Condorcet winner criterion: Difference between revisions

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==Commentary==
On a one-dimensional [[political spectrum]], the beats-all winner will be at the position of the median voter.
 
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.
 
Non-ranking methods such as [[plurality voting|plurality]] and [[approval voting|approval]] cannot comply with the Condorcet criterion because they do not allow each voter to fully specify their preferences. But instant-runoff voting allows each voter to rank the candidates, yet it still does not comply. A simple example will prove that IRV fails to comply with the Condorcet criterion.