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. |
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. |
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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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T = U + U<sup>2</sup> |
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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].) |
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[[Category:Voting theory]] |
[[Category:Voting theory]] |