Nanson's method

The Borda count can be combined with an Instant Runoff procedure to create a hybrid election method that satisfies some desirable properties. This method is also called Nanson's modified method as devised by the mathematician Edward J. Nanson. The method works like this:

Candidates are voted for on ranked ballots as in the Borda count. Then, the points are tallied in a series of rounds. In each round, the candidate with the fewest points is eliminated, and the points are re-tallied as if that candidate were not on the ballot.

Nanson's original method eliminates those choices from a Borda count tally that are at or below the average Borda count score, then the ballots are retallied as if the remaining candidates were exclusively on the ballot. This process is repeated if necessary until a single winner remains.

Nanson's method is currently used to elect a student society at Trinity College-University of Melbourne, the Assembly and Canonry of the Anglican Diocese of Melbourne, the University Council and academic committees at the University of Melbourne, and the University Council at the University of Adelaide, all in Australia.

Instant Borda Runoff satisfies the Condorcet criterion: since Borda always ranks the Condorcet winner over the Condorcet loser, the Condorcet winner will never be eliminated. As compared with the Borda count, however, Instant Borda Runoff does not satisfy the Summability criterion, the Monotonicity criterion, the Participation criterion, and the Consistency criterion, while it does satisfy the Majority criterion, the Smith criterion, and the Independence of Clone Candidates criterion.