The monotonicity criterion for instant runoff voting states that ranking a candidate lower can never help them, and ranking a candidate higher can never hurt them. 

For an election to have a non-monotonic outcome means that a different candidate might have won if some number of voters had ranked that winning candidate lower. Any voting method in which votes are counted in rounds has some possibility of a non-monotonic outcome, including two-round runoff elections and IRV. However, IRV makes any exploitation of this possibility for strategic purposes nearly impossible.

To understand how this could work in an IRV election, let’s start by examining a hypothetical case in a two-round runoff election in which two candidates will advance to the final round. A voter could choose to vote strategically if they felt confident that: 

(1) their favorite candidate would advance to the final round, and 

(2) the race for the second spot in the final round would be a very close race between a candidate who might defeat their favorite candidate and a candidate who would probably lose to their favorite candidate.

The voter may try to help their favorite candidate win the general election by voting for the weaker opponent in the preliminary election. If their assumptions are true and their choice to not vote for their favorite candidate in the first round truly helped that candidate win in the later round, that would be a non-monotonic result in a two-round runoff system. 

For this property to influence voting, it is not enough that (1) and (2) are true; the voters would also have to know they are true. 

FairVote has not identified any IRV election in which any group of voters has attempted to exploit the possibility of non-monotonicity for strategic purposes. Doing so successfully would require a highly unusual set of circumstances and a detailed and accurate understanding of how the electorate will rank the candidates. Because this is prohibitively difficult, the issue of monotonicity under IRV is largely academic - it has never had any impact on any IRV campaign and is unlikely to have any impact in the future. 

There is one known case of a possibly non-monotonic result in a U.S. IRV election which depends on how strictly one defines the criterion -- the 2009 mayoral race in Burlington, VT. Learn more about this election on Fairvote's Data on ranked choice voting page https://www.fairvote.org/data_on_rcv#research_rcvwinners).

See this chart (https://infogram.com/comparison-of-voting-systems-1g0n2o0ggln924y) for how single-winner ranked choice compares to other voting methods in terms of evaluative criteria.