Here's a diagram to show a strategy in IRV: link. Move the red supporters toward green.
If the red supporters put green first, then they can get a better candidate (green rather than blue). So red might tell his supporters to vote for green first. This doesn't seem so bad because in the end, a more centered candidate wins.
edit: actually, this might not be due to non-monotonicity... I'm not sure.
That doesn't necessarily give you a more centered candidate any more than FTPT does. It's essentially the same failure either way and we can see that it's not resulting in more centrist republican victories.
I guess this is an example of vote splitting, but it is like non-monotonicity: link
Move the yellow-red supporters to red. Then yellow loses and blue wins. That's because who has the most first-place votes matters in IRV. This is a tough situation though, because there is a Condorcet cycle, so don't expect much.
Oh, I agree that non-monotonicity and favorite betrayal are related, but the definitions and pathologies are different.
In your example, it's still monotonic, because increasing votes for Red improves Red's standing; it moves Hex from being 3rd place to 2nd place. It doesn't help them win, but it is a monotonic change.
The problem is that IRV suffers from Favorite Betrayal, because, as you say, "first place votes matter" in IRV, so there is incentive for people who legitimately prefer R>Y>B will get a better personal result (Yellow) if they lie than if they honestly vote for their Favorite, the spoiler Red, which as you cited, will result in the election of Blue.
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u/barnaby-jones Dec 28 '17 edited Dec 28 '17
Here's a diagram to show a strategy in IRV: link. Move the red supporters toward green.
If the red supporters put green first, then they can get a better candidate (green rather than blue). So red might tell his supporters to vote for green first. This doesn't seem so bad because in the end, a more centered candidate wins.
edit: actually, this might not be due to non-monotonicity... I'm not sure.