Gibbard-Satterthwaite theorem: Difference between revisions
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The '''Gibbard-Satterthwaite theorem''' states that every unimposing [[voting system]] (one in which every preference order is achievable) which chooses between three or more candidates, must be either dictatorial or manipulable (i.e. susceptible to [[tactical voting]]). It follows from [[Arrow's impossibility theorem]]. |
The '''Gibbard-Satterthwaite theorem''' states that every unimposing [[voting system]] (one in which every preference order is achievable) which chooses between three or more candidates, must be either dictatorial or manipulable (i.e. susceptible to [[tactical voting]]). It follows from [[Arrow's impossibility theorem]]. |
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==Statement== |
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For every voting rule, one of the following three things must hold: |
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# The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner |
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# The rule limits the possible outcomes to only two alternatives |
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# The rule is susceptible to [[strategic voting]]: some voter's sincere ballot may not defend their opinion best. |
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[[Category:Voting theory]] |
[[Category:Voting theory]] |
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[[Category:Voting system criteria]] |
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{{fromwikipedia}} |
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