The Math of Ranked Choice Voting
A town of 100 people is electing a mayor. Three candidates are running, Lena, Dave and Rob. Every voter ranks all three from favorite to least favorite, and the ballots break down like this.
| Voters | 1st choice | 2nd choice | 3rd choice |
|---|---|---|---|
| 45 | Rob | Lena | Dave |
| 35 | Lena | Dave | Rob |
| 17 | Dave | Lena | Rob |
| 3 | Dave | Rob | Lena |
Most American elections only count the first column. Rob has 45 first-place votes, more than anyone else, so Rob wins.
But every Lena voter ranked Rob dead last, and so did 17 of the 20 Dave voters. That's 52 people, more than half the town, and Rob is their new mayor.
The rule that elected Rob is called plurality voting. The candidate with the most votes wins, even when most voters wanted someone else. It hands the prize to the bigger number, and under plurality the bigger number can fall well short of a majority.
Rob won because the voters who didn't want him split between Lena and Dave. It's called the spoiler effect, and anyone who has thought about voting for a third candidate has felt it. You're told not to waste your vote, and under plurality that advice is correct. A vote for the candidate you like best can help elect the candidate you like least. So people vote for the lesser evil, third candidates stay small, and their small numbers become proof that nobody outside the two big parties can win.
Political scientists call this Duverger's law, after the French scholar Maurice Duverger. Elections decided by plurality tend to leave voters with just two parties.[1]
Ranked choice voting fixes this kind of split. Instead of marking one candidate, you rank them in order, first choice, second choice, third choice. If a candidate gets more than half of the first-choice votes, that candidate wins, same as today. If nobody does, the candidate with the fewest first-choice votes is eliminated. Every ballot that had that candidate on top now counts for its next choice instead. The count repeats until one candidate has a majority.
Here's the same town, counted with ranked choice.
| Candidate | Round 1 | Round 2 |
|---|---|---|
| Rob | 45 | 48 |
| Lena | 35 | 52 |
| Dave | 20 | eliminated |
Dave had the fewest first-choice votes, so he was eliminated after round one. Each of his 20 ballots moved to that voter's second choice. Seventeen went to Lena and three went to Rob, and Lena won 52 to 48.
Lena is also the candidate who beats each rival one-on-one. She tops Rob 52 to 48 and Dave 80 to 20, and only three people in the whole town ranked her last.
The Dave voters are the ones plurality punishes. On a ranked ballot they put Dave first and their next choice second. If Dave has the support to win, he wins. If he doesn't, their votes move to their second choice and still count in the final round. Nobody has to choose between voting for who they want and voting against who they fear. Dave's first-choice total also becomes an honest measure of how many people actually wanted him.
Maine elected its governors the same way the town elected Rob. Angus King won in 1994 with 35.4 percent of the vote. John Baldacci was re-elected in 2006 with 38.1 percent, and Paul LePage won in 2010 with about 38 percent.[2] Each time, more than six in ten voters had chosen someone else.
In 2016 Maine voters decided to change the count and passed a ballot question adopting ranked choice voting. The next spring, the state's highest court advised that the new system clashed with the Maine Constitution for general elections to state offices like governor and the legislature. Lawmakers answered by passing a law that put ranked choice on hold and would repeal it automatically unless the constitution was amended.[3] Voters fought back. They gathered enough signatures to force a statewide vote on the legislature's law, and in June 2018 they struck down the delay with 54 percent.[4]
The court's objection only covered state offices. Races for Congress fall under the U.S. Constitution, which leaves the method of electing representatives to the states, so Maine began ranking candidates for Congress and in party primaries. The first big test came that November in the 2nd Congressional District. Republican Bruce Poliquin led the first count by 2,171 votes, but with four candidates on the ballot, nobody had a majority. The two independents were eliminated, their ballots moved to their voters' next choices, and Democrat Jared Golden won.
| Candidate | Round 1 | Final round |
|---|---|---|
| Bruce Poliquin | 134,184 | 138,931 |
| Jared Golden | 132,013 | 142,440 |
| Tiffany Bond | 16,552 | eliminated |
| William Hoar | 6,875 | eliminated |
Poliquin sued to overturn the result. A federal judge upheld it, noting that the U.S. Constitution is "perfectly silent" on how states must elect their representatives.[5]
Golden's 142,440 votes were a majority of the ballots still in the count at the end. Along the way, 8,253 ballots, under 3 percent of all ballots cast, ran out of choices when Bond and Hoar were eliminated. A ballot keeps counting only while it still has a candidate left on it, so a voter who ranks just one candidate drops out of the count when that candidate is eliminated.
In April 2026 Maine's high court unanimously advised that extending ranked choice to general elections for governor and the legislature would be unconstitutional.[6] Maine voters have approved ranked choice twice, and their governors are still elected by plurality.
Australia has elected its House of Representatives with ranked ballots, which Australians call preferential voting, since 1918.[7] Ireland has used a multi-seat form of ranked voting for its parliament since independence in 1922, a version that also makes it much harder to rig district lines. Irish voters were asked in 1959 and again in 1968 to switch to plurality voting. Both times they said no.[8] Alaska adopted ranked choice for its general elections in 2020,[9] survived a repeal attempt by 743 votes in 2024,[10] and votes on another repeal this November.[11]
No voting system is perfect. In 1951, economist Kenneth Arrow proved that once there are three or more candidates, every method of turning voters' rankings into a single result can, in some situations, break at least one basic rule of fairness.[12] Ranked choice has its own rare failure. In Alaska's 2022 special election for the U.S. House, Nick Begich would have beaten both Mary Peltola and Sarah Palin in one-on-one races. He finished third in first-choice votes, was eliminated, and Peltola won.[13] A study of 182 American ranked choice races that went past the first round found that kind of miss in just two of them.[14]
A candidate like Rob, who would lose one-on-one to every rival, can never win a ranked count. Plurality elected him anyway. Under ranked choice he's either eliminated along the way or makes it to the end and loses, because winning takes a majority of the ballots still in play, and a majority prefers each of his rivals to him.
Nineteen states have now banned ranked choice voting, most recently Ohio in March 2026, and every one of those bans went through a Republican-controlled legislature.[15][16] The people deciding whether to keep plurality are the ones who won under it.
A ranked ballot is a simple grid, with the candidates' names down the side and columns for 1st, 2nd and 3rd choice across the top. You fill in one bubble per column, so you can say who you want and who you'd accept. Under plurality, the town of 100 elected the candidate more than half of it ranked last. Under ranked choice, it elected the candidate who beat everyone one-on-one. Wherever elections are still counted by plurality, 45 people can beat 55.