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The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots. That is to say, in single winner elections no winner is harmed by up-ranking and no loser is helped by down-ranking. Douglas Woodall called the criterion mono-raise.
Raising a candidate x on some ballots while changing the orders of other candidates does not constitute a failure of monotonicity. E.g., harming candidate x by changing some ballots from z > x > y to x > z > y would violate the monotonicity criterion, while harming candidate x by changing some ballots from z > x > y to x > y > z would not.
The monotonicity criterion renders the intuition that there should be neither need to worry about harming a candidate by up-ranking nor it should be possible to support a candidate by counter-intuitively down-ranking. There are several variations of that criterion; e.g., what Douglas R. Woodall called mono-add-plump: A candidate x should not be harmed if further ballots are added that have x top with no second choice. Noncompliance with the monotonicity criterion doesn't tell anything about the likelihood of monotonicity violations, failing in one of a million possible elections would be as well a violation as missing the criterion in any possible election.
Of the single-winner ranked voting systems, Borda, Schulze, ranked pairs, maximize affirmed majorities, descending solid coalitions, and descending acquiescing coalitions are monotonic, while Coombs' method, runoff voting, and instant-runoff voting are not. The multi-winner single transferable vote system is also non-monotonic.