How it works, precisely
With n options, a first place is worth n−1 points, a second n−2, and so on down to 0 for last. Each option's points are summed.
The Dowdall variant (used in Nauru) awards 1, 1/2, 1/3… and weights top places far more heavily. The scale changes the result — this is not an implementation detail.
Placet uses the classic n−1, n−2, … 0 scale, which keeps the gaps readable: one point of difference is exactly one rank gained on one ballot.
A worked example
Three options, five ranked ballots. First place is worth 2 points, second 1, third 0.
| Ballots | 1st | 2nd | 3rd |
|---|---|---|---|
| 2 voters | Lyon | Bordeaux | Lille |
| 2 voters | Lille | Bordeaux | Lyon |
| 1 voter | Bordeaux | Lyon | Lille |
- Lyon: 2×2 + 1×1 = 5 points.
- Lille: 2×2 = 4 points.
- Bordeaux: 2×1 + 2×1 + 1×2 = 6 points.
Bordeaux wins while being almost nobody's first choice — it is everybody's second. That is exactly what Borda set out to capture, and exactly what his critics hold against him.
Where it comes from
Jean-Charles de Borda — sailor, mathematician and physicist — presented his memoir on election by ballot to the Royal Academy of Sciences in 1770; it was published in 1781. His observation was simple: ordinary voting can elect a candidate the majority rejects.
The idea is older. The Majorcan philosopher Ramon Llull described pairwise comparison and ranking procedures at the end of the thirteenth century — manuscripts rediscovered only in 2001. Nicholas of Cusa proposed a points-based method for electing the Holy Roman Emperor in 1433.
The Academy of Sciences used Borda's method to elect its members until Napoleon, who joined in 1797, had it dropped. Borda had already answered the charge of manipulability in advance: his scheme, he said, was only intended for honest men.
Where it is used
- Parliamentary elections in Nauru and minority seats in Slovenia.
- Sporting and cultural awards: the Ballon d'Or, MVP trophies, literary prizes.
- Setting an agenda or a collective priority, when every option must be compared.
- Team decisions where you want the least divisive option.
Limits and pitfalls
- Rewards broad consensus
- Takes the whole ranking into account
- Simple to calculate
- Very sensitive to "clone" candidates
- Open to tactical ranking
- Can sideline a divisive favourite
Frequently asked questions
Borda or Condorcet?
Borda measures average satisfaction and always returns a result; Condorcet looks for the champion of every duel but may find none. Borda is more robust in practice, Condorcet more demanding in theory.
Do I have to rank every option?
Ideally yes: an incomplete ballot distorts the relative points. That is the method's real cost, and why it becomes tiring beyond seven or eight options.
Why is last place worth zero?
So that only the GAPS between ranks matter. Adding a constant to every rank would leave the final order unchanged; starting from zero simply makes it easier to read.