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A minimal extension of Bayesian decision theory

机译：贝叶斯决策理论的最小扩展

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Savage denied that Bayesian decision theory applies in large worlds. This paper proposes a minimal extension of Bayesian decision theory to a large-world context that evaluates an event by assigning it a number that reduces to an orthodox probability for a class of measurable events. The Hurwicz criterion evaluates as a weighted arithmetic mean of its upper and lower probabilities, which we derive from the measurable supersets and subsets of . The ambiguity aversion reported in experiments on the Ellsberg paradox is then explained by assigning a larger weight to the lower probability of winning than to the upper probability. However, arguments are given here that would make anything but equal weights irrational when using the Hurwicz criterion. The paper continues by embedding the Hurwicz criterion in an extension of expected utility theory that we call expectant utility.
机译：野蛮人否认贝叶斯决策理论适用于大世界。本文提出了将贝叶斯决策理论的最小扩展范围扩展到大世界环境，该大世界环境通过为事件分配一个可减少一类可测量事件的正统概率的数字来评估事件。 Hurwicz准则是其上概率和下概率的加权算术平均值，它是根据可测量的超集和的子集得出的。然后，通过将较高的权重分配给较低的获胜概率，而不是较高的概率来解释关于Ellsberg悖论的实验中报告的歧义厌恶。但是，这里给出的论点在使用Hurwicz准则时将使除权重相等之外的任何事情都不合理。本文继续通过将Hurwicz准则嵌入到期望效用理论的扩展中，我们称之为期望效用。

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