Uncovered set: Difference between revisions

{{definition|Select the candidate or candidates that are not Fishburn losers. A candidate ''i'' is a Fishburn loser if there is some other candidate ''j'' such that every candidate that pairwise beats ''j'' also pairwise beats ''i'' and there is at least one candidate that pairwise beats ''i'' but does not pairwise beat ''j''.}}It is a nonempty subset of the Smith set. When there are pairwise ties, a likely equivalent definition is: <blockquote>In voting systems, the '''Landau set''' (or '''uncovered set''', or '''Fishburn set''') is the set of candidates ''x'' such that for every other candidate ''z'', there is some candidate ''y'' (possibly the same as ''x'' or ''z'') such that ''y'' is not preferred to ''x'' and ''z'' is not preferred to ''y''. </blockquote>'''Independence of covered alternatives''' says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the [[uncovered set]]. Independence of covered alternatives implies [[Smith criterion|Smith]] and thus [[Condorcet criterion|Condorcet]]. If a method is independent of covered alternatives, then the method fails monotonicity if perfect ties can always be broken in favor of a choice W by using ballots ranking W first.