My accounts of utilitarianism and the alternatives to it are all about uncertainty. Actually, they are mostly stated in terms of risk, which can be understood as objective or universally agreed probability. But our work on utilitarianism shows how our basic account is compatible with a much wider range of ways of representing uncertainty. These include convex sets of probability measures, infinitesimal probabilities, non-additive capacities, Anscombe-Aumann acts, and given mild assumptions, Savage acts.
This gives our theory some flexibility, but as soon as one looks at computer science (reasoning with uncertainty), economics (decision making under uncertainty), and physics (quantum probability), it is apparent that the range of different representations of uncertainty that are taken seriously is vast. Work in progress explores these further in the context of our treatment of utilitarianism. But a perhaps more fundamental problem is which of these representations are relevant for ethics in the first place.
I have long been sympathetic to the idea that comparatives, or more likely, a distinguished class of comparatives, are more fundamental when it comes to basic normative and evaluative problems than concepts that seem to presuppose a lot of quantitative or numerical structure. For example, “E is more likely than F” seems to me (and a long tradition) to be much simpler and easier to understand than “The probability of E is 0.6 while the probability of F is 0.4.”
Branden Fitelson had been taking a similar view in the context of confirmation theory, and this has lead us to a joint project on comparative likelihood. While various sets of axioms governing comparative likelihood are known to lead to various representations of uncertainty, there is little work on the foundations of such axioms. We offer a new way of thinking about this, and argue that our approach leads to Dempster-Shafer belief functions. These include probability measures as a special case.