Condorcet method: Difference between revisions

Added some clarification on Condorcet cycles, Smith//Score, and added section on how Condorcet can be modified to allow fractional votes in pairwise matchups.
m (Mentioned that Condorcet can be done on rated ballots, added Smith//Score as a Condorcet method, and made some other minor changes.)
(Added some clarification on Condorcet cycles, Smith//Score, and added section on how Condorcet can be modified to allow fractional votes in pairwise matchups.)
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== Simple explanation ==
 
If one candidate defeatsis preferred by a majority over all othersother candidates in head-to-head contests, that candidate is the [[Condorcet Criterion|Condorcet Winner]]. This can be determined through use of ranked or rated ballots. In rare occasions, eacha candidategroup of candidates is defeatedpreferred by ata leastmajority oneover all other (e.g.candidates rockone-on-one, paper,but scissors),no soone therecandidate in the group is nopreferred Condorcetby Winnera majority over all of the other candidates in the group. In that case it is necessary to use some tiebreaking procedure.
 
== Casting ballots ==
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* '''[[Schulze method|Schulze]]''' with several reformulations/variations, including '''Schwartz Sequential Dropping (SSD)''' and '''Cloneproof Schwartz Sequential Dropping (CSSD)'''<sup>1</sup>
* '''[[Approval-Condorcet Hybrids]]''', such as '''[[Definite Majority Choice]]''', use an [[Approval Cutoff]] to augment the Condorcet pair wise array. Many believe that such a method would make a good first-round public proposal.
*'''[[Smith//Score]]''' chooses the candidate with the highest summed or average score in the Smith Set. (This can only be done with rated ballots).
 
<sup>1</sup> There are different ways to measure the strength of each defeat in some methods. Some use the margin of defeat (the difference between votes for and votes against), while others use winning votes (the votes favoring the defeat in question).
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* [B] indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column caption
 
In this election, Nashville is the Condorcet winner and thus the winner under all possible Condorcet methods.
 
== Variants ==
 
Condorcet methods can be modified to allow a voter to give a fraction of a vote, rather thaonly either n no vote or a whole vote, to a candidate in a pairwise mat chupThis is akin to the fractional support that can be given in cardinal methods that allow more than 2 distinctions, such as [[Score Voting]]. . This is most easily accomplished by allowing voters to equally rank candidates, and also rate each of them, so that if, say, Candidates A and B are equally ranked, and A is rated a 10/10 and B a 4/10, then (10-4)/10 = 60% or 0.6 of a vote goes to A in the A vs. B match-up. Both A and B would each get one vote as usual against all candidates they are ranked above.
== Use of Condorcet voting ==