[vintermann]

The Condorcet property (not method) is easy enough to understand.

"Imagine this candidate ran in a two person race against each of the other candidates in turn. If he'd win ALL those races individually, he should win when running against all of them at the same time too."

Now, explaining various methods which guarantee this property is not as easy - nor is it easy to understand why you might prefer one such method to another.

But this isn't actually a big deal. In the many, many countries that use proportional representation, it's the outcome ("parties share of seats in parliament should be roughly the same as parties share of votes in the election") which is agreed upon. The actual mathematics to achieve it are somewhat counterintuitive and not many people are aware of them, but that doesn't matter. We can all see it works, and so we would in an election with, say, Ranked Pairs.