A Condorcet social choice function elects the candidate that beats every other candidate under simple majority when such a candidate exists. Various extensions of Condorcet’s simple majority principle that deal with situations that have no simple majority winner have been proposed.Nine Condorcet social choice functions are analyzed and compared on the basis of how well they satisfy a number of conditions for social choice functions. The conditions include several generalizations of Condorcet’s Principle. Remarks on the relative merits of the nine basic functions are included.
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