This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details.(March 2024) (Learn how and when to remove this message)
Limit of collective decision-making rules
In cooperative game theory and social choice theory, the Nakamura number measures the degree of rationality
of 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 [ja] (1947–1979), a Japanese game theorist who proved the above fact
that the rationality of collective choice critically depends on the number of alternatives.[1]
^Suzuki, Mitsuo (1981). Game theory and social choice: Selected papers of Kenjiro Nakamura. Keiso Shuppan. Nakamura received Doctor's degree in Social Engineering in 1975 from Tokyo Institute of Technology.
In cooperative game theory and social choice theory, the Nakamuranumber measures the degree of rationality of preference aggregation rules (collective...
artist in the Netherlands. Throughout her career, Nakamura has accumulated five number-one songs and a number-one album in France. She was awarded a Victoires...
Christopher Hikaru Nakamura (born December 9, 1987) is an American chess grandmaster, streamer, YouTuber, five-time U.S. Chess Champion, and the reigning...
Shinsuke Nakamura (Japanese: 中邑 真輔, Hepburn: Nakamura Shinsuke, born February 24, 1980) is a Japanese professional wrestler. He is currently signed to...
only if the cardinal number of X {\displaystyle X} is less than the Nakamuranumber of v {\displaystyle v} . (See Nakamuranumber for details.) Because...
Vidit Gujrathi and Gukesh D from India, and Fabiano Caruana and Hikaru Nakamura from the United States. The former three all faced one another in rounds...
by French-Malian singer Aya Nakamura. It was released on 24 August 2018. The song peaked at number one in France and number 7 in Wallonia. The song's music...
Seisaku Nakamura (中村 誠策, Nakamura Seisaku, c. 1924 – June 19, 1943) was a Japanese man convicted for serial killings in his teenage years. He is also...
minimum number of alternatives that can form such a cycle (voting paradox) is 3 if the number of voters is different from 4, because the Nakamuranumber of...
Ataru Nakamura (中村 中, Nakamura Ataru) (born 28 June 1985) is a Japanese singer, songwriter and actress. After signing with Avex Trax, Nakamura released...
Shunsuke Nakamura (Japanese: 中村 俊輔, Hepburn: Nakamura Shunsuke, born 24 June 1978) is a Japanese former professional footballer. He is currently a first-team...
Kazuo Nakamura RCA was a Japanese-Canadian painter and sculptor (born Vancouver October 13, 1926; died Toronto April 9, 2002) and a founding member of...
of Nakamura's effort had been spent on analysis of al-Ghazali's works, a number of which Nakamura has translated to the Japanese language. Nakamura's Islam...
Masatoshi Nakamura (中村 雅俊, Nakamura Masatoshi, born 1 February 1951) is a Japanese actor and singer from Onagawa, Miyagi. He graduated from Keio University...
theorem Independence of irrelevant alternatives Instant-runoff voting Nakamuranumber Quadratic voting Rock paper scissors Simpson's paradox Smith set Marquis...
Keito Nakamura (中村 敬斗, Nakamura Keito, born 28 July 2000) is a Japanese professional footballer who plays for Ligue 1 club Reims and the Japan national...
Emi Nakamura is a Canadian-American economist. She is the Chancellor's Professor of Economics at University of California, Berkeley. Nakamura is a research...
Hajime Nakamura (中村 元, Nakamura Hajime, November 28, 1912 – October 10, 1999) was a Japanese Orientalist, Indologist, philosopher and academic of Vedic...
Akimasa Nakamura (中村 彰正, Nakamura Akimasa, fl. 1990s) (born 1961) is a Japanese astronomer. He is a prolific observer of asteroids and comets, as well...
decision-making Justice (economics) Liberal paradox Mechanism design Nakamuranumber Rational choice theory Rule according to higher law Voting system Amartya...
Jin Nakamura (中村仁, Nakamura Jin, born 1 February 2006) is a Japanese racing driver currently competing in Super GT and Super Formula Lights. He was runner...
Alice Orcutt Nakamura (born 1945) is an American-Canadian economist and writer. She is a fellow of the Canadian Economics Association, which is the highest...
Hachidai Nakamura (中村 八大, Nakamura Hachidai, January 20, 1931 – June 10, 1992) was a Japanese songwriter and jazz pianist. Hachidai Nakamura was born...
Yasunobu Nakamura (中村 泰信 Nakamura Yasunobu) is a Japanese physicist. He is a professor at the University of Tokyo's Research Center for Advanced Science...
Global Information
