The Borda method is most likely to respect the Condorcet principle

Summary We prove that in the class of weighted voting systems the Borda Count maximizes the probability that a Condorcet candidate is ranked first in a group election. A direct result is that the Borda Count maximizes the probability that a transitive, binary ranking of the candidates is preserved in a group election. A preliminary result, but one of independent interest, is that the Borda Count maximizes the probability that a majority outcome betweenany two candidates is reflected by the group election. All theorems are valid when there is a uniform probability distribution on the voter profiles and can be generalized to other uniform-like probability distributions. This work extends previous results of Fishburn and Gehrlein from three candidates to any number of candidates.This work is a portion of my doctoral dissertation The Geometric Investigation of Voting Techniques: A Comparison of Approval Voting, Positional Voting Techniques and the Borda Count written under Don Saari at Northwestern University, Evanston, Illinois.