Hmm. I thought Louisiana featured an open primary with a run-off between the top two if nobody got over 50%.

Yeah, that's how it's done. I thought that's what you meant.

What I was referring to is a system where instead of voting for a single candidate, you rank the candidates in order of preference. So in yesterday's election, I might have voted McClintock > Arnold > Jim Weir > Georgy > Bustamante. There are a whole bunch of algorithms for determining a winner which usually produce the same winner in realistic scenarios, but have different behavior in various corner cases.

The simplest (but not best) method is as follows: If a candidate actually gets 50% of the first-choice votes, they win (this part is common to all methods). Otherwise, you find the candidate with the least number of first-choice votes and remove him from consideration. The candidate's name is deleted from every vote which included it--if the candidate was somebody's first choice, their second choice becomes their new first choice, etc. This process is repeated until some candidate has 50% of the first-choice votes.

The benefit of a system like this is that it is generally optimal for a voter to list the candidates in the order that they actually prefer them. You can vote for a minor candidate without "wasting" your vote, as you can still indicate a preference between the major candidates which will have as much weight as if you had not voted for the minor candidate. And, depending on exactly which algorithm is chosen, there is a good chance in a multi-candidate race that a "consensus" candidate will be found the winner.

--John