This paper is a discussion note on Isaacs, Hájek and Hawthorne (2022), which claims to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of that proposal. In particular, I show that if the proposal is applied to a bounded 3-dimensional space, then one has to reject at least one of the following: • If A is at most as probable as B and B is at most as probable as C, then A is at most as probable as C. • Let A∩C=B∩C=∅. A is at most as probable as B if and only if (A∪C) is at most as probable as (B∪C). But rejecting either statement seems unattractive.

中文翻译：

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分配不可测集的后果 不精确的概率


本文是关于 Isaacs、Hájek 和 Hawthorne （2022） 的讨论说明，它声称基于不可测性的数学现象为不精确概率提供了新的动机。在本说明中，我澄清了该提案的一些后果。特别是，我表明，如果该提案应用于有界三维空间，那么必须至少拒绝以下一项： • 如果 A 最多与 B 一样可能，B 最多与 C 一样可能，那么 A 最多与 C 一样可能。• 设 A∩C=B∩C=∅。当且仅当 （A∪C） 与 （B∪C） 的概率一样大时，A 的概率最多与 B 一样大。但拒绝任何一种说法似乎都没有吸引力。