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Monotonicity: Difference between revisions
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== Details ==
This criteria is one of several sub-cases of the [[Monotonicity criterion]]. A [[voting system]] satisfies the ''Mono-raise criterion'':
{{Definition|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 looser way of phrasing this is that in a non-monotonic system, voting for a candidate can cause that candidate to lose. Systems which fail the monotonicity criterion suffer a form of [[tactical voting]] where voters might try to elect their candidate by voting against that candidate.
[[Plurality voting]], [[Majority Choice Approval]], [[Borda count]], [[Schulze method|Schulze]], [[Maximize Affirmed Majorities]], and [[Descending Solid Coalitions]] 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.<ref>Some parts of this article are derived from text at https://web.archive.org/web/20090610060543/http://condorcet.org/emr/criteria.shtml which was released to the [[project:public domain|public domain]].</ref><ref>Mono-raise test copied from https://electowiki.org/w/index.php?title=Mono-raise_criterion&oldid=15949</ref>
In deterministic single winner elections that is to say no winner is harmed by up-ranking and no loser can win by down-ranking. If the method relies on chance, then up-ranking a candidate can not decrease that candidate's chance of winning, nor can down-ranking the candidate increase it. Douglas R. Woodall called the criterion '''mono-raise'''.<ref name="Woodall-Monotonicity">{{cite journal| title = Monotonicity and single-seat election rules| last = Woodall| first = Douglas R.| journal = Voting matters| volume = 6| pages = 9–14| year = 1996|url=http://www.votingmatters.org.uk/ISSUE6/P4.HTM}}</ref>
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