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Condorcet: Candidates
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In a Condorcet election votes are often counted, and results illustrated, in the form of matrices such as those below. In these matrices each row represents each candidate as a 'runner', while each column represents each candidate as an 'opponent'. The cells at the intersection of rows and columns each show the result of a particular pairwise comparison. Certain cells are left blank because it is impossible for a candidate to be compared with herself.
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Condorcet voting: Devised by an 18th century French mathematician named Marquis de Condorcet, this system asks voters to rank their preferences from top to bottom: say Bush over Nader over Gore. The results are used to compare candidates in pairs: this voter would prefer Bush to Nader, Bush to Gore, and Nader to Gore. If, as seems likely, Florida's Nader voters were closer to Gore than to Bush, Condorcet voting would have elected Gore. (The French may have had a remedy for voting woes - Condorcet lost his head in the revolution.)
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Condorcet voting violates the common sense principle of requiring a minimum level of core support because it puts no particular weight on a first choice over a second choice. In a large field of candidates, a candidate can win without being a single voter’s first choice. By putting such extreme emphasis on breadth of support, it shares one of approval voting’s downsides of encouraging candidates to be seen as the “least offensive” candidate rather than a leader who takes strong policy positions that might alienate some voters.
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Condorcet voting asks voters to rank the candidates (1st choice, 2nd choice, ...). The information on the ballots is used to determine who would win in a round robin tournament among the candidates. (Note that you can tell, from the ranking information on the ballots, whether more people prefer Bush over Kerry or vice versa. And similarly for every other pair of candidates.) If there is a candidate that would beat every other candidate in the race, that candidate wins the election. Otherwise, there is a circular tie - for example, A beats B, B beats C, and C beats A.
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In a Condorcet election the voter ranks the list of candidates in order of preference. So, for example, the voter gives a '1' to their first preference, a '2' to their second preference, and so on. In this respect it is the same as an election held under non-Condorcet methods such as instant runoff voting or the single transferable vote. Some Condorcet methods allow voters to rank more than one candidate equally, so that, for example, the voter might express two first preferences rather than just one.
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Condorcet's rule would need a threshold low enough to include several central candidates; then all voters may choose the 1 with the broadest appeal. Instead of a percentage, the threshold could be a number of slots for the [5] candidates with the most first-place votes.
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