In particular, if there is already a Condorcet winner, they win the election.

When a Condorcet winner exists, he does not necessarily win a runoff election due to insufficient support in the first round.

They always suffice to determine whether there is a Condorcet winner.

In certain circumstances an election has no Condorcet winner.

There can be more than one weak Condorcet winner.

Another question would be the ability to elect a Condorcet winner in case there is one.

The Condorcet winner, if one exists, is the sole member of the Smith set.

If weak Condorcet winners exist, they are in the Smith set.

Here is an example in which there is no Condorcet winner:

In this scenario, the winner is also the Condorcet winner.