Condorcet paradox: Difference between revisions
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This is paradoxical, because it means that majority wishes can be in conflict with each other. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals.
Another way of thinking about the Condorcet paradox in the context of [[Condorcet methods]] is that just because, say, candidate A is better than candidate B by majority rule when only they are running, doesn't mean that candidate B isn't better than candidate A when more candidates are running.
For example, suppose we have three candidates, A, B and C, and that there are three voters with preferences as follows
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== Notes ==
Often the number of candidates in the cycle is mentioned as (number of candidates)-cycle i.e. a cycle between 3 candidates will be called a 3-cycle.
Note that there is no fair and deterministic resolution based solely off of the ranked preferences to this trivial example because each candidate is in an exactly symmetrical situation. ▼
When a [[Condorcet method]] is used to determine an election, a voting paradox among the ballots can mean that the election has no [[beats-all winner]]. The several variants of the Condorcet method differ chiefly on how they [[Condorcet method#Resolving ambiguities|resolve such ambiguities]] when they arise to determine a winner.
▲Note that there is no fair and deterministic resolution based solely off of the ranked preferences to this trivial example because each candidate is in an exactly symmetrical situation.
Because of Condorcet cycles, there is not always a single unambiguous "majority winner" (which contrasts to how there is always a [[Utilitarian winner|utilitarian winner]]). However, most Condorcet methods still do narrow down their selection of a final winner to a best set of candidates. Most Condorcet advocates unambiguously agree that the [[Smith set]] is a minimum standard for a Condorcet method to choose from (i.e. whichever set a Condorcet method narrows its selection down to, it must be a subset of the Smith set, meaning that the Condorcet method must be [[Smith-efficient]].) One of the most prominent subsets of the Smith set that some advocates prefer is the [[Schwartz set]].
It is believed to be uncommon for Condorcet cycles to occur, happening in about 9% of elections, depending on the scenario and makeup of the electorate. See [[W:Condorcet paradox#Likelihood%20of%20the%20paradox|w:Condorcet_paradox#Likelihood_of_the_paradox]]
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