What is it?
Condorcet voting is an electoral system in which the definition of "fairness" is that the winner of an election should be preferred to each other candidate in the election by a majority of the electorate. In other words, in an electoral race between this winner and any one of the other candidates, the other candidate will lose. Condorcet showed that sometimes there is no such candidate because three overlapping majorities may favor three different candidates in a circular preference.

How to use Condorcet voting
Voters are asked to indicate how they would vote in each possible two-way race between the candidates. Rather than putting several binary choices on the ballot, voters are asked to rank the candidates. The rankings on all ballots are then used to tabulate the results of the two-way races. If no candidate wins all two way races, then some specific method of resolving the circular preference would have to be used. This is a weakness of the system congruent to the weakness of a two-way race wherein no winner can be selected because each candidate receives the same number of votes.