Borda count

How e dey work, well well

With n options, first place carry n−1 points, second n−2, and so on down to 0 for last. Dem add each option points.

Di Dowdall variant (Nauru dey use am) give 1, 1/2, 1/3…: e dey weight top places heavy pass. Di scale dey change di result — no be small implementation detail.

Placet dey use di classic n−1, n−2, … 0 scale, wey make di gaps easy to read: one point na exactly one rank wey you gain for one ballot.

Example wey get figures

Three options, five ranked ballots. First place na 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 win even though almost nobody put am first — na everybody second choice. Na exactly wetin Borda wan capture, and na exactly wetin im critics dey use against am.

Where e come from

Jean-Charles de Borda — sailor, mathematician and physicist — carry im paper on election by ballot go di Royal Academy of Sciences for 1770; dem publish am for 1781. Im point simple: normal voting fit elect candidate wey di majority no want.

Di idea old pass dat. Di Majorcan philosopher Ramon Llull describe pairwise comparison and ranking since end of di 13th century — na for 2001 dem come find di manuscripts. Nicholas of Cusa propose points method for 1433 to elect di Holy Roman Emperor.

Di Academy of Sciences use Borda method to elect members; according to one tradition wey Duncan Black report, Napoleon, wey join for 1797, na im make dem drop am — but people dey argue dat story. Dem credit Borda with dis answer to di manipulation talk: im scheme, e talk, na for honest people only.

Where dem dey use am

Parliament elections for Nauru and minority seats for Slovenia.
Sports and culture awards: Ballon d'Or, MVP trophies, book prizes.
To set agenda or collective priority, when you must compare all di options.
Team decisions where you want di option wey dey divide people less.

Limits and wahala

✓ GOOD SIDE

E reward broad agreement
E take di whole ranking into account
E simple to calculate

✕ BAD SIDE

E dey sensitive to "clone" candidates
E open to tactical ranking
E fit push aside favourite wey divide people

Clones fit spoil am

If you add weak options wey resemble one rival, im average go fall. To write di list of options come turn political work.

Tactical burying

To rank di most serious rival last by mouth dey pay, and nobody fit catch am well.

E fail di Condorcet criterion

Option wey win every duel fit still lose di Borda count. Di two methods dey answer different questions, and Borda accept dat.

Questions wey people dey ask

Borda or Condorcet?

Borda dey measure average satisfaction and e dey always give result; Condorcet dey look for di champion of all duels, but e fit find none. Borda strong pass for practice, Condorcet strict pass for theory.

I must rank all di options?

Ideally yes: incomplete ballot dey spoil di relative points. Na di real cost of di method, and na why e dey tire people once options pass seven or eight.

Why last place na zero?

So dat na only di GAPS between ranks go count. If you add same number to every rank, di final order no go change; to start from zero just make am easy to read.

Sources

Di main books and papers wey dis page stand on.

Borda, Jean-Charles de, Mémoire sur les élections au scrutin, Histoire de l'Académie royale des sciences, année 1781, partie « Mémoires », Imprimerie royale, Paris, p. 657-665 — lu en 1770, volume effectivement imprimé en 1784, 1781.
Black, Duncan, The Theory of Committees and Elections, Cambridge University Press, 1958.
Saari, Donald G., The Borda Dictionary, Social Choice and Welfare, 7(4), 279-317, 1990. DOI ↗
McLean, Iain et Urken, Arnold B. (dir.), Classics of Social Choice, University of Michigan Press, 1995.