Uncovered set: Difference between revisions
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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.
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):
T = U + U<sup>2</sup>
where U [is] the tournament matrix. The alternatives represented by rows in T where all non-diagonal entries are non-zero form the uncovered set.<ref>https://play.google.com/store/books/details?id=tGsQl-wxbKAC&rdid=book-tGsQl-wxbKAC&rdot p.176</ref></blockquote>(The square of a matrix can be found using matrix multiplication; here is a [https://www.youtube.com/watch?v=3c2rzaO1h28 video] explaining how to do so. The pairwise matrix and its squared matrix can be added together using [https://www.purplemath.com/modules/mtrxadd.htm matrix addition].)
[[Category:Voting theory]]
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