If an alternative X loses, and the ballots are changed only by placing X in lower positions, without changing the relative position of other candidates, then X must still lose.
It is considered a good thing if a voting system is monotonic. If a voting system is not monotonic, it can encourage tactical voting, as there will be situations in which a voter will be encouraged to bury their favorite (i.e. rank their favorite option lower than their sincere preference).
Approval voting and the Borda count are monotonic, while Coombs' method and Instant-runoff voting are not.
Some parts of this article are derived from text at http://condorcet.org/emr/criteria.shtml
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