Uncovered set: Difference between revisions
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The Banks set<ref>http://spia.uga.edu/faculty_pages/dougherk/svt_13_multi_dimensions2.pdf "The Banks set (BS) is the set of alternatives resulting from strategic voting in a successive elimination procedure"</ref> (the set of candidates who could win a [[:Category:Sequential comparison Condorcet methods|sequential comparison]] contest for at least one ordering of candidates when voters are strategic), [[Copeland]] set (set of candidates with the highest Copeland score), and Schattschneider set are all subsets of the uncovered set. <ref name="Seising 2009 p. ">{{cite book | last=Seising | first=R. | title=Views on Fuzzy Sets and Systems from Different Perspectives: Philosophy and Logic, Criticisms and Applications | publisher=Springer Berlin Heidelberg | series=Studies in Fuzziness and Soft Computing | year=2009 | isbn=978-3-540-93802-6 | url=https://books.google.com/books?id=yCBqCQAAQBAJ | access-date=2020-03-13 | page=350}}</ref>
The '''Banks set''' is a subset of the Smith set because when all but one candidate in the Smith set has been eliminated in a sequential comparison election, the remaining Smith candidate is guaranteed to pairwise beat all other remaining candidates, since they are all non-Smith candidates, and thus can't be eliminated from that point onwards, meaning they will be the final remaining candidate and thus win.
The '''Dutta set''' (also known as Dutta's minimal covering set) is the set of all candidates such that when any other candidate is added, that candidate is covered in the resulting set. It is a subset of the Smith set because all candidates in the Smith set cover (i.e. have a one-step beatpath, direct pairwise victory) all candidates not in the Smith set.
One way that has been suggested to find the uncovered set is:<blockquote>This suggests the use of the outranking [pairwise comparison] matrix and its square to identify the uncovered set (Banks, 1985):
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