Borda Count

The Borda count is a voting rule in social choice theory that assigns evenly spaced scores to the positions in each voter's complete ranking of the candidates without ties. With candidates, each voter awards points to the first-ranked candidate, to the second, and so on down to 0 for the last (Saari 1999, p. 10568).

If is the position of candidate in voter 's ranking, with position 1 best, then the total score over voters is

The candidates attaining the maximum score are the winners. Ties require a separate tie-breaking rule if a single winner is wanted. Using the scores , , ..., 1 gives the same ranking of candidates, since it adds to every total.

Each voter contributes one point to a candidate for each other candidate ranked below it. Thus also counts the individual pairwise preferences for over its opponents. This is different from counting victories in pairwise majority comparisons.

For example, suppose three voters rank above above , while two rank above above . The total scores for , , and are 6, 7, and 2. Here is the Condorcet winner and is ranked first by a majority, yet wins the Borda count.