What I have posted there applies also here: What you think, McGrath, only works if you make the unrealistic and uncontrollable assumption that there is no tactical voting by voters in the ranking of preferences. But if there is, you can have anything, for instance:
Let us assume that there are only three candidates next time: Bush, Dem, Nader. Then a Bush preferer could rank against his personal wishes: Bush, Nader, Dem. Not because he prefers Nader to Dem, but because he never believes Nader could make it. He ranks Nader higher than he truly believes to damage Dem, the only one he fears.
It has been analysed from all angles by people who know a lot more about mathematics than you and I. The bottom line: There is no voting system that is inherently better than others and has no disadvantages. It can be shown that in the voting system you propose the least preferred can win under certain circumstances. In the present American system it can happen that the most preferred does not, but it cannot happen that the least preferred wins.
Like in presidentail elections (grin), your only choice is between different disadvantages (and advantages).