The problem with non-monotonicity is that we know IRV must be electing the wrong candidate in at least one of the two elections in the non-monotonic pair.

For instance, say we operate on the premise that X was indeed the rightful winner in the “before” election. Then X necessarily must also be the rightful winner in the “after” election, since X has even more support in the “after” election than in the “before” election. Yet IRV does not elect X in the “after” election.

Likewise, if we operate on the premise that X was indeed not the rightful winner of the “after” election, then X also cannot be the rightful winner of the “before” election, since X has even less support in the “before” election than in the “after” election. Yet IRV elects X in the “before” election.

This means that, statistically speaking, IRV elects the wrong winner in at least half of all non-monotonic elections. So if an election forms either half of a non-monotonic election pair, like either of the two above, we know there is at least a 50% chance that the wrong winner was elected.