What does this mean, and is monotonicity significant in real world elections?
In terms of the frequency of non-monotonicity in real-world elections: there is no evidence that this has ever played a role in any IRV election — not the IRV presidential elections in Ireland, nor the literally thousands of hotly contested IRV federal elections that have taken place for generations in Australia, nor in any of the IRV elections in the United States. True, in theory, in a close election, if enough supporters of candidate A knew enough about the likely rankings of other voters they could, in some rare situations vote strategically as follows: Instead of ranking their true favorite as number one, they could give that first ranking to the weaker of the two likely opponents in the likely final match-up with A, in hopes of helping their favorite candidate win in the final runoff tally. Indeed you can see this happen in traditional runoff systems or in “open primary” systems – consider Rush Limbaugh’s “operation chaos” strategy in the 2008 Democratic presidential nomination
