  We generalize standard credal set models for imprecise probabilities to
include higher order credal sets -- confidences about confidences. In doing so,
we specify how an agent's higher order confidences (credal sets) update upon
observing an event. Our model begins to address standard issues with imprecise
probability models, like Dilation and Belief Inertia. We conjecture that when
higher order credal sets contain all possible probability functions, then in
the limiting case the highest order confidences converge to form a uniform
distribution over the first order credal set, where we define uniformity in
terms of the statistical distance metric (total variation distance). Finite
simulation supports the conjecture. We further suggest that this convergence
presents the total-variation-uniform distribution as a natural, privileged
prior for statistical hypothesis testing.
