The Borda Count

The Borda Count is a voting procedure in which each voter ranks the candidates first to last. Then each candidate is given n-j points, where n is the total number of candidates and j is that candidate's rank. For example, with n=5 candidates, the following table tells how to distribute the points for each voter's ranking.

The Borda Count, named after Jean Charles de Borda, doesn't throw away a voter's second, third, fourth, etc. choices. It uses all of a voter's choices in determining the winner of the election. It happens to be the voting method used in the major college football rankings.

In our beverage example, the Borda Count gives...

Dr. Pepper = 6x2 + 0x1 + 9x0 = 12 points
Pepsi = 5x2 + 4x1 + 6x0 = 14 points
Coke = 4x2 + 11x1 + 0x0 = 19 points

Thus Coke is the Borda Count winner! Four of the people like Coke the best and the other 11 like it second best. No one is dramatically disappointed!

What's the moral? We used three different voting procedures (plurality, runoff, Borda Count) and received three different winners! The election outcome may depend on the voting procedure and not the preferences of the voters!