Condorcet winner criterion: Difference between revisions
FIxed compromise candidate HTML mess, and added the picture that was linked so it's now inline. Rewrote some parts to emphasize the link between CW and compromise strategy.
(Distinguishing the Condorcet winner criterion from the Condorcet loser criterion. Also, the abbreviation "PC" stands for "personal computer", and anyone who uses that abbreviation for anything else is being a jerk. :-P) |
(FIxed compromise candidate HTML mess, and added the picture that was linked so it's now inline. Rewrote some parts to emphasize the link between CW and compromise strategy.) |
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===Compromise candidate===
On a one-dimensional [[political spectrum]], the beats-all winner will be at the position of the median voter.
[[File:Left,_Center,_Right.png]]
Supposing this is the voter distribution, with three candidates '''L'''eft, '''C'''enter, and '''R'''ight, with voters concentrated in each area of the distribution as given, with the yellow voters preferring Left, the green preferring Center, and the blue preferring Right. Then the Condorcet winner is Center, because a majority - the Center voters plus the Left voters - prefers Center to Right, and another majority refers Center to Left.
[[Instant-runoff voting]], which does not pass the Condorcet criterion, fails to detect Center's support and thus Center is eliminated early. However, if the majority preferring Center to the IRV winner knew this in advance, they could have used [[compromising]] strategy to force Center to be elected anyway. See below.
Note that the "Center" candidate is only the center of the voters' distribution. If this were a conservative party primary, the center of the distribution would likely be a conservative candidate, not a centrist.
===Equilibrium point for various voting methods===
The Condorcet winner/[[Smith set]] is a common [[equilibrium]] point in many voting methods. This is because a majority/plurality of voters have no incentive to deviate towards another candidate.
An example for [[Approval voting]]:
35: A>B|>C
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==Strategic implications==
Every Condorcet method is susceptible to burial in at least some elections, and Condorcet is also incompatible with [[later-no-harm]] and [[later-no-help]]. However, if a method
==Criticism==
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