Real races. Real spoilers.

Every race on this page happened, and every number comes from an official count or a published study, with the source printed beside it. The pattern has no party. A pick-one ballot split the right in 1912 and the left in 2000. Ranked choice squeezed out a Democrat in Burlington and a Republican in Alaska.

We don’t claim to know who would have won with score voting. Nobody cast score ballots in these races. What the numbers show is what each ballot threw away.

The spoiler effect has no party

Under a pick-one ballot, two candidates with overlapping voters split them, and the side that fields one candidate too many loses. It has hit both sides.

Florida, 2000

The presidency came down to 537 votes. Ralph Nader drew 97,488.

After thirty-six days of recounts and lawsuits, George W. Bush’s certified margin over Al Gore in Florida stood at 537 votes, out of nearly six million cast. On the same ballot, Ralph Nader drew 97,488 votes, 181 times the margin.

You don’t have to believe every Nader voter preferred Gore. You need almost none of them to. If one Nader voter in 180 had marked Gore instead, the presidency changes hands.

Nader didn’t spoil the race because he was a bad candidate. The ballot gave his voters no way to say “Nader first, but Gore over Bush,” so that part of what they thought was thrown away. A score ballot has room for all of it.

And if this reads like a left-wing grievance, look at 1912.

Drawn to the same scale

Nader’s votes in Florida97,488
Bush’s margin over Gore537
That sliver is the whole margin.

Source: Certified Florida results, 2000 (Florida Dept. of State): Bush 2,912,790; Gore 2,912,253; Nader 97,488; 5,963,110 votes cast.

In the book: chapter 2, “The Plurality Problem”

The 1912 election

More than half the country voted for one of two Republicans. Woodrow Wilson won with 41.8 percent.

Theodore Roosevelt, denied the Republican nomination, ran anyway on a third-party ticket. He and William Howard Taft split the Republican electorate nearly down the middle.

Together they drew 50.6 percent of the popular vote. Woodrow Wilson, with 41.8 percent, won the presidency.

1912 hurt the right. 2000 hurt the left. The spoiler effect punishes whichever side fields one candidate too many, and it has been doing it for more than a century.

“The spoiler effect has no party.”

Score the Vote, ch. 2

Share of the popular vote

Woodrow Wilson (D)41.8%
Theodore Roosevelt (Progressive)27.4%
William Howard Taft (R)23.2%
Roosevelt and Taft together50.6%

Source: 1912 presidential popular vote

In the book: chapter 2, “The Plurality Problem”

When ranked choice misfires

Ranked choice is a real improvement on pick-one, and the book gives it a chapter of credit. These are its two best-documented failures. One squeezed out a Democrat, the other a Republican.

Burlington, 2009

One election, three winners. The candidate who beat everyone head-to-head finished third.

Burlington, Vermont, elected its mayor by ranked choice: five candidates, 8,980 ballots. Republican Kurt Wright led on first choices with 2,951. Progressive Bob Kiss had 2,585. Democrat Andy Montroll had 2,063, so he was eliminated, and Kiss beat Wright in the final round, 4,313 to 4,061.

The same ballots record every head-to-head matchup. Montroll beat Kiss 4,064 to 3,476, and beat Wright 4,597 to 3,664. The candidate preferred over each finalist never reached the final round, because the count never checked.

The next March, Burlington repealed ranked choice, 3,972 to 3,669, in a vote that was partly a verdict on Kiss himself. In 2021 the city brought ranked choice back for council races, 64 to 36 percent. Voters’ relationship with it is complicated. The math of 2009 isn’t.

Here the candidate squeezed out was a Democrat. In Alaska, it was a Republican.

Three ways to count the same ballots

Who wins Burlington’s 2009 mayoral race under three counting rules
Count	Winner
First choices only	Wright (R)
Ranked-choice rounds	Kiss (Progressive)
Head-to-head	Montroll (D)

Montroll, head-to-head, on the same ballots

Montroll 4,0643,476 Kiss

Montroll 4,5973,664 Wright

Source: Official tabulation, Burlington mayoral election, Mar. 3, 2009. Head-to-head tallies: Bristow-Johnson, Constitutional Political Economy 34 (2023). Repeal: Burlington Question 5, Mar. 2, 2010. Re-adoption for council races: Burlington city ballot, March 2021.

In the book: chapter 9, “RCV: Credit Where It’s Due”

Alaska, 2022

The same squeeze, statewide. The candidate who beat both finalists was eliminated first.

Alaska’s August 2022 special election for its only U.S. House seat had three candidates: Democrat Mary Peltola and Republicans Sarah Palin and Nick Begich. First choices: Peltola 75,799, Palin 58,973, Begich 53,810. Begich, in third, was eliminated.

