What you're describing seems to be a form of
approval voting (with the slight tweak that it adds a "neutral" option rather than just being approve/disapprove). In theory, there are strong arguments for it, but the problem is that it's one of the voting systems most susceptible to being gamed through strategic voting. Most committed partisans, if they see their favorite candidate in first or second place in the polla, would have an incentive to approve only that candidate and disapprove all the others. If they approve someone else, they know they'll decrease the chance of their favorite candidate getting in. Votes who approve of both leading candidates but prefer one would have an especially strong incentive to disapprove of the other.
One of the features I value most in a voting system is its ability to encourage the sincere expression of preferences, by guaranteeing voters that "voting their conscience" won't result in worse electoral outcomes. IRV scores pretty well on that metric (there
are ways of gaming it out, but they require a level of acumen and foreknowledge that no voter would reasonably bother with), while alternative vote scores poorly, for the reasons I detailed.
