Quick Answer
A Condorcet count reads every ranked ballot as a set of head-to-head contests. For each pair of candidates it asks which one this voter put first, and adds it up. A candidate who beats every other candidate one on one is the Condorcet winner, and where one exists, a Condorcet method elects them.
Sometimes no such candidate exists, because head-to-head results can form a loop. That is the Condorcet paradox, and it is why the method needs a published completion rule. Three are supported: Schulze, ranked pairs and minimax.
This article is general information, not legal advice. Confirm what your governing documents allow before adopting a new method.
The Pairwise Matrix
Take three candidates and 100 ranked ballots. Compare them two at a time:
| Contest | Result |
|---|---|
| Alvi vs Bourne | Alvi 55, Bourne 45. Alvi wins. |
| Alvi vs Cruz | Alvi 52, Cruz 48. Alvi wins. |
| Bourne vs Cruz | Bourne 60, Cruz 40. Bourne wins. |
Alvi beats both rivals, so Alvi is the Condorcet winner and is elected. Notice this did not require Alvi to lead on first preferences. A candidate can be nobody's favorite and still be the person a majority prefers to each alternative, which is the case Condorcet is built to catch.
Two reading rules make truncated ballots behave sensibly:
- A ranked candidate beats every candidate the ballot left unranked.
- Between two unranked candidates, the ballot expresses no preference at all.
The Condorcet Paradox
Now change one contest:
| Contest | Result |
|---|---|
| Alvi vs Bourne | Alvi wins |
| Bourne vs Cruz | Bourne wins |
| Cruz vs Alvi | Cruz wins |
Alvi beats Bourne, Bourne beats Cruz, and Cruz beats Alvi. There is no candidate who beats everyone. This is a genuine cycle, not an error, and it is the reason Condorcet methods come in named varieties: each one is a published rule for breaking a cycle in a defensible way.
Every rule below elects the Condorcet winner whenever one exists. They only differ inside a cycle.
The Three Completion Rules
| Rule | How it decides | Notable users |
|---|---|---|
| Schulze (beatpath) | X beats Y if the strongest chain of head-to-head wins from X to Y is stronger than the chain back. A chain is only as strong as its weakest link. | Debian, Wikimedia, many open-source projects |
| Ranked pairs (Tideman, 1987) | Lock in victories from the largest margin downward, skipping any that would close a cycle. Whoever is left undefeated wins. | Used where an auditable lock-in order is wanted |
| Minimax (Simpson-Kramer) | Score each candidate by the strength of their worst defeat. The smallest worst defeat wins. | The simplest to explain and hand-check |
Schulze is the default and the most widely deployed. If your bylaws name a rule, use that one.
Where equal margins leave a rule with no published order, as can happen under ranked pairs, the count works through every possible order and accepts the answer only if all of them agree. Where they do not, the tie is reported rather than invented away.
Single Winner Only
Condorcet is a single-winner method here, deliberately. Multi-seat Condorcet has no standard definition, and offering one would mean inventing a rule and putting your board's name on it. For a multi-seat board, use single transferable vote, which is the established proportional answer.
Condorcet Compared
| Condorcet | Instant runoff | Borda | |
|---|---|---|---|
| Elects the head-to-head winner | Always, when one exists | Not always | Not always |
| Can eliminate a strong candidate early | No | Yes | No |
| Needs a tiebreak rule | Only inside a cycle | For eliminations | For equal points |
| Explaining it to members | Hardest | Moderate | Easy |
| Seats | One | One | One or several |
Condorcet's practical cost is explainability. "The candidate a majority prefers to each of the others" is a sentence any member accepts. Beatpath strength is not. If your election is contentious, budget time to explain the count before ballots open, not after results publish.
Running a Condorcet Election Online
Condorcet is the Ranked choice question type with the counting method set to Condorcet. The ballot is the same ranked ballot used by instant runoff, STV and Borda, so voters see nothing unusual.
You can select the completion rule: Schulze, ranked pairs or minimax. The results publish the full pairwise matrix, so any member can verify each head-to-head contest for themselves, and any cycle is shown rather than quietly resolved. Weighted elections count weight rather than ballots throughout.
Elections up to 25 voters are free, and paid elections start at $4.99.
Frequently Asked Questions
Q: What is a Condorcet winner?
The candidate who would beat every other candidate in a one-on-one contest, based on how voters ranked them. Where such a candidate exists, every Condorcet method elects them.
Q: What is the Condorcet paradox?
A situation where head-to-head results form a loop, such as A beating B, B beating C and C beating A, so no candidate beats everyone. It requires a published completion rule to resolve.
Q: What is the Schulze method?
A Condorcet completion rule that compares the strongest chains of head-to-head wins between candidates, where a chain is only as strong as its weakest link. Debian and Wikimedia both use it.
Q: What is the difference between ranked pairs and minimax?
Ranked pairs locks in victories from the largest margin down, skipping any that would create a cycle. Minimax simply scores each candidate by their worst defeat and elects the one whose worst defeat is smallest.
Q: Can Condorcet voting fill multiple seats?
Not in any standard way, which is why it is offered as a single-winner method only. For a multi-seat board, single transferable vote is the established proportional method.
Ready to run one? Create your election, or compare every method in the voting methods series.
This article is general information, not legal advice. We recommend you do your own research and confirm anything you plan to act on. Where this article states law, the section is cited so you can read the primary source yourself rather than take our word for it — that is what the citations are for. Election requirements also turn on your own governing documents, which we have not seen, and statutes are amended. For advice about your community, consult a qualified attorney licensed in your state.
We work hard to verify every citation against the primary source, but laws change and errors happen. If you spot an inaccuracy, email [email protected] and we will correct it. See our editorial standards for how these pages are researched and checked.
How does your organization currently handle votes?
Compare your approach with other community leaders.
Related Resources
Free: Nonprofit Election Guide
A step-by-step guide covering IRS requirements, state AG filing, conflict-of-interest disclosures, voting thresholds, and record retention for nonprofit board elections.
No spam. Unsubscribe anytime.
