Condorcet ranking: Difference between revisions
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A '''Condorcet ranking''' is an ordering of candidates such that every candidate at a given rank [[pairwise beat]]<nowiki/>s every lower-ranked candidate. In other words:
* The [[Condorcet method | Condorcet]] winner, if one exists, is ranked first.
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1 C</blockquote>A and B pairwise tie (2 vs. 2), but both beat C (2 vs. 1), so a generalized (or perhaps "weak") Condorcet ranking would be A=B>C.
When there are [[Condorcet cycle|Condorcet cycles]], there won't be a Condorcet ranking (though it may still be possible to fill in certain parts of the [[Order of finish|order of finish]] i.e. if 5 candidates pairwise beat all others, with 3 candidates in a cycle and pairwise beaten by the 5, but otherwise pairwise beating all others, and 2 candidates pairwise beaten by all others except pairwise tied with each other, then the 5 candidates are in the first 5 places of the Condorcet ranking, with the 2 candidates both in 9th place, with the 3 candidates in the cycle guaranteed to be ranked either 6th, 7th, or 8th, depending on which [[Condorcet completion method]] is used).
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 ==
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