Jean-Charles de Borda
Borda was born in Dax in the South West of France in 1733 in a family of little nobility - he was Chevalier, that is knight and not Count as written in Mathias Risse (2005) even though the pun “Count de Borda”/“Borda count” opposed to the “Marquis de Condorcet” was amusing and clever.
He studied at the College Royal Henry-le-Grand (a College of Jesuits at that time) in La Fleche, a small town near Le Mans. The most famous pupil of this College was Descartes and La Fleche is also well known for being the city where David Hume settled while in France and where he wrote most of A Treatise of Human Nature. Borda became a member of the military engineering corps, worked on ballistics and became a member of the Academie Royale des Sciences. He participated in the American war of independence as a French Navy officer but was taken prisoner by the British. Later, he worked on the metric system as chairman of the Commission des Poids et Mesures (Committee of Weights and Measures). He died in 1799.Borda’s work in social choice is rather limited: nine pages in Histoire de l’Academie Royale des Sciences pour 1781, published in 1784. In his “Memoire sur les elections au scrutin”, Borda presents his system: the so-called Borda count. Each voter ranks the candidates without ties: one point is attributed to the candidate ranked last in the voter’s ranking, two points are attributed to the candidate ranked just before the last one, and so on, the top candidate obtaining a number of points that is equal to the number of candidates. Note that we could start from zero up to the number of candidates minus one, or even, as indicated by Borda, start from any number and add the same fixed number when we go from one rank to the rank that is just above it. The points obtained by a candidate are added and the winner(s) is (are) the candidate(s) who has (have) obtained the greatest number. However, there is more in these nine pages. First, an example is given where a plurality winner is a Condorcet loser. This demonstrates that, in Borda’s view, the plurality rule is flawed. On the other hand, there is no proof that, in non-trivial cases, a Borda winner cannot be a Condorcet loser. However, Borda derives simple inequalities for the case when there is a Borda winner that coincides with a plurality winner.