| #voters | their vote |
|---|---|
| 9 | A>B>C |
| 6 | B>A>C |
| 5 | C>B>A |
In IRV, C has the least votes and hence is eliminated, and her votes transfer to B, so B wins over A. However, if two A>B>C voters had voted C>B>A (maximally dishonestly – completely reversing their preference order to lie as much as they could possibly lie), then:
| #voters | their vote |
|---|---|
| 7 | A>B>C |
| 6 | B>A>C |
| 7 | C>B>A |
B has the least votes and is eliminated, giving her votes to A, and A wins. So voting against your preferred candidate here increases his chance of winning!
This example was posted on the net by somebody named "The Phantom." I liked it so I reposted it here.