Monotonicity criterion

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:

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.

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.

Plurality voting, Majority Choice Approval, Borda count, Cloneproof Schwartz Sequential Dropping, and Maximize Affirmed Majorities are 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

See Also

• Voting system
• Condorcet Criterion
• Generalized Condorcet criterion
• Strategy-Free criterion
• Generalized Strategy-Free criterion
• Strong Defensive Strategy criterion
• Weak Defensive Strategy criterion
• Favorite Betrayal criterion
• Participation criterion
• Summability criterion

External Links

• Election Methods Education and Research Group