A simple solution to the "third party" problem.

[Tricky]

Well I hate to stick math into a perfectly good political discussion, but the fact is, there is no perfect voting system. It is a mathematical impossibility. The example Tricky gave is known as the Condorcet method and a Condorcet winner will not always exist. For example, a three person election (candidates A, B, and C):

5 voters -> A then B then C
4 voters -> B then C then A
3 voters -> C then A then B

A beats B 8-4, B beats C 9-3, and C beats A 7-5. So who wins?

Here is a more complicated example (from Beyond Numeracy by John Allen Paulos). We will say there are 5 candidates and 55 voters:

18 voters prefer A to D to E to C to B
12 voters prefer B to E to D to C to A
10 voters prefer C to B to E to D to A
 9 voters prefer D to C to E to B to A
 4 voters prefer E to B to D to C to A
 2 voters prefer E to C to D to B to A

(snip)

That's an interesting way of looking at it, JesFine, and I can certainly see the argument behind each position. However, my proposal meant to simply avoid a costly run-off. In a run-off, the two top vote-getters would go head to head and all of the voters for the other candidates would select one of those two. By using ranked preferences ("Condorcet", eh? I'll have to remember that) the runoff would be unnecessary. In the situation above, all 25 of the losers' votes would go to B, since the voters for the bottom three candidates all prefrred B to A.

No, it might not be fair, but as you point out, elections by their nature are not fair, just better than other methods. My logic in proposing this system was that under many state and local governments, run-offs are held between the top two vote-getters. This system would simply eliminate the need for that run-off. In a presidential race, the cost of a run-off would be staggering, especially if they have to go out campaigning again.

Agreed, this would lead to rather byzantine voting stategies, ("I want C, but if he doesn't get it then B because he has the best chance of winning and I want anybody but A") but I think that it is fair if clearly stated and agreed to in advance. And we don't let Floridians vote.