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
Famous quotes containing the words comparison with the, comparison with, comparison and/or criterion:
“Clay answered the petition by declaring that while he looked on the institution of slavery as an evil, it was ‘nothing in comparison with the far greater evil which would inevitably flow from a sudden and indiscriminate emancipation.’”
—State of Indiana, U.S. public relief program (1935-1943)
“He was a superior man. He did not value his bodily life in comparison with ideal things. He did not recognize unjust human laws, but resisted them as he was bid. For once we are lifted out of the trivialness and dust of politics into the region of truth and manhood.”
—Henry David Thoreau (1817–1862)
“In comparison to the French Revolution, the American Revolution has come to seem a parochial and rather dull event. This, despite the fact that the American Revolution was successful—realizing the purposes of the revolutionaries and establishing a durable political regime—while the French Revolution was a resounding failure, devouring its own children and leading to an imperial despotism, followed by an eventual restoration of the monarchy.”
—Irving Kristol (b. 1920)
“... the condition of women affords, in all countries, the best criterion by which to judge the character of men.”
—Frances Wright (1795–1852)