Condorcet paradox: Difference between revisions
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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.
Note that the above example demonstrates Condorcet
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) more voters who prefer someone else over the [[Utilitarian winner]]. If "intensity of preference" information is included, the cycle can be resolved by electing the candidate with the highest summed or average score in the cycle, as in [[Smith//Score]] and [[Smith//Approval]].
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