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- Nakamura_number abstract "In cooperative game theory and social choice theory, the Nakamura number measures the degree of rationalityof preference aggregation rules (collective decision rules), such as voting rules.It is an indicator of the extent to which an aggregation rule can yield well-defined choices.If the number of alternatives (candidates; options) to choose from is less than this number, then the rule in question will identify "best" alternatives without any problem.In contrast,if the number of alternatives is greater than or equal to this number, the rule will fail to identify "best" alternatives for some pattern of voting (i.e., for some profile (tuple) of individual preferences), because a voting paradox will arise (a cycle generated such as alternative socially preferred to alternative , to , and to ).The larger the Nakamura number a rule has, the greater the number of alternatives the rule can rationally deal with.For example, since (except in the case of four individuals (voters)) the Nakamura number of majority rule is three,the rule can deal with up to two alternatives rationally (without causing a paradox).The number is named after Kenjiro Nakamura (1947–1979), a Japanese game theorist who proved the above factthat the rationality of collective choice critically depends on the number of alternatives.".
- Nakamura_number wikiPageID "28926447".
- Nakamura_number wikiPageRevisionID "546008329".
- Nakamura_number hasPhotoCollection Nakamura_number.
- Nakamura_number subject Category:Cooperative_games.
- Nakamura_number subject Category:Economics_theorems.
- Nakamura_number subject Category:Social_choice_theory.
- Nakamura_number subject Category:Voting_systems.
- Nakamura_number subject Category:Voting_theory.
- Nakamura_number type Abstraction100002137.
- Nakamura_number type Cognition100023271.
- Nakamura_number type Communication100033020.
- Nakamura_number type Content105809192.
- Nakamura_number type Contest107456188.
- Nakamura_number type CooperativeGames.
- Nakamura_number type EconomicsTheorems.
- Nakamura_number type Event100029378.
- Nakamura_number type Game100456199.
- Nakamura_number type Idea105833840.
- Nakamura_number type LegalSystem105903229.
- Nakamura_number type Message106598915.
- Nakamura_number type Plan105898568.
- Nakamura_number type PlanOfAction105902545.
- Nakamura_number type Proposition106750804.
- Nakamura_number type PsychologicalFeature100023100.
- Nakamura_number type SocialEvent107288639.
- Nakamura_number type Statement106722453.
- Nakamura_number type System105902872.
- Nakamura_number type Theorem106752293.
- Nakamura_number type VotingSystem105904135.
- Nakamura_number type VotingSystems.
- Nakamura_number type YagoPermanentlyLocatedEntity.
- Nakamura_number comment "In cooperative game theory and social choice theory, the Nakamura number measures the degree of rationalityof preference aggregation rules (collective decision rules), such as voting rules.It is an indicator of the extent to which an aggregation rule can yield well-defined choices.If the number of alternatives (candidates; options) to choose from is less than this number, then the rule in question will identify "best" alternatives without any problem.In contrast,if the number of alternatives is greater than or equal to this number, the rule will fail to identify "best" alternatives for some pattern of voting (i.e., for some profile (tuple) of individual preferences), because a voting paradox will arise (a cycle generated such as alternative socially preferred to alternative , to , and to ).The larger the Nakamura number a rule has, the greater the number of alternatives the rule can rationally deal with.For example, since (except in the case of four individuals (voters)) the Nakamura number of majority rule is three,the rule can deal with up to two alternatives rationally (without causing a paradox).The number is named after Kenjiro Nakamura (1947–1979), a Japanese game theorist who proved the above factthat the rationality of collective choice critically depends on the number of alternatives.".
- Nakamura_number label "Nakamura number".
- Nakamura_number label "中村ナンバー".
- Nakamura_number sameAs 中村ナンバー.
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- Nakamura_number sameAs Q6960251.
- Nakamura_number sameAs Q6960251.
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- Nakamura_number wasDerivedFrom Nakamura_number?oldid=546008329.
- Nakamura_number isPrimaryTopicOf Nakamura_number.