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A voting system is monotonic if it satisfies the following so-called monotonicity criterion given below. In mathematics, monotonicity usually refers to the different concept of a monotonic function.
The monotonicity criterion for voting systems is the following statement:
A slicker, though looser, way of phrasing this is that in a non-monotonic system, voting for a candidate can cause that candidate to 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
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