Condorcet method
A Condorcet winner might not always exist in a particular election because the preference of a group of voters selecting from more than two options can possibly be cyclic — that is, it is possible (but very rare) that every candidate has an opponent that defeats them in a two-candidate contest. (This is similar to the game rock paper scissors, where each hand shape wins against only one opponent and loses to another). The possibility of such cyclic preferences in a group of voters is known as the Condorcet paradox. However, there always exists a smallest group of candidates that beats all candidates not in the group, known as the Smith set, which is guaranteed to only have the Condorcet winner in it when one exists; many Condorcet methods always elect a candidate who is in the Smith set when there is no Condorcet winner, and are thus said to be "Smith-efficient".  The Condorcet winner is also usually but not necessarily the utilitarian winner (the one which maximizes social welfare).