Complex sentence: A Condorcet winner will not always exist in a given set of votes, which is known as Condorcet's voting paradox, but when voters rank candidates on a left-to-right axis and always prefer candidates closer to themselves, a Condorcet winner always exists.
Split into simpler sentences: A Condorcet winner will not always exist in a given set of votes, which is known as Condorcet's voting paradox. When voters identify candidates on a left-to-right axis and always prefer candidates closer to themselves, a Condorcet winner always exists.