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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Ordinal utility ： ウィキペディア英語版 Ordinal utility In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. The ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask ''how much'' better it is. For example, suppose George tells us that "I prefer A to B and B to C". George's preferences can be represented by a function ''u'' such that: :$u(A)=9,\; u(B)=8,\; u(C)=1$ But the only meaningful message of this function is the order $u(A)>u(B)>u(C)$; the actual numbers are meaningless. Hence, George's preferences can also be represented by the following function ''v'': :$v(A)=9,\; v(B)=2,\; v(C)=1$ The functions ''u'' and ''v'' are ordinally equivalent – they represent George's preferences equally well. Contrast this with cardinal utility theory: the latter claims that the differences between preferences are also important. In ''u'' the difference between A and B is much smaller than between B and C, while in ''v'' the opposite is true. Hence, ''u'' and ''v'' are ''not'' cardinally equivalent. The ordinal utility concept was first introduced by Pareto in 1906. == Notation == Suppose the set of all states of the world is $X$ and an agent has a preference relation on $X$. It is common to mark the weak preference relation by $\backslash preceq$, so that $A\; \backslash preceq\; B$ reads "the agent wants B at least as much as A". The symbol $\backslash sim$ is used as a shorthand to the indifference relation: $A\backslash sim\; B\; \backslash iff\; (A\backslash preceq\; B\; \backslash and\; B\backslash preceq\; A)$, which reads "The agent is indifferent between B and A". The symbol $\backslash prec$ is used as a shorthand to the strong preference relation: $A\backslash prec\; B\; \backslash iff\; (A\backslash preceq\; B\; \backslash and\; B\backslash not\backslash preceq\; A)$, which reads "The agent strictly prefers B to A". A function $u:\; X\; \backslash to\; \backslash mathbb$ is said to ''represent'' the relation $\backslash preceq$ if: :$A\; \backslash preceq\; B\; \backslash iff\; v(A)\; \backslash leq\; v(B)$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ordinal utility」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.