Condorcet Method - Single-method Systems

Single-method Systems

Some Condorcet methods use a single procedure that inherently meets the Condorcet criteria and, without any extra procedure, also resolves circular ambiguities when they arise. In other words, these methods do not involve separate procedures for different situations. Typically these methods base their calculations on pairwise counts. These methods include:

• Copeland's method: This simple method involves electing the candidate who wins the most pairwise matchings. However, it often produces a tie.
• Kemeny-Young method: This method ranks all the choices from most popular and second-most popular down to least popular.
• Minimax: Also called Simpson, Simpson-Kramer, and Simple Condorcet, this method chooses the candidate whose worst pairwise defeat is better than that of all other candidates. A refinement of this method involves restricting it to choosing a winner from among the Smith set; this has been called Smith/Minimax.
• Nanson's method
• Dodgson's method
• Ranked Pairs: This method is also known as Tideman, after its inventor Nicolaus Tideman.
• Schulze method: This method is also known as Schwartz sequential dropping (SSD), cloneproof Schwartz sequential dropping (CSSD), beatpath method, beatpath winner, path voting and path winner.

Ranked Pairs and Schulze are procedurally in some sense opposite approaches (although they very frequently give the same results):

• Ranked Pairs (and its variants) starts with the strongest defeats and uses as much information as it can without creating ambiguity.
• Schulze repeatedly removes the weakest defeat until ambiguity is removed.

Minimax could be considered as more "blunt" than either of these approaches, as instead of removing defeats it can be seen as immediately removing candidates by looking at the strongest defeats (although their victories are still considered for subsequent candidate eliminations).