LYCOS RETRIEVER 
Condorcet: Condorcet Winner
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A "Condorcet Winner" is a candidate who would beat any opponent in a simple majority vote (2-man race). Unfortunately there are cyclic election examples where no Condorcet Winner exists. But when one does exist, it seems difficult (but possible!) to dispute that he ought to be the election winner. And so, much fear and gnashing of teeth arose from the realization that the Approval Voting system (and hence the Range Voting system) could fail to elect a Condorcet Winner.
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The typical way of representing the votes of a Condorcet election are in a matrix. For example, the following might be the result of a Condorcet election between three candidates. Each number corresponds to the number of voters who chose the candidate for that row over the candidate for that column. In this case, Bob Jones is the Condorcet winner, John Hennessy second place.
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Condorcet ... may not produce a definitive winner. In an election among Candidates A, B and C, Candidate A may be preferred to B, B preferred to C, and C preferred to A. In this situation, a “fallback” method must break the tie. This potential need for a fallback could punish sincere voters. Condorcet also is a difficult system to count by hand when many people vote. Hand-counting is important if there is a problem with voting machines or concerns about software.
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One family of Condorcet methods consists of systems that first conduct a series of pairwise comparisons and then, if there is no Condorcet winner, fall back to an entirely different, non-Condorcet method to determine a winner. The simplest such methods involve entirely disregarding the results of pairwise comparisons. For example, Black is a method that involves finding the Condorcet winner if it exists, but using the Borda count instead if there is an ambiguity (it is named after Duncan Black).
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A little over a decade after Borda made his proposal, Condorcet became interested. Probably after carefully examining Borda's example and his emphasis on using pairwise outcomes to measure merit, Condorcet proposed using the head-to-head elections to rank candidates. For Condorcet, the candidate who wins all pairwise comparisons is the winner. (In Borda's example, Candy is the Condorcet winner while Alice is the Condorcet loser.) Without doubt, the Condorcet winner enjoys a distinct appeal with its rugged ``winner take all" sense of individualism. This intuitive sense probably explains why the Condorcet winner has become the widely used standard to judge the merits of other procedures.
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Condorcet or Approval Voting should be promoted to state legislators for use in public elections (stress fairness, and a way to avoid the spoiler effect). Condorcet is the fairest method. Approval Voting is the cheapest and easiest alternative to implement, it frees voters to vote for their favorite candidates, and it ... makes good choices of winners. IRV allows minor party voters to freely vote for their favorite candidates as 1st choices - only as long as those candidates have no chance of winning.
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Condorcet Winner