Keynesian Uncertainty Can Only Be Represented by Imprecise, Non Additive, Interval Valued Probability or Decision Weights Like Keynes’s C: Ordinal Probability Can’t Represent Keynesian Uncertainty

M. E. Brady
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Abstract

J M Keynes’s two logical relations of rational degree of probability, α, 0≤α≤1 and Evidential Weight of the Argument, w, 0≤w≤1, where w measures the degree of completeness of the evidence, can’t be represented or associated with ordinal probability, although Keynes’s theory of probability can easily deal with ordinal probability with the aid of Keynes’s principle of indifference if symmetries are present. α can be, in some limited instances, represented by a numerical, precise, definite, exact, additive probability if, and only if, w=1, although, in general, for w<1, it must be represented by an non additive interval estimate of probability or by a decision weight, like Keynes’s original, path breaking innovation of his conventional coefficient, c. Nowhere in Boole’s 1854 The Laws of Thought is any concept of ordinal probability discussed analyzed or applied in any detail. This is because ordinal probability can never deal with overlapping estimates of probability, which creates problems of non comparability, non measurability or incommensurability that Boole and Keynes solved with interval valued probability.
凯恩斯的不确定性只能用不精确的、非加性的、区间值的概率或决策权值来表示,就像凯恩斯的C一样:有序概率不能代表凯恩斯的不确定性
凯恩斯的两个逻辑关系:有理概率度α, 0≤α≤1和论证的证据权重w, 0≤w≤1,其中w衡量证据的完备程度,这两个逻辑关系不能表示或与有序概率相关联,尽管凯恩斯的概率论在存在对称性的情况下可以借助凯恩斯的无差异原理轻松处理有序概率。α可以,在某些有限的情况下,用一个数值的,精确的,确定的,精确的,可加性的概率表示,当且仅当,w=1,尽管,一般来说,对于w<1,它必须用概率的非可加性区间估计或一个决定权重来表示,就像凯恩斯最初的,开创性的创新,他的传统系数,c。布尔的1854年《思想法则》中没有任何地方讨论过,分析过或应用过任何细节的有序概率概念。这是因为有序概率永远无法处理概率的重叠估计,这就产生了布尔和凯恩斯用区间值概率解决的不可比较性、不可测量性或不可通约性问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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