  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.
