In the election system we have today, each voter chooses a single candidate, and whichever candidate is chosen most often wins. But what if there is a candidate that everyone likes, but doesn't pick as their #1.
In a Condorcet election, one would rank the candidates in order of preference, so for example Shaggy might write on his ballot:
1. Dennis Kucinich
2. Ron Paul
3. Barack Obama
4. John McCain
Where Kucinich is his first choice, Ron Paul is his second most preferred, and so on.
What's unique about this system is how the ballots are tallied. The winner is whichever person would win the most one on one contests between any of the two candidates. Confusing? Here's an example:
There are 3 voters: A, B, C, and D, and there are 4 candidates: Ron Paul, Mike Huckabee, Mitt Romney, and Dennis Kucinich.
Voter A:
1. Mike Huckabee
2. Dennis Kucinich
3. Mitt Romney
3. John McCain
Voter B:
1. John McCain
2. Dennis Kucinich
3. Mike Huckabee
4. Mitt Romney
Voter C:
1. John McCain
2. Dennis Kucinich
3. Mike Huckabee
4. Mitt Romney
Voter D:
1. Mitt Romney
2. Dennis Kucinich
3. Mike Huckabee
4. John McCain
So now we look at each possible match up:
Mitt Romney vs. John McCain: Tied 2-2
Mitt Romney vs. Dennis Kucinich: Dennis Kucinich wins 3-1
Mitt Romney vs. Mike Huckabee: Mike Huckabee wins 3-1
Mike Huckabee vs. John McCain Tied 2-2
Mike Huckabee vs. Dennis Kucinich Dennis Kucinich wins 3-1
John McCain vs. Dennis Kucinich Tied 2-2
Dennis Kucinich wins because he is preferred or equal to all of the other candidates (of course, with millions of voters there would be not ties like we have here).
Through a popular-vote election like we have in place today, John McCain would win because he's more often chosen as the #1 choice then any other candidate. But Dennis Kucinich would win a Condorcet election because no one hates him, even though no one picks him as their first choice.