Gibbard-Satterthwaite theorem: Difference between revisions
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(Fixing link to w:Gibbard–Satterthwaite theorem, adding link to old English Wikipedia version (oldid=13601023), and noting that this theorem is derived from It is derived from Arrow's impossibility theorem and Gibbard's theorem (and is not merely "related")) |
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{{Wikipedia}} |
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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 |
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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 is derived from [[Arrow's impossibility theorem]] and [[Gibbard's 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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==Further Reading== |
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* https://www.rangevoting.org/GibbSat.html |
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[[Category:Voting theory]] |
[[Category:Voting theory]] |
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[[Category:Voting system criteria]] |
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{{stub}} |
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{{fromwikipedia}} |
{{fromwikipedia|Gibbard–Satterthwaite theorem|oldid=13601023}} |
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Revision as of 10:35, 4 February 2024
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 is derived from Arrow's impossibility theorem and Gibbard's theorem.
Statement
For every voting rule, one of the following three things must hold:
- The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner
- The rule limits the possible outcomes to only two alternatives
- The rule is susceptible to strategic voting: some voter's sincere ballot may not defend their opinion best.
Further Reading
Portions derived from "Gibbard–Satterthwaite theorem" revision 13601023. |