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Weighted averaging, Jeffrey conditioning and invariance

机译：加权平均，Jeffrey条件和不变性

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Jeffrey conditioning tells an agent how to update her priors so as to grant a given probability to a particular event. Weighted averaging tells an agent how to update her priors on the basis of testimonial evidence, by changing to a weighted arithmetic mean of her priors and another agent's priors. We show that, in their respective settings, these two seemingly so different updating rules are axiomatized by essentially the same invariance condition. As a by-product, this sheds new light on the question how weighted averaging should be extended to deal with cases when the other agent reveals only parts of her probability distribution. The combination of weighted averaging (for the events whose probability the other agent reveals) and Jeffrey conditioning (for the events whose probability the other agent does not reveal) is a comprehensive updating rule to deal with such cases, which is again axiomatized by invariance under embedding. We conclude that, even though one may dislike Jeffrey conditioning or weighted averaging, the two make a natural pair when a policy for partial testimonial evidence is needed.
机译：Jeffrey条件告诉代理程序如何更新其先验，以便为特定事件赋予给定的概率。加权平均告诉代理，如何通过更改其先验和另一代理的先验的加权算术平均值，根据证明证据更新其先验。我们显示，在它们各自的设置中，这两个看似如此不同的更新规则通过基本相同的不变性条件公理化。作为副产品，这为以下问题提供了新的启示：应如何扩展加权平均以处理其他代理仅显示其概率分布的一部分的情况。加权平均（对于其他代理揭示的概率的事件）和杰弗里条件（对于其他代理没有揭示的概率的事件）的组合是处理此类情况的综合更新规则，再次根据不变性公理化嵌入。我们得出的结论是，即使可能不喜欢Jeffrey条件或加权平均，但当需要部分证明证据的政策时，两者自然形成一对。

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