Condorcet ranking: Difference between revisions
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A '''Smith ranking''' ('''Smith set ranking''') is the same as a Condorcet ranking, except instead of being defined in terms of the Condorcet winner and Condorcet loser, it is defined in terms of the [[Smith set]] and [[Smith set#Smith loser set|Smith loser set]]. When there is a multi-member Smith set, the candidates in the Smith set may be ranked in any order so long as they are all ranked above non-Smith set candidates, with the same applying for the Smith loser set candidates with regards to being ranked lower than non-Smith loser set candidates.
When there is a Condorcet ranking (one doesn't always exist), the Smith ranking will be the same as the Condorcet ranking. There will always be at least one Smith ranking, and it is possible to have more than one (each of which will differ only on the order in which Smith or Smith loser candidates are ranked). The simplest way to find a Smith ranking is to find the [[Copeland's method|Copeland]] ranking (the ranking of all candidates such that the candidates with the most ([[Pairwise counting#Terminology|pairwise victories]] minus pairwise defeats) are ranked first, the candidates with the second-most (pairwise victories minus pairwise defeats) are ranked second, etc.)
The '''generalized Smith ranking''' is a Smith ranking where all candidates in the Smith set are equally ranked and the same holds for the Smith loser set; for example:
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