So, everybody's third choice gets elected, or they take turns holding the office, or what? Weighted voting can work for corporate directors or other committees, but for a chief executive? Even the electoral college sounds better.
In single transferable vote systems the winner is almost always one of the two candidates with the most first preferences; the minor party candidates get progressively eliminated and the corresponding votes distributed to the next in preference order (instead of being thrown away). In US terms such a system might have got Bush senior over the line against Clinton because he would (I presume) have been preferred by most voters who voted for that fellow with big ears. In the coming election it might help Gore overcome Bush because Gore would be strongly preferred by most voters who are planning to waste their votes on Nadir. A system based on weights would, as you suggest, have an excessive (political) centrist tendency. Tim