# Nakamura Number

### Some articles on nakamura number, number, nakamura:

Cooperative Game - Solution Concepts - The Core of A Simple Game With Respect To Preferences
... The Nakamura number of a simple game is the minimal number of winning coalitions with empty intersection ... Nakamura's theorem states that the core is nonempty for all profiles of acyclic (alternatively, transitive) preferences if and only if is finite and ... have a maximal element if and only if the cardinal number of is less than the Nakamura number of ...
Cooperative Game - Properties For Characterization - Properties For Simple Games
... The Nakamura number of a simple game is the minimal number of winning coalitions with empty intersection ... According to Nakamura's theorem, the number measures the degree of rationality it is an indicator of the extent to which an aggregation rule can yield well-defin ... no no no no The restrictions that various axioms for simple games impose on their Nakamura number are also studied extensively ...
Arrow's Impossibility Theorem - Other Possibilities - Approaches Investigating Functions of Preference Profiles - Limiting The Number of Alternatives
... Nakamura's theorem (about the core of simple games) gives an answer more generally ... It establishes that if the number of alternatives is less than a certain integer called the Nakamura number, then the rule in question will identify "best" alternatives without any problem if the ... Since the Nakamura number of majority rule is 3 (except the case of four individuals), one can conclude from Nakamura's theorem that majority rule can deal with up to two alternatives rationally ...

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One may confidently assert that when thirty thousand men fight a pitched battle against an equal number of troops, there are about twenty thousand on each side with the pox.
Voltaire [François Marie Arouet] (1694–1778)