Condorcet ranking: Difference between revisions

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The most direct generalization of the Condorcet ranking to handle Condorcet cycles is the Smith set ranking, which is meant to ensure that anytime the candidates can be divided into two groups such that everyone in the first group beats everyone in the second group, then everyone in the first group is ranked higher.
 
The fastest way to find the Condorcet (and Smith) ranking is to find the [[Copeland]] ranking. If every candidate at a given rank has only one more pairwise victory than all candidates at the next-lowest rank (i.e. the number of pairwise victories per candidates incrementally decreases as you go down the order), then there is a Condorcet ranking, otherwise there is only a Smith ranking.
 
== Smith set ranking ==