Gibbard's theorem is a result in game theory and social choice, proved by Allan Gibbard, showing that no game form allowing an unrestricted range of participant preferences can guarantee all of the following at once: that it is not a dictatorship in which one player's choice always determines the outcome, that it is not limited to only two possible outcomes, and that no participant ever has an incentive to misrepresent their true preference to obtain a better result.
Facts
StatementIf a game form is not dictatorial and has at least 3 possible outcomes, then it is not strategyproof. 1 Classification
Statement Form Connections
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In Branch
Source Gibbard's theorem - Wikipedia
Proved By
Source Allan F. Gibbard curriculum vitae (University of Michigan)
Sources
1. Gibbard's theorem - Wikipedia
Simple majority vote
If there are only 2 possible outcomes, a game form may be strategyproof and not dictatorial.
References section
Allan Gibbard published "Manipulation of voting schemes: A general result" in Econometrica, Vol. 41, No. 4, pages 587-601 in 1973.
In Branch: Game Theory, Lead sentence
Gibbard's theorem is a key result in game theory showing that there is no universal non-dictatorial mechanism.
In Group: Mechanism Design, Lead paragraph
Gibbard's theorem is a key result in game theory showing that there is no universal non-dictatorial mechanism.
View the SourceAllan F. Gibbard curriculum vitae (University of Michigan)
Proved By: Allan Gibbard, PDF page 1 to 9, PublicationsQuote, Proved By: Allan Gibbard, PDF page 1 to 9, Publications
Manipulation of Voting Schemes: A General Result
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