How it works, precisely
As long as a Condorcet winner exists, this variant is strictly identical to Condorcet: chance never intervenes.
Lots are drawn only when there is a cycle, and not from anywhere: Placet draws from the SMITH SET, the smallest group of options that beat every option outside it. A dominated option therefore has no chance of being selected.
The result is not reproducible: that is the price of a guaranteed decision. When the stakes are high, announce the draw to the group before running it.
A worked example
Three options, a perfect cycle — the textbook case of the paradox.
| Duel | Result | Winner |
|---|---|---|
| Lyon vs Bordeaux | 6 – 3 | Lyon |
| Bordeaux vs Lille | 6 – 3 | Bordeaux |
| Lille vs Lyon | 6 – 3 | Lille |
- Lyon beats Bordeaux, Bordeaux beats Lille, Lille beats Lyon: the cycle is complete.
- No option wins all its duels: plain Condorcet stops here.
- All three form the Smith set; the draw picks one, each with a one-in-three chance.
Chance does not replace the vote: it only settles between options the group has made strictly equivalent. Any other tie-break would introduce a bias nobody voted for.
Where it comes from
Drawing lots is no last resort: it was the ordinary method of Athenian democracy, which allotted most public offices by kleroterion and reserved election for technical roles.
It survives in modern electoral law as a tie-break: many electoral codes, the French one included, settle exact ties by lot or by age. Several US states do it literally, drawing a card or flipping a coin.
In social choice theory, lotteries have serious standing: they are the only known way to stay both neutral between options and anonymous between voters when preferences deadlock. Randomisation restores a form of fairness that determinism cannot offer.
Where it is used
- Decisions that absolutely must land today, on a divisive subject.
- Groups split into three clear camps, where a cycle is likely.
- Breaking exact ties, instead of a contestable casting vote.
- Any situation where deadlock costs more than an imperfect choice.
Limits and pitfalls
- Always a result
- Keeps the consensus logic
- Discourages tactical deadlocks
- An accepted element of chance
- Hard to explain
- Can surprise in a paradox
Frequently asked questions
Is chance always involved?
No, almost never. As long as one option wins all its duels, it is declared the winner exactly as in plain Condorcet. The draw exists only for cycles.
What is the Smith set?
The smallest group of options such that each member beats every option outside it. In a cycle, it is the leading pack: the draw only ever picks options genuinely in contention.
Is this really democratic?
As much as the alternatives, and more honest. In a cycle, EVERY tie-break rule — alphabetical order, seniority, the chair's vote — privileges someone. Lots are the only tie-break that favours nobody, and they only apply between options the group itself has placed level.