Coherent sets of desirable gamble sets is used as a model for representing an agents opinions and choice preferences under uncertainty. In this paper we provide some results about the axioms required for coherence and the natural extension of a given set of desirable gamble sets. We also show that coherent sets of desirable gamble sets can be represented by a proper filter of coherent sets of desirable gambles.
We present standard results about representations of strictly proper measures of accuracy. We also show the same results hold when measuring accuracy of previsions more generally.
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.
What do measures of accuracy which are risk-weightedly strictly-proper look like? Some results.
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.
What does the space of all possible worlds look like? Especially when we have beliefs-about-beliefs.