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
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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(candidates being listed in decreasing order of preference):
:Voter 1: A > B > C
:Voter 2: B > C > A
:Voter 3: C > A > B
If C is chosen as the winner, it can be argued that B should win instead, since two voters (1 and 2) prefer B to C and only one voter (3) prefers C to B. However, by the same argument A is preferred to B, and C is preferred to A, by a margin of two to one on each occasion.
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Condorcet cycles can arise either from honest votes, or from strategic votes. Some cycle resolution methods were invented primarily to elect the "best" candidate in the cycle when the cycle is created by honest voters, whereas others were invented on the assumption that most cycles would be artificially induced so that a faction could change the winner to someone they preferred over the original winner by strategically exploiting the cycle resolution method, and therefore attempt to make such strategic attempts fail or backfire, though this can sometimes mean that these cycle resolution methods elect "worse" candidates if the cycle was induced by honest votes.
Condorcet cycles can never appear in [[Cardinal voting|cardinal methods]] when deciding the winner, because if some candidate (Candidate A) has a higher summed or average score than another candidate (Candidate B), then A will always have a higher summed or average score than every candidate that B has a higher summed or average score over. However, there will still be (if there is no change in voter preferences after the election, and those voters' preferences would create a cycle for 1st place i.e. the winner if ran through a Condorcet method)
==See also==
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