Imprecise Probability

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.

What happens when we use a decision theory to judge itself? Theories that diverge from Expected Utility Theory often recommend using EUT, thus undermining themselves.

Cases where every credence undermines its own adoption seem to lead to epistemic dilemmas. We move to considering indeterminate credences and look at what is determinately recommended of you. By doing this, we propose that the epistemic dilemmas are avoided.

We investigate the supervaluational Kripkean account of truth and show how it can apply to finding rational indeterminate credences in undermining scenarios. Our construction is general and could apply to a whole range of domains.

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.

We argue that the model of probabilities needs revising when non-classical logics are considered. For strong-Kleene logic we suggest a belief-pair, and for supervaluational logic adopt imprecise probability.

We suggest that accuracy considerations should apply to the imprecise by using: what a set recommends is the set of what the individuals in it recommend. This results in a surprisingly nice picture of accuracy for the imprecise.