No, this could also happen with, say, some voting bloc shifting someone up deeper in the order – though it would (I think) require more than 3 candidates for an example like that. So, for instance, a change of some voters from A>B>C>D to A>C>B>D could change an election from C winning to C losing.
How do voters moving from C>A>B to A>C>B improve B’s rankings?
The point of the monotonicity criterion is that it is one of the “commonsense” criteria for a voting algorithm; in this case that individual voters improving their esteem of a candidate should not have a negative effect on that candidate’s results. There’s additional value in this criterion in that a voter should always be able to rank their candidates in their most preferred order, in order to yield the best overall results for their preferred candidate.
All the commonly accepted social-choice criteria are equally reasonable-seeming but also equally mutually impossible. They include things like:
- Irrelevant alternatives – we should be able to safely ignore candidates we know won’t win without altering the election results. (As @mmascari helpfully pointed out, even plurality voting fails this one)
- Condorcet criterion – if a candidate can beat every other candidate in a one-on-one vote, they should be the victor in a group election
- Consistency – If we split the electorate into two groups and give them separate elections, if those two groups separately agree on the winner, then the whole electorate should agree on the same winner if considered together.
- Reversal symmetry – if we ran another election with every voting bloc’s preferences reversed (e.g., A>B>C becomes C>B>A), we should get a different winner.
- Participation – The best way for a voter to help their preferred candidate to win should not be for them to abstain.
Instant Runoff Voting fails all these criteria.
Of course, Arrow’s Impossibility Theorem demonstrates that all social choice functions with more than two outcomes fail some desirable and commonsense criterion.
My issue is not so much with IRV but with the lack of reflection on which social choice criteria should be compromised. IRV is probably better than plurality voting, but there’s reason to socially make a determination about which criteria are important to preserve and which criteria are expendable. This determination could have implications for which social choice metric we “should” be using.
Of course, to do that we would probably want to hold some kind of vote.
I’ll stop now since my Gödel senses are tingling.