In this 100-voter example election, under IRV, "A" wins.
("B," with the fewest top-rank votes, is eliminated in the first round
then A wins 55 to 45 over "C".) This is a fairly realistic scenario
of the sort that arises with voters and candidates positioned along a one-dimensional line.

Now suppose
eight voters in the bottom faction cleverly (but dishonestly) switch their top-two
preference order, "betraying" their favorite C.
Result:

#voters

Their (new) Vote

45

A>B>C

10

B>A>C

18

B>C>A

27

C>B>A

Then
"C" is eliminated in the first round,
and then in the second round "B" wins over "A" 55-to-45.
From those 8 voters' point of view, this was an improvement.
The betrayal worked.