How e dey work, well well
From di rankings, dem build di duel matrix: for each pair of options, how many ballots put one before di other. Dem no ask di voter anything pass ranking.
Di Condorcet winner na di option wey win ALL im duels. When e exist, na only one — and no other method fit claim say e represent majority preference better.
When di duels form circle (A beat B, B beat C, C beat A), no winner dey: na di Condorcet paradox, na property of di group preferences, no be counting bug. Placet go show am plain instead make e crown anyhow winner.
Di question come shift go di Smith set: di smallest group of options wey beat every option outside am. Placet randomised variant dey draw from dat set.
Example wey get figures
Three options, five ranked ballots. Compare dem two by two.
| Duel | Result | Winner |
|---|---|---|
| Bordeaux vs Lyon | 3 – 2 | Bordeaux |
| Bordeaux vs Lille | 3 – 2 | Bordeaux |
| Lyon vs Lille | 3 – 2 | Lyon |
- Bordeaux win im two duels: na im be di Condorcet winner.
- Lyon win one out of two, Lille no win any.
- Di final ranking dey follow how many duels each win: Bordeaux, Lyon, Lille.
With one-round voting, Lyon for don win on first choices. Di duels show say majority prefer Bordeaux — na di information wey normal voting dey throw away.
Where e come from
Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet, publish im essay for 1785 on how to apply analysis to di probability of majority decisions. Mathematician, Enlightenment philosopher and later member of di Legislative Assembly, e show say normal voting fit elect option wey di majority go reject for head-to-head.
Im proposal: compare every option with every other one, two by two, and crown di one wey win every time. Na so e come see di problem wey now carry im name — di Condorcet paradox — when di duels dey go round in circle.
Di idea come sleep till di 20th century. Duncan Black wake am for « The Theory of Committees and Elections » (1958). Meanwhile Kenneth Arrow don publish im impossibility theorem for 1951 (Nobel for Economics, 1972): no collective ranking method fit satisfy small reasonable conditions all together.
Ramon Llull don describe pairwise procedure since end of di 13th century, for manuscripts wey dem only find for 2001 — five centuries before Condorcet.
Where dem dey use am
- Di Debian project dey elect im leaders with Condorcet method (Schulze variant), like plenty free software projects.
- Wikimedia, KDE, Gentoo and several software foundations dey use am for internal votes.
- Heavy team decisions, where di legitimacy of di result matter like di result itself.
- Any choice where you suspect say compromise go beat favourites wey dey cancel each other.
Limits and wahala
- E pick di true agreement
- E no dey fall for tactical voting
- E hard to manipulate well well
- Sometimes no winner at all (paradox)
- Longer ballot to fill
- E complex to count
Questions wey people dey ask
Wetin be di Condorcet paradox?
Na when di group preferences dey go round in circle: one majority prefer A pass B, anoda majority prefer B pass C, and third one prefer C pass A. No option win all im duels. E no be error — na possible property of collective preferences, even though each single ballot make perfect sense.
Wetin Placet dey do if cycle happen?
E go announce am, instead make e cook winner. Di ranking by duels won still dey show, but no decision dey presented as settled. If you still wan decide, di randomised Condorcet variant dey draw from di Smith set.
Person fit manipulate Condorcet vote?
Na among di hardest to manipulate. Di Gibbard-Satterthwaite theorem (1973-1975) show say no serious method dey completely safe, but to manipulate Condorcet need make you know other people intentions well well, and e dey easily turn against di person wey try am.
Condorcet or majority judgment?
Condorcet dey compare options against each other; majority judgment dey grade each one on im own scale. Condorcet dey find di champion of di duels when e exist; majority judgment dey always give result and e dey measure di level of support.