Probability Filters

We show that representing imprecise probabilities by using probability constraints closed under merely finite consequence, the probability filter model, avoids objections by Walley to the credal set model. We show that it encompasses the model of sets of desirable gambles.

We propose representing a (possibly imprecise) epistemic state using a probability filter focusing on probabilistic properties, such as whether pr(A)>0.2. It is very expressively powerful.

We show that Moss’s model of uncertainty is at least as expressively powerful as every other current imprecise probability framework. And we give a Dutch Book argument for certain failures of consistency.