I am looking for the simplest possible example of instant runoff voting failing the monotonicity criterion. By “simplest possible” I mean the scenario with the fewest number of candidates $(3)$ and the fewest number of votes switched $(1?, 2?)$ that still demonstrates the effect. I'm guessing that the result is the same, but for the sake of specificity, let's say we want the case where increasing support for a candidate causes them to lose the election in round two (as opposed to decrease support causing them to win).
The wikipedia article (https://en.wikipedia.org/wiki/Monotonicity_criterion#Instant-runoff_voting_and_the_two-round_system_are_not_monotonic) uses an example with 3 candidates and 2 votes being switched, but with $100$ total votes. I’m wondering what the minimum number of total votes needed is. Also, is there a general proof to show that the solution really is the minimum?
Thanks in advance for your insights! -James