A runoff is the system of holding a plurality election (most typically). If no candidate gets a certain threshold of votes (usually 50%), then a second election takes place with the top two finishers from the first round. A runoff can mitigate some vote-splitting issues that can happen when multiple similar candidates fracture the vote for their platform. But it can have some fairly disastrous results, too. Like this:
Runoff Failure Example
% of voters Their ranking
35% Republican > Democrat > Progressive
32% Democrat > others
33% Progressive > Democrat > Republican
A runoff would put the Republican and the Progressive in the second round, but...
- A huge 65% majority of voters would prefer to have the Democrat over the Republican
- And and even larger 67% majority of voters would prefer to have the Democrat over the Progressive
This is essentially what occurred in the 2007 French presidential election. Royal (socialist) and Zarkozy (conservative) went to the runoff, where Sarkozy won. But polls show that Bayrou (the relative centrist) would likely have beaten either of those two in a head-to-head matchup.
With more candidates, this effect can become arbitrarily more severe because of this "center squeeze effect."
The aggregate effect of the chaos resulting from this failure can be seen via Bayesian Regret calculations. Here are some sample figures (see “Top2Runoff” in the second table) showing that Top-Two Runoff does considerably worse than several other systems, such as Borda, Condorcet, Approval Voting, and Score Voting.