Borda count

The Borda count is a positional voting system in which each candidate receives points based on their rank in each voter's preference ordering, and the candidate with the highest total score wins. Proposed by the French mathematician and naval officer Jean-Charles de Borda in 1770, the system awards n-1 points for a first-place ranking, n-2 for second place, and so on, where n is the number of candidates.

The Borda count violates Arrow's independence of irrelevant alternatives: the social ranking of two candidates depends on how voters rank other candidates relative to them. A candidate who is broadly acceptable — ranked second or third by most voters — can win the Borda count even if no voter ranks them first. This property makes the Borda count resistant to the election of polarizing candidates but vulnerable to strategic manipulation: voters have incentives to misreport their preferences to boost a compromise candidate or to bury a strong competitor.

The system is used in practice by the Australian House of Representatives (as the primary vote in its preferential system), the Heisman Trophy selection, and various academic and professional elections. Its defenders argue that it captures intensity of preference better than simple plurality, since a second-place ranking contributes information that plurality discards. Its critics argue that the information it captures is precisely what makes it manipulable — the very feature that allows compromise candidates to win also allows strategic voters to distort the outcome.

From a systems perspective, the Borda count illustrates the trade-off between preference intensity and strategic robustness in collective choice mechanisms. No system can simultaneously capture intensity, satisfy IIA, and be strategy-proof. The Borda count makes one trade-off; plurality makes another; Condorcet methods make a third.