Any non-dictatorial voting rule over three or more outcomes can be manipulated by strategic voting.
Gibbard and Satterthwaite's result, proved independently in 1973 and 1975. It closes the escape route from Arrow: no voting rule is both non-dictatorial and strategy-proof, so tactical voting is structural.
In practice
- Voters in a three-way race abandon their first choice to stop their last, which is manipulation the system cannot design out.
- A ranked committee vote produces a different winner when one member ranks strategically, and the member has done nothing wrong.
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- Law & Politics
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- What can be proved and measured about power