Gibbard's theorem¶
In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973.
Core Idea¶
Gibbard's theorem is treated here as the recurring socialscienceshumanitiesarts identity summarized by this source-grounded definition: In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold.
Scope of Application¶
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Formal statement. Let \mathcal{N} = {1, \ldots, n} be the set of agents, which can also be called players or voters, depending on the context of application.
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Formal statement. Let g be a function that, to each n -tuple of strategies (s1, \ldots, sn) \in \mathcal{S}1 \times \cdots \times \mathcal{S}n , maps an alternative.
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ExamplesSerial dictatorship. If there is still several non-eliminated candidates after all ballots have been examined, then an arbitrary tie-breaking rule is used.
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Extensions. Gibbard's 1978 theorem states that a nondeterministic voting method is only strategyproof if it's a mixture of unilateral and duple rules.
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Extensions. Nondeterministic methods have been devised that approximate the results of deterministic methods while being strategyproof.
Clarity¶
A clear use of Gibbard's theorem names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973.
Manages Complexity¶
Gibbard's theorem compresses multiple socialscienceshumanitiesarts details into a stable diagnostic relation. The source shows both the central mechanism—this property is desirable for a democratic decision process: it means that once the agent i has identified her own preferences Pi , she can choose a strategy si^(Pi) that best defends her preferences, with no need to know or guess the strategies chosen by the other agents.—and the practical.
Abstract Reasoning¶
- Type the carrier. Identify the socialscienceshumanitiesarts entities to which the claim applies.
- State the relation. Use the source-grounded identity: In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973.
- Check operation and conditions. Gibbard's theorem is itself generalized by Gibbard's 1978 theorem and Hylland's theorem, which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve an element of chance.
Knowledge Transfer¶
Within the home domain. Knowledge about Gibbard's theorem transfers literally when a new case preserves the same carrier type, relation, and recognition test. Let \mathcal{N} = {1, \ldots, n} be the set of agents, which can also be called players or voters, depending on the context of application. Let g be a function that, to each n -tuple of strategies (s1, \ldots, sn) \in \mathcal{S}1 \times \cdots \times \mathcal{S}n , maps an alternative. Beyond the home domain. No canonical parent is asserted for Gibbard's theorem.
Neighborhood in Abstraction Space¶
Gibbard's theorem sits in a moderately populated region (58th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Political & Strategic Game Models (11 abstractions)
Nearest neighbors
- Dot-Voting — 0.87
- Bayes Correlated Equilibrium — 0.86
- Interacting Particle System — 0.85
- Ballot-Order Effect — 0.84
- Abstract economy — 0.84
Computed from structural-signature embeddings · 2026-10-08