The Condorcet criterion is a standard for judging voting systems. It says that if one candidate would beat every other candidate in a one-on-one matchup, that candidate should win the election. A voting method that always elects this candidate “passes” the Condorcet criterion. Many popular voting methods, including ranked choice voting and the Borda count, fail this test.
How Head-to-Head Comparisons Work
Imagine an election with three candidates. Instead of looking at who got the most first-place votes, you compare every possible pair of candidates and ask: which one do more voters prefer? If candidate A beats B head-to-head, and A also beats C head-to-head, then A is the Condorcet winner. She doesn’t need to be anyone’s first choice to qualify. She just needs to be preferred by a majority in every two-way race.
This logic feels intuitive. If most people would pick A over B, and most people would also pick A over C, it seems obvious that A should win. The Condorcet criterion simply formalizes that intuition and asks whether a given voting method respects it.
Which Voting Methods Pass and Fail
Voting methods specifically designed around pairwise comparisons, often called Condorcet methods, satisfy the criterion by definition. The Schulze method, Ranked Pairs, and the Kemeny-Young method all guarantee that a Condorcet winner, when one exists, takes the election. These systems are used primarily by organizations and software communities rather than in public elections.
Several widely used methods fail the criterion:
- Plurality voting only counts first-place votes. A candidate with broad support but fewer first-place votes loses to one with a passionate but smaller base.
- Instant runoff voting (ranked choice voting) eliminates the candidate with the fewest first-place votes each round. A Condorcet winner who is many voters’ second choice can be knocked out early before those preferences ever come into play.
- Borda count assigns points based on ranking position and totals them up. A candidate can rack up more points overall while still losing head-to-head matchups against another candidate.
Alaska 2022: A Real-World Failure
The 2022 Alaska special congressional election is one of the clearest real-world examples of a Condorcet failure. Alaska used ranked choice voting (instant runoff) with three major candidates: Mary Peltola, Sarah Palin, and Nick Begich. In round one, Peltola received 40.19% of first-place votes, Palin got 31.27%, and Begich came in last with 28.53%. Because Begich had the fewest first-place votes, he was eliminated.
But Begich was the Condorcet winner. When researchers looked at the preference data from the ballots, Begich would have defeated Peltola head-to-head with roughly 52.5% of the vote. He would have defeated Palin with about 61.4% of the vote. He had broad support as a second choice across both camps, yet the ranked choice system never gave voters the chance to express that in a way that mattered. He was eliminated before his widespread appeal could surface.
This pattern, where a candidate with strong second-choice support gets knocked out early for lacking first-place votes, is the signature way instant runoff voting violates the Condorcet criterion. One consolation: IRV does guarantee that a Condorcet loser (a candidate who would lose every head-to-head matchup) can never win.
How the Borda Count Fails
The Borda count assigns points based on where each candidate falls on a voter’s ballot. In a three-candidate race, your first choice gets 2 points, your second gets 1, and your last gets 0. The candidate with the most total points wins. This sounds reasonable, but it can produce results that contradict majority preferences.
A classic example from the Marquis de Condorcet himself, using 81 voters, illustrates the problem. Candidate A wins every head-to-head matchup, making A the clear Condorcet winner. But when Borda scores are calculated, candidate B earns 109 points to A’s 101 because B is ranked second by many voters who rank A first and ranked first by many voters who rank A second. The point totals obscure the fact that a majority prefers A to B directly. Mathematically, this isn’t a fluke. For any election with three or more candidates, there are scenarios where every point-based scoring system ranks multiple candidates above the Condorcet winner.
When No Condorcet Winner Exists
The Condorcet criterion only applies when a Condorcet winner exists, and sometimes one doesn’t. This is called the Condorcet paradox, and it occurs when group preferences form a cycle. Candidate A beats B in a head-to-head matchup, B beats C, but C beats A. There’s no single candidate who defeats all others, so the group’s preferences loop back on themselves.
This isn’t just a theoretical curiosity. It can happen whenever voters’ preferences are spread across candidates in certain patterns. With three voters choosing among three options, it takes only a modest difference in priorities for a cycle to appear. The paradox shows that majority preference, taken pair by pair, doesn’t always produce a coherent ranking.
When no Condorcet winner exists, voting theorists look at the Smith set: the smallest group of candidates who each beat every candidate outside the group in pairwise matchups. Unlike a Condorcet winner, the Smith set always exists and is always unique. When a Condorcet winner does exist, the Smith set is just that one candidate. When preferences cycle, the Smith set contains all the candidates caught in the loop, and the voting system needs some other rule to break the tie among them.
Condorcet Criterion vs. Majority Criterion
A related but weaker standard is the majority criterion, which says that if more than half of voters rank a candidate first, that candidate should win. Every Condorcet-compliant method automatically satisfies the majority criterion, because a candidate favored by over 50% of voters will necessarily win every head-to-head matchup. The reverse isn’t true. A method can satisfy the majority criterion (electing first-choice majorities when they exist) while still failing to elect a Condorcet winner who lacks a first-place majority but wins every pairwise comparison.
Where Condorcet Methods Are Used
Condorcet-compliant voting methods haven’t seen wide adoption in government elections, partly because they require voters to rank candidates and the counting process is more complex than familiar systems. They are more common in organizational settings. Various open-source software communities, professional associations, and political parties use Condorcet methods for internal elections where the priority is finding the candidate with the broadest consensus rather than the most passionate support. The Schulze method, in particular, has become a popular choice for these kinds of elections because it handles cycles gracefully and is relatively straightforward to implement.
The core appeal of the Condorcet criterion is simple: it defines “the best candidate” as the one a majority would choose over any single alternative. Whether a voting system should be required to meet that standard depends on what you value most. Systems that fail the Condorcet criterion, like ranked choice voting, offer other benefits such as reducing spoiler effects. But the Alaska 2022 election showed that the tradeoff is real, and the “wrong” winner by Condorcet standards can emerge from elections with real consequences.