Condorcet ranking: Difference between revisions
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== Smith set ranking ==
[[File:Finding smith set ranking.png|thumb|543x543px|An example of finding the generalized Smith set ranking using the [[Pairwise counting|pairwise matrix]]. One way to better visualize it is to imagine the arrow starting from the top left and traveling down one cell at at a time, creating a box around a group of candidates any time there are only pairwise victories to the right of the cells that are enclosed by the arrow. For further visual clarity, imagine a green background on the cells with pairwise victories; the arrow tries to cover the fewest cells necessary for there to be an all-green background to the right. ]]
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.<ref>{{Cite web|url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.200.8245&rep=rep1&type=pdf|title=AN EXTENSION OF THE CONDORCET CRITERION AND KEMENY ORDERS|last=|first=|date=|website=|url-status=live|archive-url=|archive-date=|access-date=|quote=A first objective of this paper is to propose a formalization of this idea, called the Extended
Condorcet Criterion (XCC). In essence, it says that if the set of alternatives can be partitioned in such a
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