I think she will still win. Enough moderates and independents will rank her first for her to not get eliminated. The Democrats will rank her above the mainstream Republican, and Republicans will rank her above the Democrat.
The big problem for her is that enough Republicans might not rank her at all. She’s by no means safe.
True, we really have no idea how this new voting system will play out. Since most voters don't understand the strategic implications of IRV, it may be in the interest of the Democratic Party to encourage people to put Murkowski first and the Democrat second or not run a Democrat at all (unless they think they can actually win).
