Gibbard–Satterthwaite theorem
E494084
The Gibbard–Satterthwaite theorem is a fundamental result in social choice theory showing that every reasonable voting system with at least three options is susceptible to strategic manipulation by voters.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gibbard–Satterthwaite theorem canonical | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
impossibility theorem
ⓘ
theorem ⓘ |
| appliesTo |
deterministic social choice functions
ⓘ
voting systems with at least three alternatives ⓘ |
| assumes |
at least three possible outcomes
ⓘ
complete and transitive individual preference orderings ⓘ deterministic social choice rule ⓘ unrestricted domain of preferences ⓘ |
| author |
Allan Gibbard
NERFINISHED
ⓘ
Mark Satterthwaite NERFINISHED ⓘ |
| concerns |
manipulability of voting rules
ⓘ
strategic voting ⓘ strategy-proofness ⓘ |
| concludes |
every such voting rule is either dictatorial or manipulable
ⓘ
no strategy-proof, non-dictatorial, onto social choice function exists for three or more alternatives ⓘ |
| excludes | randomized social choice functions ⓘ |
| field |
social choice theory
ⓘ
voting theory ⓘ |
| formalizes | limits of incentive compatibility in voting ⓘ |
| hasConsequence |
any non-dictatorial rule allows some voter to benefit by misrepresenting preferences
ⓘ
dictatorship is the only strategy-proof, onto rule with at least three alternatives ⓘ |
| implies |
any reasonable voting system with at least three options is vulnerable to strategic manipulation
ⓘ
truthful voting cannot be guaranteed in general for non-dictatorial deterministic rules with three or more alternatives ⓘ |
| influenced |
development of mechanism design theory
ⓘ
research on strategy-proof mechanisms ⓘ |
| mainClaim | every non-dictatorial, deterministic, onto social choice function with at least three alternatives is manipulable ⓘ |
| namedAfter |
Allan Gibbard
NERFINISHED
ⓘ
Mark Satterthwaite NERFINISHED ⓘ |
| publishedIn | Journal of Economic Theory NERFINISHED ⓘ |
| relatedConcept |
dictatorship
ⓘ
manipulability ⓘ onto social choice function ⓘ preference profile ⓘ social choice function ⓘ strategy-proofness ⓘ |
| relatesTo |
Arrow's impossibility theorem
NERFINISHED
ⓘ
Gibbard's theorem NERFINISHED ⓘ Satterthwaite's theorem NERFINISHED ⓘ |
| topic |
collective decision-making
ⓘ
mechanism design ⓘ preference aggregation ⓘ |
| usedIn |
analysis of political elections
ⓘ
computational social choice ⓘ design of voting protocols ⓘ multi-agent systems ⓘ |
| yearProved | 1973 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.