序数效用

同时，序数效用是对单个人而言的，人际间序数效用的直接比较是没有意义的。

Meanwhile , ordinal utility is to the individual , and its interpersonal direct comparison is meaningless .

这表明，序数效用论的应用领域是有局限性的，它并不能完全取代基数效用论。

This means that the application fields of ordinal utility theory is very limited , hence it cannot replace the cardinal utility theory completely .

第三，笔者讨论了用其它规则替换Condorcet规则的问题。并结合基数效用论与序数效用论的分析，从若干例证的讨论中印证了博尔达（Berda）规则的内在矛盾。

Thirdly , this article discusses the substitution of other rule for Condorcet Rule , and proves the internal contradiction of Berda Rule through the analysis of The utility theory of base figure and The utility theory of ordinal number .

分析商品效用有基数效用论和序数效用论两种方法；

There are two methods in analyzing commodity effectiveness , namely , the cardinal effectiveness theory and the ordinal effectiveness theory .

使用价值是可以衡量的，基数效用论和序数效用论是衡量效用的两种有用方法；

The use value is measurable , and the cardinal theory of utility and the ordinal theory of utility are two useful methods that measure utility ;

而现代福利函数的诞生，使人们在只考虑个人序数效用的情况下研究社会福利函数。

But now because of modern social welfare functions coming into being , which makes it possible to consider only individual ordering utilities to study social welfare functions .

相对于序数效用论来说，基数效用论的最大优势就在于它包含了更多的信息，即关于效用差额或者说偏好强度的信息。

Compared with ordinal utility theory , the biggest advantage of cardinal utility theory is that it contains more information about the quantity of utility or strength of preference .

这样的研究领域很多，本文着重讨论了序数效用论无法解决而必须采用基数效用论的三个重要的经济问题：社会选择问题、不确定性问题以及边际效用递减问题。

These research fields are very much , and this paper mainly discusses three important economic issues : social choice problem , uncertainty problem and diminishing marginal utility problem .

在第二章中，我们在只考虑个人序数效用，而不考虑个人效用的比较和基数效用的情况下研究社会福利函数，并用拓扑学的方法证明了阿罗不可能定理。

In chapter two , we only consider individual ordering utilities , without considering the interpersonal comparability and cardinality . We use topological methods to study social welfare functions and prove Arrow impossibility theorem .

最终，在帕累托、希克斯和萨缪尔森等人的努力下，序数效用论逐渐取代基数效用论，成为主流经济学的标准分析范式。

Finally , with the efforts of Pareto , Hicks , Samuelson and other scholars , ordinal utility theory gradually replaced cardinal utility theory , and became a standard analytical paradigm of the mainstream economics .

序数效用论认为，偏好与福利是一致的，人们选择了能使偏好最大化的商品组合也就实现了福利的最大化。

The ordinal utility theory argues that preference maximization is consistent with welfare maximization , and people will realize the maximization of welfare , when they have chosen the right combination of goods which can realize preference maximization .

该方法的计算不需要各指标的权重，可对绿色产品序数和基数效用函数进行逼近，实现了绿色产品非线性效用函数的评价。

Those models , which don 't need weighting , can fulfill approximation to ordinal-number utility function and cardinal-number utility function , and realize evaluation of the non-linear utility function of green product .