Nonprobabilistic approaches to decision making have been proposed for situations in which an individual does not have enough information to assess probabilities over an uncertainty. One nonprobabilistic method is to use intervals in which an uncertainty has a minimum and maximum but nothing is assumed about the relative likelihood of any value in the interval. The Hurwicz decision rule in which a parameter trades off between pessimism and optimism generalizes the current rules for making decisions with intervals. This article analyzes the relationship between intervals based on the Hurwicz rule and traditional decision analysis using a few probability distributions and an exponential utility function. This article shows that the Hurwicz decision rule for an interval is logically equivalent to i an expected value decision with a triangle distribution over the interval; ii an expected value decision with a beta distribution; and iii an expected utility decision with constant absolute risk aversion with a uniform distribution. These probability distributions are not exhaustive. There are likely other distributions and utility functions for which equivalence with the Hurwicz decision rule can also be established. Since a frequent reason for the use intervals is that intervals assume less information than a probability distribution, the results in this article call into question whether decision making based on intervals really assumes less information than subjective expected utility decision making.

中文翻译：

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Hurwicz决策规则与三角形和Beta分布以及指数效用的决策关系

对于个人没有足够信息来评估不确定性概率的情况，已经提出了非概率决策方法。一种非概率方法是使用不确定性具有最大值和最小值的区间，但对于区间中任何值的相对可能性均不作任何假设。Hurwicz决策规则（其中参数在悲观主义与乐观主义之间进行权衡）概括了用于定期进行决策的规则。本文分析了基于Hurwicz规则的区间与使用少量概率分布和指数效用函数的传统决策分析之间的关系。本文显示，区间的Hurwicz决策规则在逻辑上等效于区间上具有三角形分布的期望值决策；ii具有beta分布的期望值决策；iii具有恒定绝对风险规避且分布均匀的预期效用决策。这些概率分布并不详尽。可能还有其他分布和效用函数，也可以建立与Hurwicz决策规则的等价关系。由于使用间隔的一个常见原因是间隔假设的信息少于概率分布，因此本文的结果令人质疑，基于间隔的决策是否真正假设的信息少于主观预期效用决策。ii具有beta分布的期望值决策；iii具有恒定绝对风险规避且分布均匀的预期效用决策。这些概率分布并不详尽。可能还有其他分布和效用函数，也可以建立与Hurwicz决策规则的等价关系。由于使用间隔的一个常见原因是间隔假设的信息少于概率分布，因此本文的结果令人质疑，基于间隔的决策是否真正假设的信息少于主观预期效用决策。ii具有β分布的期望值决策；iii具有恒定绝对风险规避且分布均匀的预期效用决策。这些概率分布并不详尽。可能还有其他分布和效用函数，也可以建立与Hurwicz决策规则的等价关系。由于使用间隔的一个常见原因是间隔假设的信息少于概率分布，因此本文的结果令人质疑，基于间隔的决策是否真正假设的信息少于主观预期效用决策。可能还有其他分布和效用函数，也可以建立与Hurwicz决策规则的等价关系。由于使用间隔的一个常见原因是间隔假设的信息少于概率分布，因此本文的结果令人质疑，基于间隔的决策是否真正假设的信息少于主观预期效用决策。可能还有其他分布和效用函数，也可以建立与Hurwicz决策规则的等价关系。由于使用间隔的一个常见原因是间隔假设的信息少于概率分布，因此本文的结果令人质疑，基于间隔的决策是否真正假设的信息少于主观预期效用决策。