We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is essential to quantum mechanical uncertainty, even if the quantum state is known, measurements may still produce an uncertain outcome. In our framework, measurements therefore play the role of acts with an uncertain outcome and our simple decision-theoretic postulates ensure that Born's rule is encapsulated in the utility functions associated with such acts. This approach allows us to uncouple (precise) probability theory from quantum mechanics, in the sense that it leaves room for a more general, so-called imprecise probabilities approach. We discuss the mathematical implications of our findings, which allow us to give a decision-theoretic foundation to recent seminal work by Benavoli, Facchini and Zaffalon, and we compare our approach to earlier and different approaches by Deutsch and Wallace.

翻译：我们提出了一个用于处理量子力学中不确定性的决策理论框架。这种不确定性具有双重性：一方面可能存在关于量子系统所处状态的不确定性；另一方面，正如量子力学不确定性的本质特征所示，即使量子态已知，测量仍可能产生不确定的结果。在我们的框架中，测量因此扮演了具有不确定结果的行动角色，而我们简单的决策理论公设确保了玻恩规则被封装在与这类行动相关的效用函数中。这种方法使我们能够将（精确的）概率论与量子力学解耦，从而为更广义的所谓不精确概率方法留出空间。我们讨论了研究结果的数学意义，这使我们能够为Benavoli、Facchini和Zaffalon近期开创性工作提供决策理论基础，并将我们的方法与Deutsch和Wallace早期提出的不同方法进行了比较。