Category:Sequential comparison Condorcet methods

The Robert's Rules of Order pairwise elimination method is a prominent example of a sequential comparison method. Sequential comparison methods can all be described in the following manner: "order all candidates from first to last, eliminate the pairwise loser between the first two candidates in the order, and repeat until there is only one candidate remaining." All sequential comparison methods are Smith-efficient and thus Condorcet methods, because at least one Smith set member will remain uneliminated after each and every pairwise comparison (since a Smith member can't lose a matchup against a non-Smith member, and a matchup between two Smith members always leaves one Smith member uneliminated). These methods can also be called "Sequential pairwise" methods or any number of other names reflecting that they are based on eliminating the loser of a runoff.

These methods require the fewest pairwise comparisons of any voting method to find a member of the Smith set. If you have a pairwise comparison table, counting the votes in sequential comparison Condorcet methods becomes a lot easier, since if at any point one of the uneliminated candidates pairwise beats all other uneliminated candidates (is a Condorcet winner), that candidate is guaranteed to win.

Note that, similar to how Approval voting can be done by mentioning each candidate one-by-one and asking voters to raise their hands when they approve of the currently mentioned candidate, sequential comparison can be done by mentioning each pair of candidates, asking voters to raise their hands to indicate who they prefer between each pair of candidates, eliminating the pairwise loser, and repeating. To find the pairwise loser for each matchup, only the number of voters who prefer one candidate over the other and the number of voters who have the opposing preference need be known (this can perhaps be found by asking the voters to raise their left arm or right arm respectively depending on which they prefer, or to not raise their arms at all if they have no preference).

See the pairwise counting article for more information. Note that a voter may be able to submit an intransitive preference when asked to actually vote in each pairwise matchup (i.e. they might be able to say A is better than B and B is better than C, but then they say that A isn't better than C, or even, that C is better than A), as opposed to ranking or rating the candidates and having their ballots be converted into pairwise preferences.