His ballots went 27,053 to Palin and 15,467 to Peltola. The other 11,290, nearly all listing no second choice, had nowhere to go and dropped out. Peltola won the final round, 91,266 to 86,026.

On those same ballots, Begich beat Peltola 87,859 to 79,451 and beat Palin 101,217 to 63,618.

Two things belong beside that. Peltola became the first Alaska Native elected to Congress, with 51 percent of the final round. And in 2024 Alaskans voted to keep ranked choice, by fewer than a thousand votes.

How often does this happen? Rarely. A study of 182 competitive U.S. ranked-choice races from 2004 to 2022 found this kind of failure twice. When it does happen, nothing on election night tells you. Ranked choice is an ally, with flaws.

Where Begich’s 53,810 ballots went

To Palin27,053
To Peltola15,467
To no one: no remaining choice, dropped from the count11,290

Begich, head-to-head, on the same ballots

Begich 87,85979,451 Peltola

Begich 101,21763,618 Palin

Source: Alaska Division of Elections, official RCV tabulation, certified Sept. 2, 2022. Head-to-head: Graham-Squire and McCune, Math Horizons 31, no. 1 (2023), confirmed by Clelland, The Mathematics Enthusiast 23, no. 3 (2026). Frequency: Graham-Squire and McCune, Representation 61, no. 1 (2025). Repeal vote: Alaska Ballot Measure 2 (2024), confirmed by the December 2024 recount.

In the book: chapter 9, “RCV: Credit Where It’s Due”

What a better ballot does

Score-style ballots aren’t a thought experiment. Real voters have used them on election day, and in Fargo and St. Louis, voters chose them by wide margins.

France, 2012

Same voters, same day, a different ballot. A different kind of candidate came out ahead.

During the 2012 French presidential election, a team of economists set up in three towns. As citizens left their real polling places, they were invited to vote again, on the same candidates, with score-style ballots. 2,340 took part.

First finding: ordinary voters used the in-between grades extensively, including on a 0-to-20 scale with almost twice as many levels as the ballot we propose.

Second, and more important: the ballot changed who came out ahead. France’s official runoff system rewards candidates with passionate bases and high negatives. The score-style ballots rewarded candidates acceptable to a broad span of voters.

“Change the ballot, and a different kind of leader wins.”

Score the Vote, ch. 8

The field experiment

voters: 2,340
towns: 3
levels on the finest scale: 21

A 0-to-20 scale: what voters used

Shaded: the eleven levels of the 0-to-10 ballot this campaign proposes.

Source: Baujard et al., Electoral Studies 34 (2014). The team tested several scales, from two levels up to twenty-one.

In the book: chapter 8, “Where Score Voting Works”

Fargo and St. Louis

When voters got to choose, they chose to evaluate everybody. Then state legislatures stepped in.

Approval voting is score voting with two levels: mark every candidate you approve of, and the most approvals wins. In 2018, Fargo, North Dakota, became the first U.S. city to adopt it, by citizen initiative, with 63.5 percent of the vote. St. Louis followed in 2020 with 68 percent.

Fargo used it in its 2020, 2022 and 2024 city elections without confusion or controversy at the polls. St. Louis has used it for its citywide primaries since 2021, and still does.

Then the legislatures moved. North Dakota’s passed a ban in 2023; Governor Doug Burgum vetoed it, and the veto held. In 2025 the legislature passed it again, and the new governor signed it. In 2024, Missouri’s Amendment 7 banned ranked choice and approval voting statewide, with an exemption for St. Louis.

Hold both facts at once. When voters in Fargo and St. Louis got to choose how they vote, they chose ballots that evaluate everybody, by margins of 27 and 36 points. When the people elected under the old rules got a say, they reached for a ban. Here’s how reform gets adopted now.

Votes to adopt approval voting

Fargo, North Dakota, 201863.5% yes
St. Louis, Missouri, 202068% yes

2018Fargo adopts approval voting by citizen initiative.
2020St. Louis adopts it. Fargo uses it for the first time.
2021St. Louis holds its first approval-voting primaries.
2022Fargo uses it again.
2023North Dakota’s legislature passes a ban. The governor vetoes it, and the veto holds.
2024Fargo uses it a third time. Missouri’s Amendment 7 bans it statewide, exempting St. Louis.
2025North Dakota passes the ban again. The new governor signs it.

Source: Fargo Measure 1, Nov 2018; St. Louis Proposition D, Nov 2020. North Dakota HB 1273 (2023, vetoed) and the 2025 ban (HB 1297); Missouri Amendment 7 (2024).

In the book: chapter 8, “Where Score Voting Works”

Every one of these races is in the book.

With the footnotes, the figures, and the case for the one ballot change that would have heard what these voters were trying to say.

Get the book See how it works