Who wins by ranked choice voting?

How it works

Ballots. Each row is one ranking and the number of voters (1 or more) who cast it. The ranking is a list of names separated by > or ,, first choice first. Names are trimmed, runs of spaces count as one, and case is ignored when matching (ana and Ana are one candidate, shown with its first spelling). A row with no name, or with the same name twice, gives no answer. The candidates are every name on any ballot.

Each round:

1. Every ballot counts as one vote (times its voters) for its highest-ranked candidate still in the count. A ballot that ranks no such candidate is exhausted and is not counted.
2. Continuing ballots = the votes counted this round.
3. If a candidate has more than half of the continuing ballots (votes × 2 > continuing), that candidate wins.
4. Otherwise the candidate with the fewest votes is removed. If several candidates have 0 votes, they are all removed together. If two or more candidates tie for the fewest votes and that number is more than 0, there is no answer: the law decides the tie (by lot in Maine).
5. Repeat with the remaining candidates.

Outputs. The winner; the number of rounds; the winner's votes in the final round; the winner's share = winner's votes ÷ continuing ballots in the final round × 100; exhausted ballots = ballots cast − continuing ballots in the final round; ballots cast = the sum of the voters over all rows; and a round-by-round account.

Round-by-round text. Each round reads Round n: <name votes, …> of <continuing> continuing; then either <name> has a majority and wins or no majority, <names> removed (several names joined by " and ", in order of first appearance). Candidates are listed by votes, most first; equal votes keep the order in which the names first appear (row by row, left to right). Rounds are joined by ; . Counts in this text are plain digits with no thousands commas, so a comma only separates two candidates. With 4,000 Ana > Ben, 3,500 Ben and 2,500 Cy > Ben, round 1 reads Round 1: Ana 4000, Ben 3500, Cy 2500 of 10000 continuing; no majority, Cy removed.

This follows FairVote's description of single-winner ranked choice voting and Maine's statute, except that the page stops at a majority instead of counting down to two candidates (the winner is the same). Overvotes and skipped rankings on paper ballots are not modeled.

Rounding. Counts are whole numbers; the share shows to 2 decimals of a percent.

Worked examples by hand

A come-from-behind win (page default). 40 Ana > Ben > Cy; 35 Ben > Cy > Ana; 25 Cy > Ben > Ana. Round 1: Ana 40, Ben 35, Cy 25 of 100. Nobody has more than 50, so Cy is removed. Round 2: Cy's 25 ballots go to Ben: Ben 60, Ana 40 of 100. Ben wins in 2 rounds with 60 votes, 60.00%, 0 exhausted.

Exhausted ballots. 45 A; 35 B; 12 C > B; 6 C > A; 2 C. Round 1: A 45, B 35, C 20 of 100; C is removed. Round 2: B gains 12, A gains 6, and the 2 ballots that rank only C are exhausted: A 51, B 47 of 98. 51 × 2 = 102 > 98, so A wins in 2 rounds, with 51 ÷ 98 = 52.04%; 2 exhausted.

First-round majority. 60 X > Y; 40 Y > Z. Round 1: X 60, Y 40, Z 0 of 100. 60 × 2 > 100, so X wins in 1 round with 60.00%.