Comparison With The Condorcet Criterion
By the majority criterion, a candidate X should win if a majority of voters answers affirmatively to the question 'Do you prefer X to every other candidate?'.
The Condorcet criterion is stronger. According to it, a candidate X should win if for every other candidate Y there is a plurality of voters that answers affirmatively to the question 'Do you prefer X to Y?'.
Satisfaction of the Condorcet criterion implies that of the majority criterion, but not vice versa. With the Condorcet criterion the individuals comprising the majorities of voters answering affirmatively may vary according to Y, but the majority criterion requires a single majority which has X as their first choice, preferred to every other candidate.
In the statement that Condorcet criterion is stronger than the majority criterion, the word criterion must be understood as a criterion that a voting system may or may not satisfy, not as a criterion that a candidate must satisfy in order to win the election.
Read more about this topic: Majority Criterion
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