# Who wins by ranked choice voting?

Counts ranked ballots by instant runoff: removes the last-place candidate round by round and moves those ballots to their next choice until someone has a majority.

- Page: https://www.acalculator.org/statistics/ranked-choice-voting-calculator
- JSON spec: https://www.acalculator.org/statistics/ranked-choice-voting-calculator.json
- Version: d65ac682dd4f

## Default answer

Example with the default inputs (Ballots [Voters 40, Ranking Ana > Ben > Cy; Voters 35, Ranking Ben > Cy > Ana; Voters 25, Ranking Cy > Ben > Ana]): Ben wins after 2 round(s), with 60% of the continuing ballots.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| ballots | Ballots | One row per ballot ranking, with how many voters cast it. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| winner | Winner | The candidate with more than half of the continuing ballots. |
| rounds | Rounds | How many rounds of counting it took. |
| winnerVotes | Winner’s votes in the last round | Ballots counting for the winner in the final round. |
| share | Winner’s share of continuing ballots | Winner’s final votes ÷ continuing ballots in the final round. |
| exhausted | Exhausted ballots | Ballots that rank no candidate still in the count by the final round. |
| total | Ballots cast | All voters, added up over the rows. |
| steps | Round by round | Each round’s count and who was removed. |

## Method

Each round: each ballot counts for its highest-ranked candidate still in the count; more than half of the continuing ballots wins; otherwise the candidate with the fewest votes is removed (all candidates with 0 votes together) and the count repeats.

## Assumptions

- Single-winner instant runoff with one last-place candidate removed per round, as in Maine law.
- A tie for last place with votes gives no answer: the law decides it (in Maine, by lot).
- Names match without regard to case or extra spaces; a ballot cannot rank one name twice.

## Worked examples

1. ballots = {"votes":40,"ranking":"Ana > Ben > Cy"} or {"votes":35,"ranking":"Ben > Cy > Ana"} gives winner = Ben, rounds = 2, winnerVotes = 60, share = 60%, exhausted = 0, total = 100. Source: https://fairvote.org/our-reforms/ranked-choice-voting-information/.
2. ballots = {"votes":45,"ranking":"A"} or {"votes":35,"ranking":"B"} gives winner = A, rounds = 2, winnerVotes = 51, share = 52.040816%, exhausted = 2. Source: https://legislature.maine.gov/statutes/21-A/title21-Asec723-A.html.
3. ballots = {"votes":60,"ranking":"X > Y"} or {"votes":40,"ranking":"Y > Z"} gives winner = X, rounds = 1, share = 60%. Source: https://fairvote.org/our-reforms/ranked-choice-voting-information/.

## FAQ

### How does ranked choice voting work?

Voters rank the candidates. Each ballot first counts for its top choice. If a candidate has more than half of the votes, that candidate wins. If not, the candidate with the fewest votes is removed, and those ballots count for their next choice. This repeats until someone has a majority.

### How do I calculate a ranked choice voting result?

Count first choices. With 40 for Ana, 35 for Ben and 25 for Cy out of 100, nobody has more than 50, so Cy is removed. Cy’s 25 ballots rank Ben next, so round 2 is Ben 60, Ana 40, and Ben wins.

### What is an exhausted ballot?

A ballot that ranks no candidate still in the count. Maine law leaves exhausted ballots out of later rounds, so the majority is counted on the continuing ballots only.

### What happens in a tie for last place?

Maine law decides a tie for last place by lot. The calculator cannot draw lots, so it stops and names the tied candidates. Remove the candidate your rules eliminate from the ballots and count again. Candidates with no votes at all are removed together, which changes nothing.

### Is the winner the same if counting continues to the last two?

Yes. Maine counts until two candidates remain; this page stops when a candidate has more than half of the continuing ballots. Removing other candidates can only add ballots to the leader, so a candidate with a majority would win either way.

### How do I type the ballots?

One row per distinct ranking, with the number of voters who cast it. Type the names in order, first choice first, separated by > or commas: Ana > Ben > Cy. Leaving names off the end is fine; ranking the same name twice is not.

## Sources

- FairVote. Ranked Choice Voting Information: how RCV works (single winner: more than half wins, otherwise the last-place candidate is removed and those ballots count for the next choice), retrieved 2026-10-18. https://fairvote.org/our-reforms/ranked-choice-voting-information/
- Maine Revised Statutes, Title 21-A, §723-A. Determination of the winner of a ranked-choice election (continuing and exhausted ballots, rounds, ties for last place decided by lot), retrieved 2026-10-18. https://legislature.maine.gov/statutes/21-A/title21-Asec723-A.html