Arrow’s impossibility theorem

E115290

impossibility theorem result in social choice theory theorem

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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All labels observed (4)

Label	Occurrences
Arrow’s impossibility theorem canonical	4
Arrow's impossibility theorem	1
Arrow’s general possibility theorem	1
Arrow’s paradox	1

Statements (47)

Predicate	Object
instanceOf	impossibility theorem ⓘ result in social choice theory ⓘ theorem ⓘ
alsoKnownAs	Arrow’s impossibility theorem ⓘ surface form: Arrow’s general possibility theorem Arrow’s impossibility theorem ⓘ surface form: 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 ⓘ surface form: Kenneth Arrow’s Nobel Prize in Economics
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 ⓘ

Referenced by (7)

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 impossibility theorem ⓘ

this entity surface form: Arrow’s paradox

Arrow’s impossibility theorem → alsoKnownAs → Arrow’s impossibility theorem ⓘ

this entity surface form: Arrow’s general possibility 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 ⓘ

this entity surface form: Arrow's impossibility theorem