One of my favourite voting systems is known as Condorcet.
In short, the 'winner' is not the person with the most votes, but rather, the person everyone is okay with.
One problem with the system is you don't always have a condorcet winner. Take the game Rock Paper Scissors for example, each one beats another.
However, I think that we can use the recent Manitoba NDP leadership election as a good example of a time when Condorcet is not only a good idea, but is the only strong option.
On the first ballot, we had the following result:
Selinger - 612
Oswald - 575
Ashton - 502
Oswald, it should be noted, was the leader of the "Rebel Alliance" of Cabinet ministers who sparked this entire leadership race. Selinger was the one who was rebelling against.
On the final ballot we saw this
Selinger - 759
Oswald - 726
What's important is what's missing.
209 delegates did not vote.
I can buy that some of them were genuinely torn between these two great options, however, it's far more likely that most of them could not stomach either, and just left.
Given the rebellion, there is reason to believe both Selinger and Oswald were polarizing. Ashton, however, always seemed to walk the middle ground.
Watching the convention, it seemed the 'second choice' of most Selinger delegates would have been Ashton; and the 'second choice' of most Oswald delegates would have also been Ashton.
If 2/5ths of Ashton's delegates are unwilling to back either Selinger or Oswald, how many of Oswald's delegates would be unwilling to back Selinger, or vice versa.
A good third of the party is liable to stay home on election day if this is any indication. It would not have been terribly different if Oswald had won.
...but Ashton? Ashton could have united the party. Potentially anyway. Ashton would have almost certainly defeated Selinger if he had made it though to the second round, while Oswald would have also lost to Ashton. Ashton, however, never got that chance as he was unable to make it to that crucial second round, and as a result, the Manitoba NDP may suffer.
A similar but more extreme case took place in Egypt. Thanks to a simple two-round system, moderate candidates never made it to the final round in the 2012 election, This forced a choice between the two extremes. Who won is irrelevant, what matters is that thanks to this fault in the voting system, Egypt is no longer a democracy.
For the Manitoba NDP the lack of Condorcet might mean a dozen or two fewer seats. Thankfully it did not mean more.