Condorcet paradox: Difference between revisions
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{{Wikipedia|Condorcet paradox}}[[Image:Condorcetparadox.png|thumb|right|A majority of the dots are closer to B than A, C than B, and A than C.]]
The '''voting paradox''', '''Condorcet paradox''', or '''Condorcet cycle''' is when no one candidate can pairwise beat or tie with all others (i.e. isn't preferred by at least half of the voters in one-on-one contests with all other candidates). If there is a Condorcet cycle, the candidates in the cycle will always be in the [[Smith set|Smith Set]] (the smallest group of candidates that can beat all others). It is a situation noted by the [[Marquis de Condorcet]] in the late 18th century,
in which collective preferences can be cyclic (i.e. not transitive), even if the preferences of individual voters are not.
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.
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