Right now I am involved in a three way race for the Indiana 80th District State Representative seat. Also in the news is the Connecticut US Senate race, in which incumbent Joe Lieberman says he will run under the "Connecticut for Lieberman Party" ticket if he loses the Democratic primary to Ned Lamont. So in that Senate race there very well be a competitive race between a Democrat, a Democrat running as an independent, and a Republican. There also happens to be a Green Party candidate, Ralph Ferrucci and two other independent candidates, John Mertens and Diana S. Urban.
Voters in my district and in CT face a dilemma. They might like one candidate better than the rest, but might decide to instead vote for a candidate that they do not like as much but has a better chance at beating the candidate that they really hate.
There is also the possibility, however slight, that Lieberman and Lamont might split the liberal vote and Republican Alan Schlesinger would win by getting a plurality of the votes.
We need a system that lets voters choose their favorite instead of forcing them to just vote against someone they dread. Run-off voting does exactly that. In the first round, voters can choose between anyone of a slate of candidates who met the requirements for being listed on the ballot. If nobody wins a majority, then the top vote getters advance to the next round and the process is repeated.
There is a similar process call Instant Run-off Voting. It allows voters to rate candidates in order of preference. Unlike other run-off voting processes, this only requires one day of voting. Here is a link to explain how it works http://instantrunoff.com/