Arrow’s impossibility theorem

E115290

Arrow’s impossibility theorem is a foundational result in social choice theory showing that no voting system can convert individual preferences into a collective ranking while simultaneously satisfying a set of seemingly reasonable fairness criteria.

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Statements (47)

Predicate Object
instanceOf impossibility theorem ⓘ
result in social choice theory ⓘ
theorem ⓘ
alsoKnownAs Arrow’s general possibility theorem ⓘ
Arrow’s paradox ⓘ
appliesTo rank-order voting systems ⓘ
social welfare functions ⓘ
assumes at least three alternatives ⓘ
complete and transitive individual preference orderings ⓘ
individuals have rational (transitive) preferences ⓘ
axiom Pareto efficiency ⓘ
completeness of the social preference relation ⓘ
independence of irrelevant alternatives ⓘ
non-dictatorship ⓘ
transitivity of the social preference relation ⓘ
unrestricted domain ⓘ
concerns aggregation of individual preferences into a social ranking ⓘ
conclusion no rank-order voting system can satisfy all Arrow axioms simultaneously ⓘ
contributedTo Kenneth Arrow’s Nobel Prize in Economics ⓘ
linked to: Kenneth Arrow
domain collective decision-making ⓘ
preference aggregation ⓘ
field social choice theory ⓘ
voting theory ⓘ
welfare economics ⓘ
formulatedBy Kenneth Arrow ⓘ
hasConsequence no universally fair rank-order aggregation rule exists ⓘ
trade-offs among fairness criteria in voting system design ⓘ
implies every social welfare function satisfying Arrow’s other axioms is dictatorial ⓘ
there is no perfect voting rule meeting all Arrow fairness criteria ⓘ
influenced axiomatic welfare economics ⓘ
mechanism design theory ⓘ
public choice theory ⓘ
theory of voting rules ⓘ
mathematicalFramework axiomatic approach ⓘ
nobelPrizeRelatedYear 1972 ⓘ
publicationYear 1951 ⓘ
publishedIn Social Choice and Individual Values ⓘ
recognizedAs foundational result in social choice theory ⓘ
relatedTo Condorcet paradox ⓘ
Gibbard–Satterthwaite theorem ⓘ
Sen’s liberal paradox ⓘ
impossibility results in social choice ⓘ
states no social welfare function satisfies unrestricted domain, Pareto efficiency, IIA, and non-dictatorship for three or more options ⓘ
strengthenedEditionYear 1963 ⓘ
usesConcept ordinal preferences ⓘ
preference ordering ⓘ
social welfare function ⓘ

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Referenced by (16)

Full triples — surface form annotated when it differs from this entity's canonical label.

Collective Choice and Social Welfare → mainTopic → Arrow’s impossibility theorem ⓘ
Arrow’s impossibility theorem → alsoKnownAs → Arrow’s paradox ⓘ
linked to: Arrow’s impossibility theorem
Arrow’s impossibility theorem → alsoKnownAs → Arrow’s general possibility theorem ⓘ
linked to: Arrow’s impossibility theorem
welfare economics → usesConcept → Arrow’s impossibility theorem ⓘ
Kenneth Arrow → notableWork → Arrow’s impossibility theorem ⓘ
Kenneth Arrow → knownFor → Arrow’s impossibility theorem ⓘ
Condorcet paradox → relatedTo → Arrow's impossibility theorem ⓘ
linked to: Arrow’s impossibility theorem
The Limits of Liberty → hasConcept → Pareto efficiency in collective choices ⓘ
linked to: Arrow’s impossibility theorem
Social Choice and Individual Values → mainSubject → Arrow impossibility theorem ⓘ
linked to: Arrow’s impossibility theorem
Social Choice and Individual Values → introducedConcept → Arrow impossibility theorem ⓘ
linked to: Arrow’s impossibility theorem
Gibbard–Satterthwaite theorem → relatesTo → Arrow's impossibility theorem ⓘ
linked to: Arrow’s impossibility theorem
Sen’s liberal paradox → relatedConcept → Arrow’s impossibility theorem ⓘ
social choice theory → hasKeyConcept → Arrow's impossibility theorem ⓘ
linked to: Arrow’s impossibility theorem
Bergson–Samuelson social welfare function → relatedTo → Arrow’s impossibility theorem ⓘ
Kenneth Arrow → notableWork → Arrow’s impossibility theorem ⓘ
subject linked to: Arrow
median voter theorem → relatedTo → Arrow’s impossibility theorem ⓘ