The false confidence theorem establishes that, for any data-driven, precise-probabilistic method for uncertainty quantification, there exists (non-trivial) false hypotheses to which the method tends to assign high confidence. This raises concerns about the reliability of these widely-used methods, and shines new light on the consonant belief function-based methods that are provably immune to false confidence. But an existence result alone is insufficient. Towards a partial answer to the title question, I show that, roughly, complements of convex hypotheses are afflicted by false confidence.

翻译：虚假置信定理表明，对于任何数据驱动、精确概率的不确定性量化方法，都存在（非平凡的）虚假假设，该方法倾向于对这些假设赋予高置信度。这引发了人们对这些广泛使用方法的可靠性的担忧，并为基于协和信念函数的方法提供了新的视角，这些方法已被证明对虚假置信具有免疫性。但仅凭存在性结果并不足够。为了部分回答标题中的问题，我大致证明，凸假设的补集受到虚假置信的困扰。