number of votes, which is equal to 1/4th of the total vote in three-winner races, 1/6th in five-winner races, and 1/11th in 10-winner races. There are several different ways to calculate the exact number of votes in this threshold (also known as a “quota”). For more information, see this post from the British Electoral Reform Society.
When electing the first winner, voters’ first choices are tallied. Those candidates who have met the threshold are elected. If fewer candidates have been elected than there are seats to fill, the surplus votes of each elected candidate are transferred to the voters’ next most preferred (not-yet-elected) candidate. If, as a consequence of the transfer process, additional candidates reach the threshold, they are elected and their surplus votes transferred. This process continues until no additional candidates reach the threshold as a consequence of surplus vote transfer.
Once there are no additional surplus votes to transfer, the candidate with the fewest votes is eliminated, and the ballots of voters who voted for the eliminated candidate now count for their next most preferred (not-yet-elected) candidate. If additional candidates reach the threshold as a consequence of this process, they are elected and their surplus votes transferred according to the process above.
This process of electing candidates, transferring surpluses, and eliminating last-placed candidates continues until the desired number of candidates have been elected.
STV produces more proportional results in larger districts (i.e. ones in which more candidates are elected at a time). STV will elect a more proportional 20-member state legislature using two 10-winner districts than it will using 10 two-winner districts.
Making Use of Extra Information
RCV asks for more information from voters—a relative ranking of the candidates—than plurality systems, which ask only for binary preferences: a filled in oval versus an empty oval.
What does RCV do with all this extra information?
As described below, the three variants of RCV use the extra information they get from voters in different ways.
IRV ignores the vast majority of the information it solicits from voters, relying heavily on voters’ first choices and a small subset of second choices.
When it does introduce additional information, it does so from the bottom up. RCV uses information on the preferences of voters for the least popular candidates as they are eliminated and, in a manner of thinking, saves votes cast for unpopular candidates. Votes flow 'upward' from the least popular toward the more popular candidates.
IRV
PBV and STV make more use of the ranking information, but to very different ends: PBV uses the extra information to supporters of popular candidates another go at electing another winner; STV uses ranking information to equalize the efficacy of each voter’s vote and minimizing wasted votes (votes that do not count toward electing a candidate).
PBV is, in effect, a “top-down” method. Like IRV, PBV introduces information on the preferences of voters for the least popular candidates to help elect the most popular candidates. However, as each candidate is elected, the counting resets. The ballots of all voters are reintroduced – including those who cast a first choice for the elected candidate(s). Votes are counted as if the winning candidate(s) was never in the race, so these voters’ votes flow “downward” to contribute to the election of subsequent candidates.
PBV
Meanwhile, in pursuit of proportionality, STV goes both ways – introducing information on the preferences of voters for the most popular candidates (at a smaller, weighted value), then the least popular (at full value), then the next most popular (at a smaller, weighted value), then the next least popular (at full value), and so on.
STV
What Happens when Voters Don’t Rank?
The extent to which any RCV system has distinctive characteristics depends significantly on how many voters rank candidates and how many candidates they rank.
As more voters rank all candidates, IRV is more likely to elect a candidate with a majority of support. If few voters rank candidates, IRV will almost always behave like single-winner plurality.
The results from STV will be more proportional as more voters rank all or most candidates. If few voters rank candidates, STV will behave a lot like Single Non-transferable Vote (SNTV), a semi-proportional system.
As more voters rank all candidates, PBV is more likely to elect candidates with the most overall support and allow the same plurality of voters to elect all candidates. If few voters rank candidates, PBV will behave more like Single Non-transferable Vote (SNTV), a semi-proportional system.
The three variants are summarized below.
Table 1: RCV Variants compared
Counting votes in RCV
Instant Run-off Voting
Under IRV, every voter’s first choice is counted. If a candidate receives more than half of the first choices, that candidate wins, just like in any other election. However, if there is no majority winner after counting first choices, the race is decided by an "instant runoff." The candidate with the fewest votes is eliminated, and voters who picked that candidate as ‘number 1’ will have their votes count for their next choice. If the ballot does not contain any additional rankings for candidates still in the race, it will “exhaust” and no longer remain in the count.
This process continues until there is a majority winner or a candidate won with more than half of the votes remaining in the count.
In a typical IRV election, candidates win in the first round with a majority of the vote. Even in contests that continue to second and subsequent rounds of counting, only the first preference of a large majority of voters’ rankings will be tabulated, leaving the remaining rankings unused.
Under PBV, counting looks a lot like IRV, except that it repeats for each winner and makes more use of voters’ rankings.
After the first winner has been elected using the procedure for IRV outlined above, the count for the second winner begins. Essentially all choices for the first winner are ignored, and the count proceeds using IRV but without that winning candidate. Essentially, a whose first choice won now has their second choice bumped up to first and all of the ballots are re-tallied. If a ballot does not contain any additional rankings for candidates still in the race, it will “exhaust” and no longer remain in the count.
The process continues, with each elected candidate being eliminated from the count, until the required number of candidates are elected. Note that, in theory at least, a voter’s vote can elect as many candidates as are up for election.
Preferential Block Voting
Single Transferable Vote
The counting in STV combines elements of IRV, PBV, and some complex math. In the first round, every voter’s first choice is counted. If any candidates receive more than the threshold percentage of first choices, those candidates win.
The threshold is defined as a percentage of vote equal to 1/(the number of candidates to be elected + 1)%. Using the example above, a candidate in a contest for a three-member city council seat must receive more than 1/(3+1)%, or 25%, of votes cast to win a seat. This means that, in a three-winner race, a candidate must win one fourth of the votes (plus one vote). Typically, more than half of candidates will be elected in the first round, with their election being easy to explain.
But then comes the complexity.
Under STV, the next stage is to redistribute the surplus votes of elected candidates. Each candidate needs only the threshold number of votes to win, and so STV, which aims to minimize wasted votes and maximizes the use of the ranking information provided by voters, takes that excess and moves them to the second-choice candidate on each voter’s ballot.
Numerous transfer formulas, including “random subset,” Gregory “fractional transfer value,” and Hare-Clark, have been devised. Almost every STV jurisdiction uses a slightly different one. The transfer formulas vary in whether they transfer a set of randomly selected ballots from the winning candidate’s haul (equal to the number of ballots in excess of the surplus that candidate has) or transfer all ballots as a fraction (so that each vote counts for less than one vote for the winning candidate and the remaining—fractional—value is transferred to the second choice). However, at their core, each transfer formula seeks to produce an outcome that is as proportional as possible to overall voter preferences by making use of the ranking information on voters’ ballots and adhering to the one-vote one-value principle.
Once the surplus votes of each elected candidate are redistributed, election administrators check whether any other candidate has won. If they have, we repeat the process of redistributing their surplus votes until no candidate is newly elected.
Then, like IRV and PBV, the candidate with the fewest votes is eliminated and their preferences distributed to the candidates who are yet to be elected or eliminated according to the preferences listed on the ballot. The process repeats until a candidate is elected. If additional candidates reach the threshold as a consequence of this process, they are elected and their surplus votes transferred according to the process above.
This process of electing candidates, transferring surpluses, and eliminating last-placed candidates repeats until the desired number of candidates have been elected.
The complexity of vote counting under STV, or, rather, the difficulty of succinctly explaining STV vote counting, is the system’s chief disadvantage.