The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. The Borda count is a single winner election method in which voters rank candidates in order of preference. ... When the single transferable vote voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. ...

Nanson method

The Nanson method is based on the original work of the mathematician Jeff Cockbreath Nanson.

Nanson's 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.

Baldwin method

This variant was devised by Joseph M. Baldwin and works like this: Joseph Mason Baldwin (9 September 1878 - 6 July 1945) born in Melbourne, Australia, was an astronomer who received his professional education at the University of Melbourne in the state of Victoria, Australia from 1896 to 1913, where he received two Bachelors, a Masters and lastly a Doctor of...

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.

Satisfied and failed criteria

The Nanson method and the Baldwin method satisfy the Condorcet criterion: since Borda always gives any existing Condorcet winner more than the average Borda points, the Condorcet winner will never be eliminated. They do not satisfy the independence of irrelevant alternatives criterion, the monotonicity criterion, the participation criterion, the consistency criterion and the independence of clones criterion, while they do satisfy the majority criterion, the mutual majority criterion, the Condorcet loser criterion, reversal symmetry and the Smith criterion. The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... Independence of irrelevant alternatives (IIA) is an axiom often adopted by social scientists as a basic condition of rationality. ... A voting system is monotonic if it satisfies the monotonicity criterion, given below. ... Statement of Criterion Adding one or more ballots that vote X over Y should never change the winner from X to Y. Complying Methods Plurality voting, Approval voting, Cardinal Ratings, Borda count, and Woodalls DAC method all pass the Participation Criterion. ... A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same alternative being selected, an election of the entire electorate also selects that alternative. ... Strategic nomination is the manipulation of an election through its candidate set (compare this to tactical voting, where the manipulation comes from the voters). ... The majority criterion is a voting system criterion, used to objectively compare voting systems. ... The mutual majority criterion is a criterion used to compare voting systems. ... Given a vote where voters rank options in order of preference, a Condorcet loser is an option that loses all of its pairwise comparisons. ... Reversal symmetry is a voting method criterion that is stated as follows: If a candidate A is the unique winner, and the individual preferences of each voter are inverted, then candidate A must not be elected. ... In voting systems, the Smith set is the smallest set of candidates in a particular election who, when paired off in pairwise elections, can beat all other candidates outside the set. ...

Use of Nanson and Baldwin

Nanson's method was used in city elections in the U.S. town of Marquette, Michigan in the 1920s.^[1] It was formally used by the Anglican Diocese of Melbourne and in the election of members of the University Council of the University of Adelaide. It was used by the University of Melbourne until 1983. Motto: (Out Of Many, One) (traditional) In God We Trust (1956 to date) Anthem: The Star-Spangled Banner Capital Washington D.C. Largest city New York City None at federal level (English de facto) Government Federal constitutional republic  - President George Walker Bush (R)  - Vice President Dick Cheney (R) Independence from... Marquette is a city in the U.S. state of Michigan. ... 1920 (MCMXX) was a leap year starting on Thursday. ... The term Anglican describes those people and churches following the religious traditions of the Church of England, especially following the Reformation. ... Melbournes CBD has grown to straddle the Yarra River in three major precincts. ... The University of Adelaide (colloquially Adelaide University or Adelaide Uni) is a public university located in Adelaide. ... The Old Quad Building, formerly Old Law The University of Melbourne, located in Melbourne, Victoria, is the second oldest university in Australia, and the oldest in Victoria. ... 1983 (MCMLXXXIII) was a common year starting on Saturday of the Gregorian calendar. ...

Note

1. ^  See: Australian electoral reform and two concepts of representation