Borda count

The Borda count is a voting system used for single-winner elections in which each voter rank-orders the candidates.

Variants

• The Borda count method can be extended to include tie-breaking methods.
• Ballots that do not rank all the candidates can be allowed in three ways.
• One way to allow leaving candidates unranked is to leave the scores of each ranking unchanged and give unranked candidates 0 points. For example, if there are 10 candidates, and a voter votes for candidate A first and candidate B second, leaving everyone else unranked, candidate A receives 9 points, candidate B receives 8 points, and all other candidates receive 0. This, however, allows strategic voting in the form of bullet voting: voting only for one candidate and leaving every other candidate unranked. This variant makes a bullet vote more effective than a fully-ranked vote. This variant would satisfy the Plurality criterion and the Non-compulsory support criterion.
• Another way, called the modified Borda count, is to assign the points up to k, where k is the number of candidates ranked on a ballot. For example, in the modified Borda count, a ballot that ranks candidate A first and candidate B second, leaving everyone else unranked, would give 2 points to A and 1 point to B. This variant would not satisfy the Plurality criterion or the Non-compulsory support criterion.
• The third way is to employ a uniformly truncated ballot obliging the voter to rank a certain number of candidates, while not ranking the remainder, who all receive 0 points. This variant would satisfy the same criteria as the Borda count.
• A proportional election requires a different variant of the Borda count called the quota Borda system.
• A voting system based on the Borda count that allows for change only when it is compelling, is called the Borda fixed point system.
• A procedure for finding the Condorcet winner of a Borda count tally is called Nanson's method or Instant Borda runoff.