The Borda Voting Method

Don Saari argues that the only fair way for a group of people to select one candidate from N candidates through a vote.is to use a method proposed by Borda. Voters rank their candidates in an ordered list, and then the candidates are awarded points based on their rankings in each of the voters lists. For example, in an election whith three candidates, a candidate may get 3 points for being ranked first, 2 points for being ranked second, and 1 point for boing ranked third. If there is uniform spacing between point rewards and if voters choose a ranking for all candidates, omitting no candidate, then the system can be argued to present a result which accurately reflects the will of the voters.

Points to draw attention to:

• The system demands that voters be rational: the requirement that they rank all candidates in a single ordered list prevents cycles, where a confused voter in individual votes would choose A over B, choose B over C, and choose C over A.
• The Borda system also causes cancellation of cycles where voter 1 prefers A over B over C, voter 2 prevers B over C over A, and voter 3 prefers C over A over B. Reflection on a two-candidate election suggests that this is the proper behavior.
• When a voter is truly neutral about two candidates, ranking the candidates in arbitrary order cannot alter the results in a fashion that the neutral voter will care about. However, if a voter is not familiar with a candidate and does not rank them at all, the election could be skewed unless the voter's left-over points are assigned evenly to the candidates that the voter did not rank.
• Arrow's argument, that a dictatorship is the only voting system in which the results of the vote don't change if the voting procedure changes, is avoided. Borda's method is to argue that there is no desire to chose a voting scheme which preserves results in the face of fluctuating voting procedure. The voting procedure should be fixed, and if it is fixed so that candidates receive equally-spaced point values for their place in voters' ranked lists, the result is matmematically stable.