I like the idea but don't agree that all you do is vote above the cutoff. If there are 10 choices and I approve of 3, but I know my 7 and 9 are the only possible winners, I'll likely vote 1 2 3 7.
I don't think that works. Polls tell you the levels of support of the candidates, they don't give you the probability of each candidate winning which is what you need to figure out the expected value of the winner.