No, it doesn't, no matter how many times misinformed IRV-advocates make this claim. IRV – if nobody "truncates their ballot" – elects a winner preferred by a majority over one other candidate. Call this winner W, and the rival he beats R. Unfortunately, it is entirely possible for every candidate (except R) to beat W by a voter-majority, and for some other candidate C to be preferred not only over W, and R, but in fact over every candidate, and still IRV elects W and refuses to elect C.
| #voters | Their Vote |
|---|---|
| 7 | C>W>R>A>B>D |
| 6 | W>C>B>R>A>D |
| 5 | A>W>C>R>B>D |
| 8 | B>C>A>R>D>W |
| 9 | R>C>B>A>D>W |
| 9 | D>C>A>B>W>R |
In this 44-voter example W wins with IRV. However, W is pairwise-defeated by every candidate except R. C pairwise-defeats every candidate including both R and W – but IRV refuses to elect C. C also has more top-rank votes than W, indeed W is top-ranked by the second-fewest voters.