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. Clearly, non-monotonicity is very counterintuitive, although some do defend such systems (see Instant-runoff voting). Furthermore, although all voting systems are vulnerable to tactical voting, systems which fail the monotonicity criterion suffer an unusual form, where voters might try to elect their candidate by voting against that candidate.

The Borda count is monotonic, while Coombs' method and Instant-runoff voting are not. Approval voting is monotonic, using a slightly different definition, because it is not a preferential system: you can never help a candidate by not voting for them.

Some parts of this article are derived from text at http://condorcet.org/emr/criteria.shtml