Condorcet winner criterion: Difference between revisions

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An [[electoral system]] satisfies the "'''Condorcet winner criterion"''', also known as the '''Condorcet criterion''', if it always chooses the Condorcet winner when one exists. The "Condorcet Winnerwinner" is sometimes referred to as the "'''Condorcet candidate"''', "'''pairwise champion'''", or '''"beats-all winner'''",. orThe "'''Condorcet winner"''' of an [[election]] is the candidate who is preferred by more voters than any other candidate in [[Pairwise counting|pairwise matchups]]. This is determined by observing whether more voters rank or score the Condorcet winner higher than each of the other candidates than the other way around.
 
The '''Condorcet winner criterion''' for a [[voting system]] is that it chooses the beats-all winner when one exists. Any method conforming to the Condorcet criterion is known as a [[Condorcet method]]. TheThough Condorcet winner criterion is sometimes referred to as simply the "Condorcet criterion", though it's important not to confuse the Condorcet winner criterion with the "[[Condorcet loser criterion]]" .
 
Mainly because of [[Condorcet paradox|Condorcet's voting paradox]], a beats-all winner will not always exist in a given set of votes. However, there will always be a smallest group of candidates such that more voters prefer anyone in the group over anyone outside of the group. If the beats-all winner exists, they will be the only candidate in this group, which is called the [[Smith set]]. Voting methods that always elect from the Smith set are known as "[[Smith-efficient]]".  
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