IRV challenges the power of the two parties. It eliminates the “Don’t vote for the [non-Dem or Republican] candidate or you’re wasting your vote.” argument because you can vote for your preferred candidate first, then list the major party candidate. The major party candidate still gets your vote if your preferred candidate doesn’t win.
It does have its own problems though.
from the limited amount I’ve read and leftist friends I talk to, they want it to prevent “another Bush V Gore”
(IE: they wanted all Nader’s votes to have gone to Gore)
New York City had a variant this system for local elections way back in the 1930s or so, but abolished it when it led to two Communists being elected to the City Council. (I may be off a bit on the details, but that it what I recall studying in a Poli Sci class back in my college days.)