How it works, precisely
From the rankings, a matrix of duels is built: for each pair of options, how many ballots put one ahead of the other. Nothing more is asked of the voter than a ranking.
The Condorcet winner is the option that wins ALL its duels. When one exists it is unique — and no other method can claim to represent majority preference better.
When the duels form a cycle (A beats B, B beats C, C beats A), there is no winner: that is the Condorcet paradox, a property of the group's preferences rather than a counting bug. Placet reports it honestly instead of crowning an arbitrary winner.
The question then shifts to the Smith set: the smallest group of options that beat every option outside it. Placet's randomised variant draws from that set.
A worked example
Three options, five ranked ballots. Compare them two at a time.
| Duel | Result | Winner |
|---|---|---|
| Bordeaux vs Lyon | 3 – 2 | Bordeaux |
| Bordeaux vs Lille | 3 – 2 | Bordeaux |
| Lyon vs Lille | 3 – 2 | Lyon |
- Bordeaux wins both its duels: it is the Condorcet winner.
- Lyon wins one of two, Lille none.
- The final ranking follows the number of duels won: Bordeaux, Lyon, Lille.
Under a single-round vote, Lyon might have won on first choices. The duels reveal that a majority prefers Bordeaux — the information ordinary voting throws away.
Where it comes from
Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet, published his essay on the application of analysis to the probability of majority decisions in 1785. A mathematician, Enlightenment philosopher and later member of the Legislative Assembly, he showed that ordinary voting can elect an option the majority would reject in a head-to-head.
His proposal: compare every option with every other, two at a time, and crown the one that wins each time. In doing so he discovered the obstacle that now bears his name — the Condorcet paradox — where duels run in a circle.
The idea then slept until the twentieth century. Duncan Black revived it in « The Theory of Committees and Elections » (1958). Meanwhile Kenneth Arrow had published his impossibility theorem in 1951 (Nobel Prize in Economics, 1972): no collective ranking method can satisfy a handful of entirely reasonable requirements at once.
Ramon Llull had described a pairwise procedure as early as the late thirteenth century, in manuscripts recovered only in 2001 — five centuries ahead of Condorcet.
Where it is used
- The Debian project elects its leaders by a Condorcet method (the Schulze variant), as do many free software projects.
- Wikimedia, KDE, Gentoo and several software foundations use it for internal votes.
- Weighty team decisions, where the legitimacy of the result matters as much as the result.
- Any choice where you suspect a compromise would beat favourites who cancel each other out.
Limits and pitfalls
- Picks the true consensus
- Immune to tactical voting
- Very hard to manipulate
- Sometimes no winner at all (paradox)
- A longer ballot to fill in
- Complex to count
Frequently asked questions
What is the Condorcet paradox?
A situation where group preferences run in a circle: one majority prefers A to B, another prefers B to C, and a third prefers C to A. No option wins every duel. It is not an error — it is a possible property of collective preferences, even though each individual ballot is perfectly coherent.
What does Placet do when there is a cycle?
It says so, rather than manufacturing a winner. The ranking by duels won is still shown, but no decision is presented as settled. If you need to decide anyway, the randomised Condorcet variant draws from the Smith set.
Can a Condorcet vote be manipulated?
It is among the hardest to manipulate. The Gibbard-Satterthwaite theorem (1973-1975) establishes that no non-trivial method is completely immune, but manipulating Condorcet requires very precise knowledge of everyone else's intentions, and easily backfires.
Condorcet or majority judgment?
Condorcet compares options against each other; majority judgment grades each on an absolute scale. Condorcet finds the champion of the duels when one exists; majority judgment always returns a result and measures the level of support.