Condorcet paradox: Difference between revisions

 

However, most Condorcet methods still do narrow down their selection of a final winner to a [[:Category:Condorcet-related sets|best set]] of candidates. Most Condorcet advocates unambiguously agree that the [[Smith set]] is a minimum standard for this best set (i.e. a Condorcet method must be [[Smith-efficient]], meaning that it always picks someone in the Smith set.) However, some advocates further prefer subsets of the Smith set i.e. they prefer some members of the Smith set over others, though they still agree that anyone in the Smith set would be better than anyone not in the Smith set. One of the most prominent of these subsets 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]]

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]].

 

 

==See also==