The only flaw I can see with this is if one person romps it and all the other candidates only get 1 vote in the first round and are effectively eliminated? Obviously you could run the poll again without the overall winner participating, but that could drag the whole thing out.
3 votes, first, second and third choice, with some kind of weighting? People with the most first choice votes get the gig, in the event of a 3-way draw, then second choice then third choice votes come into play?
Just musing out loud.