Gibbard-Satterthwaite Theorem
Version 1.0.0 · Updated 2026-07-30
CORE DEFINITION
For any voting system with three or more alternatives, either it is dictatorial (one person decides) or it is vulnerable to strategic manipulation (voters do not vote for their true favorite but for the one most likely to win). There is no perfect, manipulation-proof democratic voting mechanism.
SCAFFOLDING EFFECT
Reduce cognitive load
Mechanism design limitations. When designing team decision-making mechanisms, do not fantasize about creating an absolutely fair and ungameable system. Accept the existence of strategic games, or introduce a 'benevolent dictator' at critical moments to break deadlocks.
Anchor fast decisions
The theorem proves that under any non-dictatorial voting rule with at least three alternatives, if the rule satisfies 'onto' (any outcome can be elected) and is non-dictatorial, then there must exist a manipulable situation—a voter can change the outcome in their favor by misreporting preferences. Its logic is related to Arrow's impossibility theorem: any rule aggregating individual preferences must compromise among fairness, non-manipulability, and rationality.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E5%90%89%E5%B7%B4%E5%BE%B7-%E8%90%A8%E7%89%B9%E6%96%AF%E7%BB%B4%E7%89%B9%E5%AE%9A%E7%90%86verified
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