Way back in 2006, Michael Bates made a pretty persuasive case for Instant Runoff Voting.
How would this have worked in, say, the recent Mississippi Senate primary? Roger Green explains the process:
In the Mississippi GOP scenario, after the June 3 primary, Thomas Carey’s votes would have been distributed to [Thad] Cochran and [Chris] McDaniel, based on who was Carey voters’ second choice. Majority would have been reached. There would have been no need for the June 24 runoff, and no chance for the Democratic party supporters to vote in the Republican primary without foregoing their opportunity to vote in their OWN primary.
Which would have avoided that whole debacle rather neatly.
I once questioned how this could be implemented on this state’s optical-ballot system, but that doesn’t really seem to be much of an issue, and besides we’ve replaced the entire fleet of scanners since then.