3-way races mainly produce crazy results due to the first-past-the-post voting system. (e.g. having 2 liberal candidates ensures that the conservative gets elected, even if a majority of the population would have preferred either of the liberals).
That's why you need instant run-off voting in the USA. It makes multi-party elections more viable.
If you're describing the system I think you're describing, California has it, and sometimes it leads to problems if theres more than 3 candidates.
For example, assume we're in a deep blue area that votes normally maybe 35% Republican with this system, meaning each Republican gets about 17%. There's a Libertarian/Constitutionalist/Whathaveyou that takes the remaining 1%. But for whatever reason, there are 4 Democrats running, as well as candidates from Peace and Freedom, the Greens, and an independent left winger. With this situation, it's entirely possible that the Elite Liberal district ends up with a run off of two Arch-Conservatives.
Really, the best system would be the one in which you list the order you support them in. So, for example, in the previous case you might put P&F first, the Greens second, the Dems third etc etc with the two Republicans being last. So when the votes come in, the candidate with the least amount of "first" votes has their votes apportioned to the other candidates until you're down to the last two, where a simple majority decides the result. In this way, you could vote for a minor party without hurting the chances of the larger party you support over the larger party you detest.
Maybe you just never heard of instant-run-off voting. I used that name because that's what's it's called in the USA, so i thought it'd be easier to communicate what i meant. England calls it the Alternative Vote, and Australia calls it Preferential Voting. It sounds exactly like what you're advocating.
Let's say each of 2 Conservatives gets 17%, and 4 Liberals each get 16% each. In first past the post voting, one of the Conservatives is automatically the winner, meaning the Liberals foolishly "split the vote" and lost a winnable election. Let me show you how IRV prevents splitting the vote by either side:
The first round of eliminations, eliminates the Liberal with the lowest primary vote. But his votes get passed onto the person that each voter put second. Now, it's highly unlikely that the people who voted #1 Liberal voted #2 as one of the arch-conservatives. Let's assume all the Liberal votes, selected the 4 Liberals ahead of the 2 conservatives, in some combination of D#1, D#2, D#3, D#4. What happens is that after the preferences are distributed, each of the remaining 3 Liberals gets his original 16% + 16% * 1/3 of the eliminated Liberal's votes.
The person with the lowest vote at this stage is one of the Conservatives, so he gets eliminated, and let's say that all his votes get passed to the other Conservative, giving that conservative 35%. The 3 remaining Liberals all have lower than 35% still, so the one who now has the lowest total is also eliminated, leaving 2 Liberals with about 32% each. This is still lower than the surviving Conservative's 35%, so the 2nd last Liberal is eliminated, and his 32% passes to the other Liberal, meaning he's the winner with 64%
That's how IRV works in practice. It does a good job of simulating how the surviving 2 candidates would have fared in a 1-1 election, but allowing multiple candidates to have a chance without screwing things up.