The Borda Voting Method
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
- 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.