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Condorcet winner criterion: Difference between revisions
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The '''Condorcet criterion''' for a [[voting system]] is that it chooses the pairwise champion when one exists. Any method conforming to the Condorcet criterion is known as a [[Condorcet method]].
== Alternative Wording of Condorcet Criterion: ==
'''Requirement:''' The voting system must allow the voter to vote as many pairwise preferences as desired.
'''Requirement:''' If there are unbeaten candidates, then the winner should be one of them.
'''Traditional definition of "beat":'''
X beats Y iff more voters vote X over Y than vote Y over X.
'''Alternative definition of "beat" that is claimed to be more consistent with the preferences, intent and wishes of equal-top-ranking voters:'''
(Argument supporting that claim can be found at the [[Symmetrical ICT]] article.)
(X>Y) means the number of ballots voting X over Y.
(Y>X) means the number of ballots voting Y over X.
(X=Y)T means the number of ballots voting X and Y at top
(a ballot votes a candidate at top if it doesn't vote anyone over him/her)
X beats Y iff (X>Y) > (Y>X) + (X=Y)T
[end of alternative definition]
With this alternative definition of the Condorcet Criterion, FBC and the Condorcet Criterion are compatible.
==Complying methods==
Black, [[Condorcet//Approval]], Smith/IRV, [[Copeland's method|Copeland]], [[Llull-Approval Voting]], [[Minmax]], Smith/Minmax, [[ranked pairs]] and variations ([[maximize affirmed majorities]], [[maximum majority voting]]), and [[Schulze method|Schulze]] comply with the Condorcet criterion.
It has been recently argued that the definition of the verb "beat" should be regarded as external to the Condorcet Criterion...and that "beat should be defined in a way that interprets equal-top ranking consistent with the actual preferences, intent and wishes of the equal-top-ranking voters. When such a definition of "beat" is used in the Condorcet Criterion definition, then the Condorcet Criterion is compatible with FBC, and there are Condorcet methods that pass FBC. Discussion and arguments on that matter can be found at the [[Symmetrical ICT]] article.
[[Approval voting]], [[Range voting]], [[Borda count]], [[plurality voting]], and [[instant-runoff voting]] do not.
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