I’ve been doing some reading into alternatives to subjective probability, and one interesting alternative is to model an assignment of subjective probability by a convex set of probability distributions, rather than a single distribution. Convex sets encompass several natural situations where you have a vague sense of probabilities, but would be unwilling to specify an exact value. For example, a range of probabilities for an event can be expressed as a convex set, as well as the idea that one event is more likely than another (without expressing exact probabilities for each event). Convexity also has a natural probabilistic interpretation: if two distributions are in the set, then any mixture of the two is also in the set.
A nice introduction to the subject is Fabio Cozman’s online tutorial Introduction to the Theory of Sets of Probabilities. For some additional surveys on related approaches, see the homepage of the Imprecise Probabilities Project.